Structural response to electronic transitions in ...

Structural response to electronic transitions in hexagonal and ortho-manganites

This work was supported by the Dutch Foundation for Fundamental Research on Matter (FOM). Printed by: PrintPartners Ipskamp B.V., Enschede, The Netherlands ISBN ..-.......-.

Rijksuniversiteit Groningen

Structural response to electronic transitions in hexagonal and ortho-manganites

Proefschrift ter verkrijging van het doctoraat in de Wiskunde en Natuurwetenschappen aan de Rijksuniversiteit Groningen op gezag van de Rector Magnificus, dr. D.F.J. Bosscher in het openbaar te verdedigen op maandag 8 oktober 2001 om 14.15 uur

door

Bas Bernardus van Aken geboren op 31 juli 1973 te Wisch

Promotor: Prof. Dr. T.T.M. Palstra

Contents 1 Introduction 1.1 Introduction . . . . . . . . 1.2 Manganites . . . . . . . . 1.2.1 LaMnO3 . . . . . . 1.2.2 Doped manganites 1.3 Crystallography . . . . . .

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2 Twin model for orthorhombic perovskites 2.1 Introduction . . . . . . . . . . . . . . . . . 2.2 The twin structure for manganites . . . . . 2.3 Crystal structure . . . . . . . . . . . . . . 2.3.1 GdFeO3 rotation . . . . . . . . . . 2.3.2 Jahn-Teller distortion . . . . . . . . 2.3.3 Glazer’s view on the octahedra . . 2.4 Twin model . . . . . . . . . . . . . . . . . 2.5 Discussion . . . . . . . . . . . . . . . . . . 2.5.1 Intensity distribution . . . . . . . . 2.5.2 Refinement . . . . . . . . . . . . . 2.6 Conclusion . . . . . . . . . . . . . . . . . . 2.7 Appendices . . . . . . . . . . . . . . . . . 2.7.1 Data analysis . . . . . . . . . . . . 2.7.2 Implementation in refinement . . .

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3 Jahn-Teller ordering vs. ferromagnetic metal 3.1 Introduction . . . . . . . . . . . . . . . . . . . 3.2 Experimental . . . . . . . . . . . . . . . . . . 3.3 La site shift as probe for Jahn-Teller effect . . 3.4 La1−x Cax MnO3 : structure vs. x and T . . . . 3.4.1 Rotation . . . . . . . . . . . . . . . . . 3.4.2 JT order parameter . . . . . . . . . . . 3.4.3 La site shift . . . . . . . . . . . . . . . 3.5 Interpretation . . . . . . . . . . . . . . . . . . 3.5.1 Rotation . . . . . . . . . . . . . . . . . 1

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45 46 47 47

4 Structural view of hexagonal non-perovskite AMnO3 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Single crystal diffraction . . . . . . . . . . . . . . . . . 4.3 Crystal structure . . . . . . . . . . . . . . . . . . . . . 4.4 From centrosymmetry to non-centrosymmetry . . . . . 4.5 Detailed structure analysis . . . . . . . . . . . . . . . . 4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . .

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51 52 53 54 56 58 59

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61 62 64 65 66 68 70

3.6

5 The 5.1 5.2 5.3 5.4 5.5 5.6

3.5.2 JT order parameter at low temperature 3.5.3 Decreasing JT order parameter . . . . 3.5.4 Paramagnetic state . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . .

hexagonal to orthorhombic structural Introduction . . . . . . . . . . . . . . . . . Experimental . . . . . . . . . . . . . . . . High pressure synthesis . . . . . . . . . . . Y1−x Gdx MnO3 ; the influence of disorder . Discussion of the disorder . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . .

6 Asymmetry of electron 6.1 Introduction . . . . . 6.2 Electron doping . . . 6.3 Experimental . . . . 6.4 Magnetisation . . . . 6.5 X-ray diffraction . . 6.6 Electronic structure . 6.7 Conclusion . . . . . .

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phase . . . . . . . . . . . . . . . . . . . . . . . .

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transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

and hole doping in YMnO3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 Origin of the hexagonal phase 7.1 Introduction . . . . . . . . . . . . . . 7.2 Of radii and shells . . . . . . . . . . 7.2.1 Orthorhombic P nma . . . . . 7.2.2 Hexagonal P 63 cm manganites 7.3 Ferroelectricity and covalency . . . . 7.4 Discussion . . . . . . . . . . . . . . . 7.4.1 A2 O3 and Mn2 O3 . . . . . . . 7.4.2 Distortion vs ionic radius . . . 7.4.3 3d series . . . . . . . . . . . . 7.4.4 AVO3 and AFeO3 . . . . . . . 7.5 Conclusion . . . . . . . . . . . . . . .

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85 85 86 86 91 93 95 95 96 97 97 99

Contents

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A La0.84 Ca0.16 MnO3

101

B La0.81 Ca0.19 MnO3

103

C La0.75 Ca0.25 MnO3

105

D YMnO3

107

E ErMnO3

109

F YbMnO3

111

G LuMnO3

113

Samenvatting

115

List of publications

121

Nawoord

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4

Contents

Chapter 1 Introduction 1.1

Introduction

Materials science and engineering have been at the frontier of technological development since the bronze and iron ages. The industrial revolution was heavily supported by the increase in quantity and quality of available steel, nowadays there is a very large choice of different steel alloys commercially available. The current computer age relies on the development of better and ”smaller” materials for memories, data storage, processing and probing. Materials can be divided into numerous categories, depending on their origin, use or morphology. The number of applications and properties, and combinations of these, seems almost unlimited. One prime example of a small but diverse group of materials is the perovskite family. Physicists, chemists and materials scientists have shown a wide interest in these materials, because of properties such as high temperature superconductivity, colossal magnetoresistance and ferroelectricity. Still new and unexplored possibilities of the perovskites appear. In spite of progress in our understanding of the properties of these materials, very basic questions like ”Why is this material a good conductor, while a similar material is an insulator ” remain a challenge. Millions of people tackle this question everyday in their kitchen, by wondering or finding out whether they can lift the steel lid of the pan or stir the sauce with the wooden spoon with their bare hands. The Wiedemann-Franz law states that the thermal conductivity is proportional to the electronic conductivity [1]. Nevertheless, the question which materials are metallic and which insulators can be complex, particularly for perovskites. The method used in our research is to investigate the structure and explore structural responses, caused by phenomena with an electronic origin, such as Jahn-Teller distortions, ferroelectricity and orbital ordering. Since the essential exchange interactions are determined by the metal-oxygen bond lengths and bond angles, a deep and profound knowledge of the structure is necessary to understand the physics behind the phenomena. The large variety of phenomena is apparent, e.g. in the LaMnO3 -CaMnO3 phase diagram, where only the La:Ca ratio is varied. Manganites, with the composition AMnO 3 (A = large lanthanide and/or alkaline earth ions such as La3+ or Sr2+ ) are one family of 5

6

Chapter 1. Introduction

the larger group of transition metal oxides, which includes other families such as ferroelectric titanites. Most manganites form perovskite crystals, including layered perovskites (the Ruddlesden-Popper phases). However, some manganites can form hexagonal layered crystal structures. The hexagonal building block is fundamentally different from the cubic building block, resulting in different physical behaviour. One of the most eye-catching properties of the manganites is the influence of a magnetic transition on the electronic conduction. Already in 1950, Jonker and Van Santen discovered that the resistance below the magnetic ordering, the Curie temperature T c , exhibits a positive thermal coefficient, indicating metallic-like behaviour and a negative gradient above Tc [2]. This brings about a maximum in the resistivity curve near Tc . Despite much progress, the implications of this behaviour were only explored in 1993, when a reduction of the resistance was observed in thin films under application of an external magnetic field by Chahara et al. [3] and Von Helmolt et al. [4]. This reduction was only 50% of the zero field resistance. A year later it proved to be possible to reduce the resistivity by several orders of magnitude [5]. The term Colossal Magnetoresistance (CMR) was born. The new term is a superlative of Giant Magnetoresistance, which is observed in the resistance of ferromagnetic/nonmagnetic multilayers by switching an external field. Giant magnetoresistance is caused by introducing interfaces in spin polarised conductors and is restricted below Tc , whereas CMR is a bulk property which originates from magnetic ordering and is usually confined to the vicinity of Tc . The electronic transport properties of the transition metal oxides strongly interact with the magnetic properties and with the crystal lattice. Many properties and transitions cannot be described by simple one electron models. These compounds are thus part of the strongly correlated electron systems. The strong coupling between the electrons and the lattice brings about that a small change in the chemical composition, like the ratio between trivalent and divalent ions at the A site or the average ionic radius of the ions on the A site, can induce large changes in the physical properties. A similar change can occur due to external effects, such as a magnetic field, a hydrostatic pressure or the temperature. The behaviour of the manganites is a case in point showing the interaction between chemical composition, experimental conditions and physical properties. LaMnO3 and CaMnO3 are both antiferromagnetic insulators. At first sight a mixture of LaMnO 3 CaMnO3 is expected to show no spectacular effects. But, in their phase diagram we find ferromagnetism, metallicity and several regions with spin and charge orderings. An important aspect in the unexpected rich phase diagram is the small but relevant distinction in crystal structure, although both compounds are perovskites. LaMnO3 consists of deformed MnO6 octahedra, whereas the octahedra are perfect in CaMnO3 . The origin of the deformation is the crystal field splitting of the 3d orbitals. The discovery of CMR led to many articles starting with ”The discovery of colossal magnetoresistance initiated a lot of research.” and, ultimately, to this thesis. One of the focal points of the thesis is the phase region near 20% CaMnO3 , where a transition occurs from the ferromagnetic insulator to the ferromagnetic metal. The ferromagnetic insulator is intriguing by itself, since ferromagnetism is commonly associated with metallic behaviour.

1.2. Manganites

7

Furthermore, the orbital ordering in LaMnO3 is not observed above 20% doping. The exact influence of dopant concentration and temperature on the orbital ordering is unknown. There are in the literature contradictory opinions on the influence of the orbital ordering on the electronic properties. The other focal point is the structure of and transition to the hexagonal manganite. These manganites are found if the average ionic radius of the A site ions becomes at least as small as the radius of yttrium. The two most obvious differences with the perovskite structure of the orthomanganites are the pseudo two-dimensional character of the structure and the anomalous fivefold trigonal bipyramidal co-ordination of the Mn ion by the anions. These bipyramids form corner-shared layers, but there is no direct Mn−O−Mn interaction between the layers. The interest in these compounds is the combination of ferroelectricity and magnetism and the compatibility of these compounds with thin film techniques. The combination of ferroelectricity and magnetism is conflicting with the general picture that ferroelectricity is caused by ”d0 ” ions, like Ti4+ and Nb5+ , and magnetism by atoms or ions with partially filled bands, like Mn, Fe and Ni.

1.2 1.2.1

Manganites LaMnO3

AMnO3 compounds, like LaMnO3 and CaMnO3 , have a crystal structure that is of the perovskite type, see Fig. 1.1. The perovskite crystal structure can be regarded as a threedimensional network of corner sharing MnO6 octahedra, with the Mn ions in the middle of the octahedra. Eight octahedra form a cube, with the A site in its centre. In the cubic perovskite, the A site is twelvefold surrounded by oxygen ions. But typically the ionic radius of the A ion is smaller than the volume, enclosed by the oxygen ions. This volume can be reduced by rotating the octahedra with respect to each other. Inevitably the twelve A−O bond lengths become inequivalent.

E

F

D

Figure 1.1: Sketch of the perovskite Pnma structure. A ions are represented by circles, MnO6 by octahedra.

8


The first report on the crystal structure of the manganites dates back to 1943 by NáraySzabó [6] and was revised by Yakel in 1955 [7]. In contrast to the single cubic unit cell reported by Náray-Szabó, Yakel proposed a monoclinic unit cell, nearly identical to the double cubic cell, but for one angle that is slightly larger than 90◦ . Although the perovskite structure itself was not under discussion, the exact modification was controversial, see references [8,9]. In 1968 it was first reported that AMnO3 has the P nma space group [10], but this report did not include LaMnO3 . Just like LaFeO3 , LaMnO3 has nearly cubic lattice parameters, which makes a structure solution and refinement very hard [11–13]. Elemans et al. were the first to report the P nma space group for pure LaMnO3 [14]. The oxygen stoichiometry of these AMnO3 compounds is very sensitive to the synthesis conditions. Stoichiometric LaMnO3 is an antiferromagnetic insulator [2]. The spins are ordered ferromagnetically in the ac plane, with the spins parallel to the a axis [15]. There is an antiferromagnetic coupling between the layers, along the b axis. The electronic configuration 3d4 in an octahedral crystal field exhibits a degenerate state with one electron occupying two eg orbitals. The Jahn-Teller theorem states that such an electronic configuration is unstable and that the degeneracy has to be lifted by a (local) distortion of the octahedra. When the degeneracy is lifted, one e g orbital is occupied. It was proposed that stoichiometric LaMnO3 has an orbital ordering of the z 2 like orbitals in the ac plane, resulting in alternatingly long and short Mn−O bonds [14,16]. The z 2 -like orbitals are alternatingly parallel to the vectors a + c and a − c, forming a checkerboard pattern in the basal plane. The orbitals are parallel to the long Mn−O bonds and perpendicular to the short Mn−O bonds. This type of ordered distortions is called antiferrodistortive.

Figure 1.2: Antiferromagnetic interaction between two Mn3+ ions with occupied, overlapping orbitals. The excited O 2p electrons have opposite spin. They are antiparallel with the ”host” ions’ spins. An identical interaction occurs between two empty orbitals, albeit with opposite spins excited from the O 2p orbital. The Mn ions are represented by a small circle for the t2g orbitals and lobes for the eg orbitals. The 3d electrons are indicated by their spins. The three t2g electrons are drawn as core spins. Empty eg orbitals are indicated by dotted lines. The quantisation axis, z, for the 3d orbitals is parallel to the crystallographic b axis in P nma, which justifies the common use of the alternative notation P bnm for this space group. The z 2 -like orbitals are obtained by taking linear combinations of the 3d x2 − y 2

1.2. Manganites

9

and 3z 2 − r2 orbitals. Cussen et al. report that for LaMnO3 these linear combinations yield orbitals that are rather similar to x2 − z 2 and z 2 − y 2 orbitals for neighbouring sites [17,18] with z parallel to the crystallographic (P nma) b axis.

Figure 1.3: For explanation of the sketch, see Fig. 1.2. In-plane ferromagnetism, mediated by superexchange of ordered t2g electrons as observed in the ac plane of LaMnO3 . Although the picture appears similar to double exchange, no real charge excitation will occur due to Coulomb repulsion, which prevents Mn2+ −Mn4+ charge disproportionation. Note that the orbital occupation difffers from Fig. 1.2. Superexchange is an exchange interaction between metal ions, mediated by their ligands. Fig. 1.2 shows a sketch of the antiferromagnetic coupling due to superexchange. This type of superexchange occurs along the b axis between the ferromagnetic layers of antiferromagnetic LaMnO3 . Ferromagnetic superexchange, as shown in Fig. 1.3, dominates the occupied-unoccupied interactions in the ac plane.

1.2.2

Doped manganites

In this section a short overview on the doped manganites is given. The section tries to give some background in the typical transitions and phase diagrams that are found. Already in the 50’s Jonker and Van Santen at Philips Natuurkundig Laboratorium, discovered for La1−x Cax MnO3 compounds that the resistivity changed from semiconducting above to metallic below the ferromagnetic ordering temperature [2, 19]. Magnetoresistance in thin films of the manganites was first reported by Chahara et al. [3] and Von Helmolt et al. [4]. The discovery of very large magnetoresistance by Jin et al., lead to a great surge in colossal magnetoresistance (CMR) research and publications [5]. Typical experiments were reported by the groups of Tokura [20] on single crystalline Sr doped LaMnO3 and Bell Labs [21] on powder samples of La0.75 Ca0.25 MnO3 . The original figure by Urushibara et al. is reproduced in Fig. 1.4. We observe that with increasing concentration of doping, x, the residual resistivity decreases. Furthermore, the magnetic phase transition temperature increases with doping. Above 10% doping the transition is accompanied by a (local) drop in the resistance below Tc . At 10%-15% doping the low temperature resistivity again increases exponentially, indicating activated behaviour of some kind. Lastly, the triangles indicate an orthorhombic, low temperature to rhombohedral, high temperature transition. The rhombohedral structure is less distorted than the orthorhombic one. Sr 2+ is


10

La1-xSrxMnO3

Resistivity (Ωcm)

103 102

X=0

101

X=0.05 X=0.15

100

X=0.1

10-1 X=0.175 X=0.2

10-2 10-3 10-4 0

100

X=0.3 X=0.5 200 300 400

500

Temperature (Κ)

Figure 1.4: Temperature dependence of resistivity for La1−x Srx MnO3 crystals. Arrows indicate the critical temperature for the ferromagnetic phase transition. Anomalies indicated by triangles are due to the structural transition. Reproduced from Ref. [20].

larger than La3+ , therefore the distortion should decrease with increasing x. Note the large density of transitions near 15% doping and 200 K. The low temperature charge ordering transition near 1/8 doping is not mentioned here. The phase diagram of La1−x Cax MnO3 was measured by Cheong and co-workers in great detail [22]. A modified version, in black and white, is given in Fig. 1.5. The undoped parent compound is LaMnO3 . It has an antiferromagnetic insulating ground state. Below 800 K, the orbitals on the Mn3+ are ordered. Above 10% doping the ferromagnetic interactions suppress the antiferromagnetic coupling and a ferromagnetic ground state is obtained. In the region of 20% to 50% Ca substitution the ground state is, like in the Sr doped samples, a ferromagnetic metal, dominated by double exchange. Double exchange is an interaction between d metal ions of different oxidation state, mediated by their ligands. It can be described by a real charge excitation, i.e. 3d4 − 3d3 → 3d3 − 3d4 , see Fig. 1.6. According to Cheong’s phase diagram, the ferromagnetic metallic phase emerges instantly above a critical concentration, at all temperatures below Tc . The overdoped compositions show a large variety of orbital and antiferromagnetic orderings, like in PrMnO3 -CaMnO3 [23]. For x = 32 , striped phases are reported [24]. The other end-member is CaMnO3 , also an insulating antiferromagnet, albeit not orbital ordered as it has only unoccupied eg orbitals. The phase diagram also shows two structural transitions. The first is the high temperature rhombohedral to orthorhombic transition. The second transition is from the orbital ordered to a non ordered structure both maintaining orthorhombic P nma symmetry.

1.3. Crystallography

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1000

Rhombohedral

800 Orthorhombic octahedra rotated

700 600 500

O’

400 300 200 100 0

O* JT CAF

Temperature (K)

900

0.0

1/8 FI

3/8

4/8

5/8

AF

CO

0.2

7/8

CO

FM

0.4

Ca x

0.6

CAF 0.8

1.0

Figure 1.5: Sketched phase diagram of La1−x Cax MnO3 , after Cheong et al. [22]. The doping induced insulator-metal transition is given at a critical concentration, x c = 0.2.

Figure 1.6: For explanation see Fig. 1.2. Double exchange between Mn3+ and Mn4+ ions. As the ’arriving’ and ’departing’ electrons at the O 2p orbital must have the same spin orientation, the coupling between the Mn3+ and Mn4+ ions is ferromagnetic.

1.3

Crystallography

X-ray diffraction This paragraph stresses what one actually measures with (single crystal) x-ray diffraction experiments. X-ray diffraction is sensitive to electrons and not to nuclei. This has both advantages and disadvantages. The intensity distribution of the diffraction spots in reciprocal space is the Fourier transform of the electron density distribution in real space. Diffraction can be described as an interference of incident radiation and space-filling identical building blocks, called unit cells. Every building block can be generated by translating one unit cell integer times along the lattice parameter vectors. This interference yields one reflection for every crystal plane [h k l]. The intensity associated with that reflection depends on the contents of the unit cell and can be zero. If


12

a class of reflections shows systematic extinctions, this is related to a symmetry element within the unit cell. Although the diffraction pattern, i.e. the observed intensities of the diffraction spots, is determined by the orientation, size and contents of the unit cell, it can also reflect a shorter scale repetition, just like a superstructure exhibits weak superlattice reflections and maintains the ’original’ reflections of the regular lattice. For example, the unit cell of orthorhombic ABO3 compounds contains four formula units, but its diffraction pattern clearly shows the signature of the single cubic perovskite, with only one formula unit per unit cell. Asymmetric region We do not need the positions of all atoms to describe the contents of the unit cell. The atoms that are necessary to generate the complete unit cell using all symmetry elements are called the asymmetric unit. A similar relationship exists between reflections in reciprocal space. The same symmetry elements that relate atoms also relate reflections, modulo the translation components of the symmetry elements. Related reflections are called equivalent reflections. Therefore, one does not need to measure the whole reciprocal space to obtain enough data for the inverse Fourier transformation to obtain the electron density distribution. The part of the reciprocal space that has to be included is the asymmetric region. Typically for orthorhombic space groups this is maximally one octant, for hexagonal structures at most one sixth of the whole reciprocal space. Non-centrosymmetric space groups need twice as much reciprocal space [25]. For example, the diffraction experiment on single crystalline ErMnO3 contained over 7000 measured reflections covering all octants of reciprocal space, see appendix E. Although the structure is refined in a non-centrosymmetric space group, still only 759 of these 7000 reflections were unique. Pnma vs. Pbnm In this paragraph the relation between P nma and P bnm is discussed. Orthorhombic AMnO3 compounds have space group P nma, this notation is in accordance with crystallographic conventions. The physics community prefers to name the doubled axis as the c axis, which yields the space group P bnm. These space groups are equivalent and are related via a simple transformation. The structure √ refinement of AMnO √ 3 in space group P nma yields for the lattice parameters: a1 ∼ 2ap , b1 ∼ 2ap , c1 ∼ 2ap , where asp is√the lattice√parameter of the cubic perovskite subcell. Space group P bnm yields a2 ∼ 2ap , b2 ∼ 2ap , c2 ∼ 2ap . The transformation from P nma to P bnm is a1 → b 2 b1 → c 2 c1 → a 2 This can easily be seen from the symmetry symbols. The mirror plane, m, in P nma is transferred from the second to the third position in P bnm. This means that the mirror plane is perpendicular to the doubled b1 axis and the doubled c2 axis, respectively. Similarly the diagonal glide plane, n, is transferred from the first to the second position; the diagonal glide plane is perpendicular to the a1 axis and the b2 axis, respectively. The symbol a

1.3. Crystallography

13

represents a glide plane perpendicular to the c1 axis with a ’glide’ component of half the vector a1 . Likewise, the symbol b represents a glide plane perpendicular to the a2 axis with a ’glide’ component of half the vector b1 . Co-ordination number The co-ordination of the atoms in a compound AB depends, in first approximation, only on the ratio of the radii. The radius ratio rule expresses that with increasing difference in radii the co-ordination of the smallest atom decreases [26]. The co-ordination number of an ion is sometimes hard to define in case of distorted perovskites. Cubic perovskites show perfect dodecahedral, twelvefold, co-ordinated A sites, with equal bond lengths. The B sites are sixfold co-ordinated. In the ortho-manganites the co-ordination of Mn is still sixfold, but with up to 20% difference in bond lengths. Due to the rotation of the octahedra, these manganites have distorted dodecahedra, with over 40% difference in bond lengths. A co-ordination number is very hard to determine with such distorted environments. It is therefore, in some cases, preferable to consider the distribution of bond lengths rather than stating a single co-ordination number. An example is given in Fig. 7.3.

references [1] G. H. Wiedemann and J. C. R. Franz, Ann. Phys. Chem. 89, 457 (1853). [2] G. H. Jonker and J. H. van Santen, Physica 16, 337 (1950). [3] K. Chahara, T. Ohno, M. Kasai and Y. Kozono, Appl. Phys. Lett. 63, 1990 (1993). [4] R. von Helmolt et al., Phys. Rev. Lett. 71, 2331 (1993). [5] S. Jin et al., Science 264, 413 (1994). [6] S. v. Naray-Szaba, Naturwissenschaften 31, 466 (1943). [7] H. L. Yakel, Acta Crystallogr. 8, 394 (1955). [8] S. v. Naray-Szaba, Naturwissenschaften 31, 202 (1943). [9] O. Zedlitz, Naturwissenschaften 31, 369 (1943). [10] S. Quezel-Ambrunaz, Bull. Soc. Fr. Min. Cristallogr. 91, 339 (1968). [11] M. Marezio, Mater. Res. Bull. 6, 23 (1971). [12] J. Rodríguez-Carvajal et al., Phys. Rev. B 57, R3189 (1998). [13] B. B. Van Aken, A. Meetsma and T. T. M. Palstra, Phys. Rev. B submitted 14 March 2001 (2001), cond-mat/0103628.

14


[14] J. B. A. A. Elemans, B. van Laar, K. R. van der Veen and B. O. Loopstra, J. Solid State Chem. 3, 238 (1971). [15] Q. Huang et al., Phys. Rev. B 55, 14987 (1998). [16] J. B. Goodenough, Phys. Rev. 100, 564 (1955). [17] K. I. Kugel and D. I. Khomskii, Z. Eks. Teor. Fiz. 64, 1429 (1973) [Sov.Phys. JETP, 37 725 (1973)]. [18] E. J. Cussen et al., J. Am. Chem. Soc. 123, 1111 (2001). [19] J. H. van Santen and G. H. Jonker, Physica 16, 599 (1950). [20] A. Urushibara et al., Phys. Rev. B 51, 14103 (1995). [21] P. Schiffer, A. P. Ramirez, W. Bao and S.-W. Cheong, Phys. Rev. Lett. 75, 3336 (1995). [22] M. Uehara, B. Kim and S.-W. Cheong, (2000), personal communication. [23] Z. Jirák et al., J. Magn. Magn. Mater. 53, 153 (1985). [24] C. Chen, S.-W. Cheong, and H. Hwang, J. Appl. Phys. 81, 4326 (1997). [25] H. D. Flack and G. Bernardinelli, Acta Crystallogr., Sect. A: Found. Crystallogr. 55, 908 (1999). [26] P. W. Atkins, Phys. Chemistry, 5th ed. (Oxford University Press, Walton street, Oxford, UK, 1993), Chap. 21, p. 741.

Chapter 2 Twin model for orthorhombic perovskites The structure of orthorhombic perovskites is a deformation of the structure of a simple cubic perovskite. The deviations from cubic symmetry are small. Therefore, domains with specific orientations of the unit cell can grow coherently on each other, a phenomenon known as twinning. The observed intensities of diffraction spots in reciprocal space are the weighted sums of the same lattice in different orientations, with a weighting factor proportional to the volume of the corresponding twin fraction. Detwinning is the process of finding the original intensity distribution, allowing a full structure refinement. The chapter covers a detailed single crystal x-ray diffraction study of twinned orthorhombic perovskites. The details and background of the detwinning process for single crystals of La1−x Cax MnO3 are presented. The diffraction pattern in reciprocal space can be indexed on a near cubic 2ap × 2ap × 2ap lattice, but does not obey cubic symmetry relations. The data are modelled in space group P nma with twin relations based on a distribution of the b axis over three perpendicular cubic axes. The twin model allows full structure determination in the presence of up to six twin fractions using the single crystal x-ray diffraction data. A general applicability for all orthorhombic perovskites is assumed.

2.1

Introduction

Generally, three basic states for manganites are distinguished, viz. the ferromagnetic metal, the paramagnetic polaronic liquid and the orbital and/or charge ordered antiferromagnetic insulating state. These states can be identified by different structural features. Metallicity induces charge delocalisation and is associated with equal Mn−O bond lengths. The charge and/or orbital ordered phases give rise to, for instance, lattice doubling. The polaronic liquid is locally characterised by small polarons. Ordered features over long range are observed via diffraction techniques. The intensity of the diffraction spots is the Fourier transform of the electron density distribution, as long as this density distribution is repetitive on the time and size scale of the experiment. 15

Chapter 2. Twin model for orthorhombic perovskites

16

Concretely, this means for x-ray diffraction experiments on perovskites that the most intense reflections are indiscernible from those of a perfect cubic perovskite. 1) The other reflections contain the distortions from the cubic lattice. The main distortions are the rotation of the octahedra and the deformation of the octahedra. The time and size scale of the experiment are determined by the wavelength and incoming energy of the x-ray beam. Typically λ = 0.71 × 10−10 m−1 and E = 17.7 kV yields an interaction time of 10−15 s and a coherence size of 10−7 m (1000 ˚ A). Doping can change the magnetic and electronic properties, which can be reflected in the details of the crystal structure. The present focus is on the structural response of phenomena of electronic origin, like Jahn-Teller distortions or orbital order. Since the metal-oxygen bond lengths and angles determine the exchange interactions, a thorough knowledge of the structure is necessary to understand the physics behind these phenomena. Typically crystal structure information is generated by neutron powder diffraction (NPD). NPD gives direct information about the interplaner distances and is very accurate in determining the changes of the lattice parameters with temperature and pressure. Using a full pattern Rietveld Analysis the atomic positions can be determined with an accuracy of 10−4 -10−3 . The alternative is single crystal x-ray diffraction (SXD). SXD is a very powerful experimental application to study the crystal structure of a large variety of materials. In contrast with powder diffraction, which maps all crystal planes to one dimension (d spacing, or angle 2θ), SXD observes all crystal plane reflections separately, even if they are related by symmetry. The relative co-ordinates of the atoms in the unit cell can be determined from the intensity distribution with a larger accuracy than by NPD. The major difference is that NPD is sensitive to the nucleus, while SXD measures the electron density, which is of interest to understand the electronic properties. Twinning can complicate the structure determination. We discern merohedral twins, having a perfect coincidence of all reciprocal lattices, and non-merohedral twins. In nonmerohedral twins, the two lattices do not coincide, giving much more reflections than expected. However, some specific reflections like 0 0 l may overlap. Usually non-merohedral twins give very large ”unit cells”, as the proposed unit cell relates to the smallest lattice that covers the observed reflections of both lattices. However, for many perovskites SXD is not used because of unconventional twinning of the crystals. Twinning of the perovskites is complex as the cubic parent structure allows not only simple twin axes and planes, but also 3D twin relations. A method is presented to analyse twinned single crystals. Moreover, this twin model allows a full structure determination including detailed information on distortions of both structural and electronic origin. Besides, it is shown that one does not need a larger data set, as is usual in the case of twinning. Using SXD, √ we observe √ a 2ap × 2ap × 2ap unit cell. It is commonly accepted that the unit cell is 2ap × 2ap × 2ap . The twinning is unique and it involves a distribution of the 1)

The intensities of the reflections are determined by the contents of the unit cell, including atomic number, atomic position and symmetry. The positions of the reflection spots are controlled by the size and orientation of the unit cell.

2.2. The twin structure for manganites

17

b axis over three perpendicular cubic axes. This leads to a large fraction, about 25%, of coinciding reflections and an only twice as large unit cell. The observed unit cell originates from a three-dimensional type of twinning that is not restricted to manganites. The model is most likely of general application for a large variety of perovskite P nma crystals.

2.2

The twin structure for manganites

The manganites have generated considerable attention because of the colossal magnetoresistance effect. The role of magnetic order has been widely discussed since double exchange, inducing the ferromagnetic order, is required to generate a metallic ground state. The role of orbital order is much less understood. While local Jahn-Teller (JT) distortions are crucial in explaining the localisation of the charge carriers in the paramagnetic state, the long range Jahn-Teller ordering has not been well studied, except for undoped LaMnO 3 . We will show that the destruction of long range orbital order is a second prerequisite for the metallic ground state. In fact, in Chapter 3 we will show that with increasing hole doping of LaMnO3 not the exceeding of a critical concentration but the suppression of the orbital order generates the metallic ground state. The orbital ordering in perovskites with degenerate eg electrons can be easily measured, whereas for degenerate t2g electrons the Jahn-Teller distortions are much smaller. Furthermore, the generally observed P nma symmetry can accommodate not only the Jahn-Teller ordering, but also a 3D rotation of the octahedra, known as the GdFeO3 rotation. We will focus on the main reason why SXD has not been widely used for these perovskites, namely twinning. Twinning in doped LaMnO3 originates from the transition of the highly symmetric cubic parent structure to the orthorhombic symmetry, that accommodates both the GdFeO3 rotation and the JahnTeller distortion. In thin films ac twinning has been observed. The solution of the twin relations in the crystals allows us to study in detail the ordering of these compounds as influenced by temperature, magnetic state and doping concentration. But for now we will focus on the twin relations. At high temperatures most AMnO3 are pseudo-cubic with a unit cell of ap = 3.9 ˚ A. Due to both the small average A site radius and the JT effect the MnO6 octahedra are rotated and distorted at lower temperatures. As a direct consequence, most La1−x Cax MnO3 crystals are twinned. Here we present an accurate description of the origin of the twinning, the detwinning process and show that we can still determine the temperature dependence of the structure by measuring only the reflections of the main fraction in one octant of the hkl space. Twinning has been reported before in AMnO3 perovskites and related structures. For instance, neutron powder experiments on LaMnO3 showed reflections, at temperatures above the Jahn-Teller transition, that could be indexed on a double cubic unit cell. But full pattern refinement was only possible in the orthorhombic space group P nma [1]. Singlecrystal electron diffraction showed a double cubic unit cell for SrSnO3 , even though CaSnO3 is orthorhombic [2]. Electron microscopy, however, showed the existence of coherent domains, with perpendicular orientations of the doubled b axis. The structure was deduced

18


via the O’Keefe-Hyde relations [3]. The experiments were carried out on single crystals of La1−x Cax MnO3 , x = 0.19, obtained by the floating zone method at the MISIS institute, Moscow. Although all crystals were twinned, small mosaicity and sharp diffraction spots were observed. Furthermore, sharp magnetic and electronic transitions indicate the good quality of the crystals, see Chapter 3. A thin piece was cut from the crystal to be used for single crystal diffractometry. The single crystal was mounted on an ENRAF-NONIUS CAD4 single crystal diffractometer. The temperature of the crystal was controlled by heating a constant nitrogen flow. Initial measurements were done at 180 K.

2.3

Crystal structure

Most structure research of perovskites focusses on the Mn−O distances and the Mn−O−Mn angles, as these parameters determine the competition between the superexchange and double exchange interactions. The approach here stresses the importance of a complete structure refinement, including the La-position and the rotation/distortion of the MnO 6 octahedra. The main deformations that determine the deviation from the cubic structure are the GdFeO3 rotation and the Jahn-Teller distortion.

Figure 2.1: Sketch of the cubic perovskite unit cell. La, Mn and O ions are represented by hatched, open and small black circles, respectively. The edges of the MnO 6 octahedron are indicated by thin lines. ˚ cubic unit cell The basic building block of the perovskite structure is a roughly 3.9 A with Mn in the centre and O at the face centres. The oxygen ions co-ordinate the Mn ions to form MnO6 octahedra. The A atoms are located at the corners of the cube. A sketch of the cubic perovskite is given in Fig. 2.1. The undistorted ’parent’ cubic structure rarely exists, for instance SrTiO3 [4], but distorts to orthorhombic or rhombohedral symmetry. The tolerance factor t is defined as:

2.3. Crystal structure

19

t= √

hrA2/3+ i + rO2− , 2(hrM n4/3+ i + rO2− )

(2.1)

where rx is the ionic radius of element x and hri denotes the average radius. For the A site, a co-ordination number of nine is assumed, values have been taken from Shannon and Prewitt [5]. For an ideal perovskite structure the ratio between the radii of the A site ion and the transition metal ion is such that the tolerance factor is equal to one. In the La-Ca system the tolerance factor varies from 0.903 to 0.943 going from LaMnO 3 to CaMnO3 .

2.3.1

GdFeO3 rotation

Due to the small radius of the A site ion, with respect to its surrounding cage, the MnO 6 octahedra tilt and buckle to accommodate the lanthanide ion. This is known as the GdFeO 3 rotation2) and yields the space group P nma. The cubic state allows one unique oxygen position. Due to the GdFeO3 rotation we need two inequivalent oxygen positions in P nma symmetry to describe the structure. O2 is the in-plane oxygen, on a general position, (x, y, z). Two opposite Mn−O2 bonds have the same length, but the perpendicular bonds do not need to be equal. O1 is the apical oxygen, located on a fourfold (x, 14 , z) position on the mirror plane. Mn−O1 bonds are always of the same length. Both in the undistorted and the distorted perovskite, the O−Mn−O bond angles are 180◦ (or near 90◦ ), but due to the buckling Mn−O−Mn bond angles are significantly less than 180◦ . A pure GdFeO3 rotation can be obtained within P nma with equal Mn-O bond lengths, as is seen in Fig. 2.2.

2.3.2

Jahn-Teller distortion

The Jahn-Teller effect originates from the degenerate Mn3+ d4 ion in an octahedral crystal field. Two possible distortions are associated with the Jahn-Teller effect. Q2 is an orthorhombic distortion, with the in-plane bonds differentiating in a long and a short one. Q3 is the tetragonal distortion with the in-plane bond lengths shortening and the out-ofplane bonds extending, or vice versa [6, 7]. The main result of the distortions Q2 and Q3 is that the Mn−O distances become different, cf. Fig. 2.3, and the degeneracy of the t2g and eg levels is lifted. In the figure the Q2 distortion is shown. For LaMnO3 , the orbital splitting is such that z 2 -like orbitals are occupied, alternatingly oriented along the x + z and x − z axis [8,9], yielding the Q2 distortion. The O2 fractional co-ordinate and this Q2 distortion are intimately related. For a Q3 distortion, only the ratio between the b lattice parameter and the a and c parameter has to change. 2)

The GdFeO3 rotation comprises only of rotating MnO6 octahedra. In the remainder of the thesis the term ”GdFeO3 rotation” will be used. Distortion is restricted to the ”Jahn-Teller distortion”.


20

x z

Figure 2.2: Sketch of the GdFeO3 rotation in the ac plane, obeying Pnma symmetry. Mn and O ions are represented by large and small circles, respectively. Open arrows indicate the movement associated with the GdFeO3 rotation. Full line indicate the unit cell.

2.3.3

Glazer’s view on the octahedra

There are three possible rotations for a rigid MnO6 octahedron. One rotation, ηy , changes the atomic positions of the O2 atom only. The others have an effect on the atomic positions of both O1 and O2. Any movement of an oxygen position will also affect the position of the La atom [10]. Glazer identified all possible sequences of rotations for the perovskite system [11]. Two of these sequences create the symmetry elements that make up the standard perovskites. In Glazer’s notation: a− b+ a− 3) yields orthorhombic P nma and a− a+ a− will result in rhombohedral R3c. As Glazer worked in a pseudocubic 2ap ×2ap ×2ap system we have to transform the rotation a− b+ a− to the orthorhombic unit cell, which gives a− b+ c0 . This means that the rotation around the c axis, ηz , is zero. By rotating the MnO6 octahedra only around the x axis, two oxygen ions are raised from their cubic position and two are lowered as is sketched in Fig. 2.4. Here we neglect the influence of a rotation ηy on these co-ordinates. This is in agreement with the observation that the four positions of O2 near the Mn at (0, 0, 0) have the same distance to the y = 0 plane, albeit two are positive and two are negative. As a result of ηz = 0 the fractional x co-ordinate of O1 is also zero. In practice small deviations are found, indicative of the non-rigid behaviour of the MnO6 octahedra. Typically in AMnO3 these two rotations and the Q2 JT distortion are observed. Another effect of the GdFeO3 rotation is that the number of formula units per unit cell is enlarged. The unit cell is doubled in the b direction, with respect to√the original cubic cell. The ac plane is also doubled, resulting in b ≈ 2ap , and a ≈ c ≈ 2ap . Despite the rotations and distortion, the structure remains in origin cubic. The shifts of the atoms 3)

p− q + r0 means that along [100] a rotation of size p is alternated positive and negative, along [010] a rotation of size q is always (arbitrarily) positive, and along [001] there is no rotation.

2.4. Twin model

21

x

z

Figure 2.3: Sketch of the Q2 JT distortion in the ac plane, obeying Pnma symmetry. Mn and O are represented by large and small circles, respectively. Closed arrows indicate the movement associated with the JT distortion. in the unit cell are small. Furthermore, Mn stays octahedrally surrounded although the Mn−O distances tend to differ and some O−Mn−O angles may no longer be perfectly 90◦ . The 180◦ O−Mn−O bond angles are intrinsic to the inversion centre at the Mn position. The small deviations from the cubic symmetry are reflected in the intensities of the reflections. To illustrate this point, we transform an arbitrary, subcell, reflection hkl to the orthorhombic setting by h0 k 0 l0 = h+l, 2k, h-l. Thus orthorhombic reflections with k 0 even and h0 and l0 both even or both odd stem from planes that already existed in the original cubic unit cell. We observe in all diffraction patterns of orthorhombic perovskites that reflections that originate from cubic crystal planes generally have higher intensities than those that do not.

2.4

Twin model

Reflections in reciprocal space are experimentally observed at a regular distance in three orthogonal directions, corresponding to a cubic lattice spacing of 7.8 ˚ A in real space. Although the three orthonormal axes have equal lengths, the threefold rotation axis along h111i, required for cubic symmetry, could not be observed. However, studying the intensity distribution of planes in hkl space with constant h, k or l showed much regularity. In Fig. 2.5 the observed intensity distribution of the reflections is plotted. The reflections are subdivided in four groups, on the basis of the number of odd indices in the double cubic setting. A twinned structure consisting of coherently oriented P nma domains is proposed.


22

ηx ηx

Figure 2.4: Rotation, ηx , of the MnO6 octahedron around the a axis. The arrows indicate the motion of the O2 ions. ˚. Due to partial overlap this results in a metric cubic system with a ≈ 2ap ≈ 7.8 A Twinning is often observed in crystals with a reduced symmetry. The orthorhombic perovskite LaMnO3 has lower symmetry than cubic SrTiO3 . Conventional twin models keep one characteristic axis unchanged and form the domains by rotation around that axis. This is commonly observed in constrained epitaxial thin films and pseudo-two-dimensional crystals like YBa2 Cu3 O7−δ . Another standard twin is inversion twinning, found in noncentrosymmetric systems. Due to the inversion twin, pseudo-centrosymmetry is obtained and the net polarisation in ferroelectric compounds is reduced to zero [12, 13]. Usually, both types of twinning have the property that either all twin domains have reflections that lie on top of each other, merohedral twins, or there is a non-commensurate set of reflections, e.g. non-merohedral twins in monoclinic unit cells. Here a more extensive form of twinning is proposed, where at a quarter of the observed reflections the reflections of different domains coincide and the other part of the observed reflections originates from a single domain only. Together they give rise to the observed metrically cubic lattice. How is this twin model derived? The transformation of cubic to orthorhombic symmetry requires a designation of a, b and c with respect to the degenerate cubic axes. There are three possibilities to position the doubled b axis along the three original cubic axes. Thus we propose that the three fractions’ b axes are oriented along the three original axes of the cubic unit cell, as sketched in Fig. 2.6. This twin model consists of a P nma unit cell, transformed by rotation along the ’cubic’ [111] axis. We still have the freedom to choose the a and c axes, perpendicular to the b axis, and rotated 45◦ with respect to the cubic axes. Therefore, this model yields √ six different √ orientations of the orthorhombic unit cell. As the differences between a/ 2, b/2 and c/ 2 are small, we observe the reciprocal superposition of the six orientations as metrically cubic. The standard refining programs can work with twin models, but only if they consist of merohedral twins. In our case, the reflections do not correspond with an orthorhombic unit cell, but with a, twice as large, pseudo cubic unit cell. In appendices 2.7.1 and 2.7.2,

2.5. Discussion

23

Number of reflections

2500 2000

EEE

EEO

OOO

EOO

1500 1000 500

00

>1

00

00 00

0 >ooo>eoo. Here we consider the transformation from the orthorhombic to the double cubic setting for the in-plane indices, h0 and l0 . Double cubic indices are calculated with h0 +l0 and h0 -l0 , therefore h00 and l00 will be both even or both odd. Reflections of the type e?o or o?e will have no intensity of the twin with b0 parallel to k 00 , as they are not originating from an ’integer’ crystal plane. In contrast with the single cubic to orthorhombic P nma transition, where orthorhombic superlattice reflections are allowed, the orthorhombic to double cubic transformation is just a new choice of reference system, that may not and cannot generate new reflections. But we have a mixing of different orientations of the b0 axis along the three cubic axes h00 , k 00 and l00 , which do generate reflections where none are observed without the twinning. We can cycle the indices of these reflections so that we get either e?e or o?o. From the corresponding twin, with b0 parallel to either a00 or c00 , we do have intensity on these e?o and o?e reflections. eoe and oeo will only have contributions from this particular setting with b0 k k 00 . eee and ooo can be cycled and in general have contributions from all six orientations. Distribution of the twins The intensity of a particular twin fraction is proportional to the volume of that twin fraction. Using the uniqueness of some reflections, i.e. belonging to only one twin fraction lattice, we can search for the orientation of the largest fraction. All b 0 axes are oriented along one of the measured double cubic axis. It is impossible to differentiate the two fractions with parallel b0 and perpendicular a0 and c0 . We considered groups of reflections with cycled indices, having either one odd, oee, or one even index, eoo. Roughly, the intensities of the reflections within these groups occurred with ratio 70:20:10. This suggested that one twin had 70% of the volume, the others 20% and 10%. These reflections are sorted to find the corresponding orientations. The sort parameter is the observed double cubic axis that corresponded with the odd indices in oee, and the even indices in eoo. Only cycled reflections that occurred three times with measurable intensity were taking into account. We found that Ia00 : Ib00 : Ic00 = 5 : 80 : 15. The

2.7. Appendices

31

constraint that all three intensities have positive values, ignores the weakest reflections. This method also ignores Bijvoet pairs, as we only measured −20 < l 00 < 2. In principal eoo and eoo should have identical intensity. If we indeed had a cubic system then these variations should be zero within standard deviation. The distribution of the intensities, with respect to the different axes, strongly suggests that the crystal is twinned.

2.7.2

Implementation in refinement

Here we describe the model and the application by SHELXL. The standard refining programs can work with merohedral twin models. However, in our case, the observed lattice does not coincide with one orthorhombic unit cell. Every observed reflection has contributions of up to six twin fractions. We measured both in the double cubic setting as in the orthorhombic setting of the main twin fraction. We transformed the h00 k 00 l00 indices to the six possible twin orientations. Three of the possibilities are given by 1 1 h0 k 0 l0 = (h00 + l00 ), k 00 , (h00 − l00 ) 2 2 1 1 h0 k 0 l0 = (l00 + k 00 ), h00 , (l00 − k 00 ) 2 2 1 1 h0 k 0 l0 = (k 00 + h00 ), l00 , (k 00 − h00 ) 2 2

(2.3) (2.4) (2.5)

The other three can be acquired by changing h0 for l0 and l0 for -h0 . A new software program TWINSXL was developed to transform the standard data file, HKLS, by using the appropriate transformation matrices from a second input file [14]. The new data file is constituted of lines of h, k, l, intensity plus standard deviation and twin fraction number. We used the ”HKLF 5” option of SHELXL to refine data. The refinement uses a crystal model for the orthorhombic structure with the normal, adjustable variables. Five variables for the twin fractions were added, the sixth fraction is calculated as the complement of the other five fractions. The sum of the appropriate calculated intensities for all fractions was compared with the observed integrated intensities.

references [1] J. Rodríguez-Carvajal et al., Phys. Rev. B 57, R3189 (1998). [2] A. Vegas, M. Vallet-Regí, J. González-Calbet and M. Alario-Franco, Acta Crystallogr., Sect. B: Struct. Sci. 42, 167 (1986). [3] M. O’Keefe and B. G. Hyde, Acta Crystallogr., Sect. B: Struct. Sci. 33, 3802 (1977). [4] A. von Hippel, R. Breckenridge, F. G. Chesley and L. Tisza, Ind. Eng. Chem. 38, 1097 (1946). [5] R. D. Shannon and C. T. Prewitt, Acta Crystallogr., Sect. A: Found. Crystallogr. 32, 751 (1976).

32


[6] J. Kanamori, J. Appl. Phys. 31, 14S (1960). [7] Y. Yamada et al., Phys. Rev. Lett. 77, 904 (1996). [8] J. B. Goodenough, Phys. Rev. 100, 564 (1955). [9] J. B. A. A. Elemans, B. van Laar, K. R. van der Veen and B. O. Loopstra, J. Solid State Chem. 3, 238 (1971). [10] T. Mizokawa, D. I. Khomskii and G. A. Sawatzky, Phys. Rev. B 60, 7309 (1999). [11] A. M. Glazer, Acta Crystallogr., Sect. B: Struct. Sci. 28, 3384 (1972). [12] C. Rao and J. Gopalakrishnan, New directions in solid state Chem., 2nd ed. (Cambridge University Press, 1997), page 385. [13] B. B. Van Aken, A. Meetsma and T. T. M. Palstra, Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 57, 230 (2001). [14] A. Meetsma, TWINSXL, software package, Solid State Chemistry, University of Groningen, 2000.

Chapter 3 Jahn-Teller ordering vs. ferromagnetic metal LaMnO3 is an antiferromagnetic insulator with a checkerboard pattern of eg orbitals, see Section 1.2.1 and Fig. 2.3. When 20% to 50% holes are introduced, a ferromagnetic ground state with degenerate eg orbitals is obtained. The LaMnO3 -CaMnO3 phase diagram of Fig. 1.5 shows the doping induced ferromagnetic insulator (FI) to ferromagnetic metal (FM) transition at a critical concentration of x ∼ 0.20. While this transition is intriguing by itself, the situation becomes more complex by the orbital order (O*) to ”not orbital ordered” (O’) transition, indicated by the gray line. Neither the exact concentration dependence of this transition nor the interaction of this orbital order transition with the magnetic ordering and the temperature- or doping-induced metal-insulator transition is known. The O*-O’ transition is typically associated with a step in the resistance or a re-entrant insulating behaviour. The first part of this chapter will show that the parameters describing the Jahn-Teller or orbital ordering and the GdFeO3 rotation can be separately obtained from the fractional atomic positions. Both the O2 position, which contains the in-plane oxygen ions of the MnO6 octahedra, and the La position are sensitive to the rotation and the deformation of the octahedra. The second part will discuss the doping and temperature dependence of the Jahn-Teller ordering, the rotation and the site shift of La1−x Cax MnO3 in the region 0.15 < x < 0.25 by single crystal diffraction. We would like to understand the sequence from the antiferromagnetic insulator via ferromagnetic insulator to ferromagnetic metal and try to find answers to questions like: 1. How does the O*-O’ transition influence these phases? 2. What is the effect of hole doping on the orbital order and JT distortion? 3. What is the nature of the disappearance of orbital order? A disappearance of the JT distortion or a disordering of the orbitals? 33

Chapter 3. Jahn-Teller ordering vs. ferromagnetic metal

34

3.1

Introduction

The basic interactions in the manganite perovskites allow three phases: a ferromagnetic metal, a charge/orbital ordered antiferromagnetic insulator and a paramagnetic polaronic liquid. Metallicity is obtained by introducing holes by doping in antiferromagnetic, insulating LaMnO3 . This doping renders La1−x Cax MnO3 , for 0.20 < x < 0.50, both metallic and ferromagnetic, as the interactions are dominated by double exchange. Although superexchange allows ferromagnetic interactions, the necessary orbital ordering induces an overall antiferromagnetic state. However, La1−x Cax MnO3 , with 0.10 < x < 0.20, has a ferromagnetic insulating ground state. This unexpected coexistence of ferromagnetic and insulating behaviour seems to contradict the conventional double and superexchange models. Originally the magnetic state was thought to be a canted antiferromagnetic phase [1], but experiments determined the magnetic state to be ferromagnetic [2]. The origin of the coexistence of ferromagnetism with insulating behaviour is not clear, but might stem from a delicate balance of charge localisation by orbital ordering (OO), due to the Jahn-Teller (JT) effect, and ferromagnetic interactions between Mn3+ -Mn4+ . The exact position of the phase line of the JT ordering transition in the composition temperature phase diagram of doped LaMnO3 is not known, and may depend on other variables, such as the tolerance factor and the magnetic ordering. The phase diagram of Sr doped manganites has been explored in great detail. Here the situation is more complicated than for Ca doping, because the number of phases is larger due to the rhombohedral structure at x > 0.18 and the pronounced charge ordering (CO) at x ∼ 1/8 [3]. Several authors reported a JT related structural phase transition above the magnetic ordering temperature, T > Tc at x ∼ 0.12. Below Tc , a transition to CO or OO is observed, where the cooperative JT distortion is significantly reduced [4,5]. As the transition temperatures are extremely concentration dependent, a comparison between the various reports is not straightforward. It is claimed that the intermediate phase is both ferromagnetic and metallic and exhibits static cooperative JT distortions [1, 5]. Some reports clearly distinguish these two properties and combine short range order of JT distortions with metallic behaviour [6]. However, a general relation between the JT ordered phase and the nature of the conductivity has not been established. Also, a coincidence of the CO transition and the re-entrant insulator-metal transition is claimed. The common metal-insulator transition is indisputably associated with the ferromagnetic ordering at Tc [1, 5–7]. The Ca doped phase diagram is somewhat less complex, as there is no orthorhombicrhombohedral structural transition. Furthermore, the phase transitions take place at higher concentrations. As a result we can probe the ferromagnetic insulating phase at concentrations far away from x = 1/8 to evade charge ordering. Here, we explore the region where the JT ordering phase line crosses the magnetic ordering phase line. We will show that the transition to the ferromagnetic metallic phase is not at fixed carrier concentration, but is controlled by the suppression of JT ordering. Conventionally, the JT ordering is observed via the Mn−O distances. We will provide evidence that the La site shift is a more accurate tool for JT ordering, as the La position is sensitive to a change in the oxygen environment.

3.2. Experimental

35

Our measurements suggest that above the JT ordering phase transition temperature, T JT , both the metallic phase and the paramagnetic phase exhibit strong JT like fluctuations. These fluctuations become long range ordered below TJT .

3.2

Experimental

The experiments were carried out on single crystals of La1−x Cax MnO3 , x = 0.16, x = 0.19 and x = 0.25, obtained by the floating zone method. The sample with x = 0.19 originated from the MISIS institute, Moscow, the other two samples were kindly provided by Drs T. Tomioka and Y. Tokura, JRCAT, Japan. Although all crystals were twinned [8], small mosaicity and sharp diffraction spots were observed. Furthermore, the sharp magnetic and electronic transitions indicate the good quality of the crystals. Simultaneous measurements of resistance R and magnetisation M were performed in a MPMS magnetometer to find the exact transition temperatures for the x = 0.19 sample. Resistance curves for the other samples were measured in Japan. They showed sharp metal-insulator transitions at the ferromagnetic ordering temperatures at T = 100 K and T = 200 K, respectively. Additionally, the x = 0.16 sample exhibits an anomaly in the resistance at T = 260 K. A thin piece was cut from the crystals to be used for single crystal diffractometry. Initial measurements were carried out on an Enraf-Nonius CAD4 single crystal 4-circle diffractometer to determine the twin relations and the twin fraction volume [8]. Temperature dependent measurements between 90 K and 300 K were performed on a Bruker APEX diffractometer with an adjustable temperature set-up. Details of the single crystal x-ray diffraction and structure refinement are given in Appendices A, B and C.

3.3

La site shift as probe for Jahn-Teller effect

The twinning of the crystals does not allow an accurate determination of the lattice parameters, as the overlap of the different twin domains effectively averages them. The relative changes in Mn−O bond lengths is thus entirely determined by the fractional atomic co-ordinates. We have shown in Chapter 2 that the O2 position in P nma space group symmetry can be seen as a superposition of a rotation and a distortion. In this section the measurements and refinement on the x = 0.19 sample will be used to show the validity and the effectiveness of this method. The temperature dependence of the resistivity is shown in zero, small and large magnetic fields in Fig. 3.1.a. The resistance has a clear maximum at 177 K. At significantly lower temperatures, T ≈ 160 K, the resistivity shows a subtle and wide transition to activated behaviour. This maximum can be suppressed by applying small fields (H < 0.1 T). Upon applying larger fields the resistance decreases not only in the local maximum but in the whole temperature range, both below the local minimum at T ≈ 160 K and above Tc . In Fig. 3.1.b, magnetisation curves are plotted in the temperature range 170 < T < 180 K with temperature steps of 1 K. For T ≤ 177 K the initial slope is constant and determined


36

30

Magnetisation (a.u.)

Resistance [Ohm]

35 0T 0.01 T 1T

25 20 15 10 5 125

150

175 200 225 Temperature [K]

(a)

250

170 K

0.06

0.04

0.02 180 K 0.00 0.000

0.025

0.050 0.075 Field (T)

0.100

(b)

Figure 3.1: a) Temperature dependence of the resistance of La0.81 Ca0.19 MnO3 at H = 0, 0.01 and 1 T. b) Magnetisation vs. applied magnetic field in temperature steps of 1 K between 170-180 K. Both measurements establish that Tc = 177 K. by the demagnetisation factor. Therefore, we establish Tc to be 177 K. Both the magnetisation curves and resistance measurements indicate a sharp transition at 177 ± 0.5 K. We propose that the observed upturn in resistance at T ≤ 160 K is a result of reentrant insulating behaviour caused by JT ordering. The well-known phase diagram by Cheong et al. [9] is modified as shown in Fig. 3.2. We propose that the FMM phase, hatched area, should be extended to the O*-O’ phase line, which indicates the JT ordered (O*) to ”not orbital ordered” (O’) transition. In analogy to conventional ferromagnetic metallic La1−x Cax MnO3 systems, with x ∼ 0.3 [10], we expect to observe a narrowing of the distribution of Mn−O bond lengths below Tc as a result of the itinerancy in the ferromagnetic, metallic regime. As soon as the JT orbital ordering sets in there will be a separation of the Mn−O bond lengths, as observed for La1−x Srx MnO3 with 0.11 < x < 0.165 [6]. The difference in bond lengths should become less pronounced in case of a charge ordered phase at the lowest temperatures [1, 4, 6]. From our full structure refinement, we can clearly observe the difference in in-plane Mn−O bond lengths, i.e. Mn−O2, both in the paramagnetic phase and in the insulating phase. However, we can not observe a decrease in this difference in the metallic regime, 160 < T < 177 K, of the x = 0.19 sample. The error bars on the bond lengths are quite large, due to the relatively low x-ray scattering factor of oxygen and the influence of the twinning, common in many perovskite materials [11, 12]. As we explained in detail elsewhere, the reflections√of the various √ twin fractions overlap indistinguishably, which averages the calculated 2a, b and 2c parameters [8]. Therefore the accuracy of the lattice parameter determination is not as good as for neutron powder diffraction. However, the refinement of the relative atomic positions within the unit cell, which are reflected in the observed intensities, is extremely accurate. Therefore it makes more sense to focus on the refined atomic positions than on the bond lengths. This holds especially for the

3.3. La site shift as probe for Jahn-Teller effect

.

7HPSHUDWXU

2¶

/D

&D 0Q2

30, 2 )00

37

)0,

[

&

GRSLQJ[

Figure 3.2: Sketched phase diagram near the FMI-FMM transition, modified from Cheong et al. [9]. The critical concentration, xc , only indicates the metal-insulator transition at T = 0. The concentrations of the three single crystals are indicated by the dash-dot lines. O2 (in-plane) oxygen position, since it completely determines the Jahn-Teller distortion. For the full structure determination, we had to derive the twin relations, which are reported elsewhere [8]. The temperature dependence of the O2 fractional co-ordinates shows a transition in xO2 , but this provides little insight into the physical mechanism. More insight is gained by using the parameters xO2 + zO2 1) and xO2 − zO2 as sketched in Fig. 3.3, see also Fig. 2.2 and Fig. 2.3 . Here, a movement of the O2 ion parallel to the vector x − z 2) , which implies that x+z = 12 , results in equal bond lengths but a Mn−O−Mn angle smaller than 180◦ . We interpret this movement, along the vector x − z, as the GdFeO3 rotation. Similarly, a shift of the O ion along the vector x + z, thereby fixing x − z = 0, results in different in-plane bond lengths Figure 3.3: Sketch of the GdFeO3 rotation (open and therefore indicates a Jahn-Teller arrow) and the JT distortion (closed arrow) in the distortion. The JT variable is defined ac plane, obeying Pnma symmetry. Mn and O are as xO2 + zO2 − 12 , thus no distortion represented by large and small circles, respectively. yields a JT parameter equal to zero.

x

z

The O2 position, (xO2 , yO2 , zO2 ) near ( 14 , 0, 14 ) is used here. The other three oxygen positions in the same xz plane of the unit cell follow from the space group symmetry. For these the shifts are also transformed according to the symmetry. 2) Note that the associated parameter is xO2 − zO2 . Where applicable the word vector is added, otherwise the variable, determined from the fractional co-ordinates, is meant. 1)


38

The undistorted cubic structure obeys both = 0 and x−z = 0. It is clear that any O2 position can be expressed uniquely as a superposition of a GdFeO3 rotation parameter, viz. xO2 − zO2 , and a JT distortion parameter, viz. xO2 + zO2 − 12 . The temperature dependence of the variables representing the GdFeO3 rotation and the Jahn-Teller distortion are plotted in Fig. 3.4. We observe a clear increase in the Jahn-Teller parameter from the room temperature phase, ≈ 0.003, to the low temperature phase with ≈ 0.006. It increases continuously down to TJT = 150 K. The rotation increases slightly with decreasing T and levels off at T ∼ 180 K. x+z − 12

0.062 JahnTeller Rotation

0.006

0.061

0.005

0.060

0.004 0.059

Rotation: x - z (-)

Jahn-Teller distortion: x + z - 1/2 (-)

0.007

0.003 0.058 0.002 100

150 200 250 Temperature (K)

300

Figure 3.4: Jahn-Teller distortion and GdFeO3 rotation of La0.81 Ca0.19 MnO3 as a function of temperature. The JT distortion increases linearly down to TJT = 150 K. A kink in the GdFeO3 rotation appears near Tc at T = 180 K. Goodenough showed the importance of interactions between the A ion, d0 , and the filled oxygen 2p orbitals in the case of a GdFeO3 rotation [13, 14]. Recently, Mizokawa et al. reported on the interplay between the GdFeO3 rotation, the orbital ordering and the A site shift in ABO3 , with B=Mn3+ (3d4 ) or V3+ (3d2 ). Their theoretical calculations suggest that the observed orbital ordering in LaMnO3 is stabilised by both a large GdFeO3 rotation and a shift of the A site ion [15]. Conversely, if a Jahn-Teller distortion is present, then the energy will be lowered if it is accompanied by a shift of the A site. In Fig. 3.5, we show the temperature dependence of the A position, (xA , 14 , zA ), with respect to the ideal position (0, 14 , 12 ). Note that the error bars and scatter are much smaller than for the O positions, due to the higher electron density at the A site. Fig. 3.5 shows a linear increase of xA with T down to TJT = 150 K. xA is roughly 5 times larger than zA for all temperatures. A small change in the gradient is observed

39

0.025

0.0052

0.024

0.0050

0.023

0.0048

xLa

0.022

0.0046

1/2-zLa 0.021

100

150

200

250

300

Fractional 1/2-z position (-)

Fractional x position (-)

3.3. La site shift as probe for Jahn-Teller effect

0.0044

Temperature (K)

Figure 3.5: xLa and zLa positions vs. T. Drawn lines are linear fits of xLa , in three stages: T < 150 K, 150 < T < 180 K and T > 180 K. For zLa a fixed ratio of 1:5 with respect to xLa is assumed. near Tc . Below TJT , xA and zA are temperature independent. This La site shift along [1 0 5] is in good agreement with the [1 0 7] direction which was assumed by Mizokawa et al. [15]. Furthermore, the observed temperature dependence is in excellent agreement with the temperature dependence of the JT effect and the rotation. Therefore, linear fits are ∂x = 0, -1.56×10−5 plotted for T < TJT , TJT < T < Tc and T > Tc . The gradients are ∂T −5 −1 and -2.05×10 K , respectively. The basic argument favouring the A site shift is that the band structure energy can be optimised by decreasing the A−O distances for the three shortest bonds and increasing the A−O bond lengths for the three next-shortest bonds. This effect is demonstrated by the cubic-tetragonal transition in WO3 [16]. The tungsten ion is octahedrally surrounded by oxygen ions. Band structure calculations show that the gap is lowered by a ferroelectric displacement of the W ion off-centre. The energy is lowered by the overlap between the empty W 5d xz and yz orbitals with the occupied O 2p x and y, respectively [16]. In cubic perovskites, the A ion is in the centre of the AO12 polyhedra. The GdFeO3 rotation distorts the AO12 polyhedron. Additionally, the minimalisation of the bondingantibonding energy will decrease the shortest A−O bonds even more by a shift of the A ion. Marezio et al. have studied the structure of the AFeO3 compounds in great detail and their data allow us to focus on the correlation between the rotation and the La site shift [17]. The relevant atomic parameters, x and z of both the O2 and the A site, are all fully correlated as shown in Fig. 3.6. The figure shows a perfect linear relation between the A site shift and the rotation parameter. Thus the shift of the A site atom is, in this system, fully determined by the rotation of the FeO6 octahedron. A fixed rotation will result in a particular A site shift. This conclusion is supported by inspection of the neutron powder diffraction data on AMnO3 [18]. An extra shift of the A site at fixed rotation must therefore indicate the presence of a further influence on the oxygen positions. In the La1−x Cax MnO3


40

system the extra influence is the ordering of the Mn3+ eg orbitals. Alonso’s data show that the JT order parameter is ∼ 0.0301(8) at T = 295 K, independent of the A ion radius [18]. The observed slope of rotation vs. site shift is identical for AMnO3 and AFeO3 within the accuracy of the measurement. The observed increase in the rotation of 0.0022, see Fig. 3.4, corresponds to an increase of 0.0017 in the La site shift, using the derived relation between rotation and A site shift. The observed La site shift is significantly larger: 0.0030.

0.13 0.12

0.10

rotation (a.u.)

zA (-) and rotation (a.u.)

0.12

0.08 0.06 0.04 0.02

rot AMnO 3 zA AMnO 3 rot AFeO 3 zA AFeO 3 1.05

1.10

Rot AMnO 3 Rot AFeO 3

0.11 0.10 0.09 0.08 0.07 0.06

1.15

1.20

ionic radius (A)

1.25

0.02

0.04

0.06

0.08

z position (-)

Figure 3.6: Left panel: The rotation and zA versus the ionic radius of AFeO3 and AMnO3 . Both parameters indicate a deviation from the cubic perovskite, and both increase with decreasing rA . Right panel: The rotation versus zA . The parameters show almost perfect correlation indicating their intimate relation. Data have been taken from References [17] (AFeO3 ) and [18] (AMnO3 ). Open and closed symbols represent AMnO3 and AFeO3 , respectively. Squares and circles represent the rotation and site shift parameter, respectively.

To summarise: the P nma symmetry allows both a rotation of the BO6 octahedra as well as a Q2 distortion of the MnO6 octahedra. It can even accommodate both deformations, cf. LaMnO3 in the orbital ordered state [12]. This behaviour is reflected by the movement of the O2 position, (x, y, z) with respect to the ideal ’cubic’ position, namely x O2 = 14 , yO2 = 0 and zO2 = 14 . To obtain the values for the rotation and the JT distortion, an accurate determination of the lattice parameters is not necessary. The bonding-antibonding energy of the A−O interaction results in a shift of the A site [16]. This A site shift is proportional to both the GdFeO3 rotation and the JT distortion.

3.4. La1−x Cax MnO3 : structure vs. x and T

3.4

41

La1−x CaxMnO3: structure vs. x and T

The structure of La1−x Cax MnO3 , x = 0.16, x = 0.19 and x = 0.25, has been determined with single crystal diffraction. Three parameters effectively describe the changes with temperature and doping. The JT order parameter, xO2 + zO2 − 12 ; the rotation parameter, xO2 − zO2 ; the La site shift.

3.4.1

Rotation

The GdFeO3 rotation is a result of the small lanthanide radius relative to the oxygen radius. The rotation also depends on the temperature. At high temperature all perovskite structures are (near) cubic, due to the thermal motion of the ions. These motions diminish with decreasing temperature, thereby decreasing the ’effective’ radius of the ions. As a result, the lanthanides prefer a narrower surrounding and this will be achieved via an increase in the tilting and buckling of the octahedra. The rotation is also sensitive to a ferromagnetic ordering. A ferromagnetic ordering is accompanied by an increase in the molar volume. For the P nma perovskites, lessening the rotation will yield an increase in molar volume. Therefore, ferromagnetic ordering will be characterised by a step in the rotation parameter, with the larger rotation in the paramagnetic phase. In Fig. 3.7 the temperature dependence of the rotation is plotted versus the temperature. The rotation-temperature curves depend strongly on the concentration. At x = 0.16, the scatter in the data is large, which makes any interpretation unreliable. The curve for x = 0.19 is shown enlarged in Fig. 3.4. A kink is observed at T ∼ 180 K, corresponding with the magnetic ordering temperature. The curve of the x = 0.25 sample shows a sharp steplike increase in the rotation at Tc . Above Tc , the rotation decreases with a similar slope as the curve for x = 0.19.

3.4.2

JT order parameter

The Mn3+ 3d4 ion is subject to a local distortion to lift the degeneracy of the eg 1 electron. The local distortions are known to order in LaMnO3 below ∼ 800 K in an antiferrodistortive fashion. In the ferromagnetic phase the JT order parameter is not necessarily exactly zero, since the O2 position is not constrained. A very small value, of the order of magnitude of the accuracy, will be considered as the absence of ordered JT distortions. In this section, a constant value independent of temperature at low temperature will be regarded as orbital ordered. The low temperature JT order parameter and the JT transition temperature strongly depend on the doping level, x. With increasing doping both variables decrease. As there are no good data between x = 0 [12] and x = 0.16 [this work] it is very hard to give detailed information about the initial decrease of the JT order parameter and transition temperature. The data for LaMnO3 show that the JT order parameter is about 0.0320(10)


42

Rotation [a.u.]

50

100

150

200

250

300

0.063

0.065

0.061

0.063

0.059

0.061

x=0.16 0.057

0.059

x=0.19 x=0.25

0.055

0.057

0.053

0.055

50

100

150 200 Temperature [K]

250

300

Figure 3.7: Rotation against temperature. The lines are guides to the eyes. The curve for x = 0.25 is shifted down by 0.001.

at room temperature and that the JT ordering reduces to 0.0060 at T = 798 K, where the orbital order is known to disappear. [12, 19] Fig. 3.8 shows that the samples with x = 0.16 and x = 0.19, enlarged in Fig. 3.4, both have a constant value for the JT order parameter at low temperature. Above T = 260 K and T = 150 K the JT order parameter decreases linearly with temperature for x = 0.16 and x = 0.19, respectively. The JT order parameter for the x = 0.25 sample is independent on temperature within the uncertainty of the experiment. The value of 0.002 is of the order of the error bars. Therefore the long range JT distortion is regarded to be zero.

3.4. La1−x Cax MnO3 : structure vs. x and T

Jahn-Teller [a.u.]

50

100

150

43 200

250

300

0.016

0.016

0.014

0.014

0.012

0.012 x=0.16

0.01

0.010

x=0.19 x=0.25

0.008

0.008

0.006

0.006

0.004

0.004

0.002

0.002

0

0.000 50

100


250

300

Figure 3.8: Jahn-Teller parameter against temperature. The lines are guides to the eyes.

3.4.3

La site shift

The La site shift is the result of the covalent interaction between the La3+ ion and the surrounding oxygen ions. The La will decrease its distance to the nearest three oxygen ions by moving along a vector [1 0 5]. The data for AFeO3 shows that the ratio xzAA = 5. As the La co-ordination is directly determined by the changes in rotation and distortion, the La site shift strongly depends on both the GdFeO3 rotation and the JT distortion. In Fig. 3.6 the A site shift in AFeO3 is plotted against the rotation. A linear dependence is observed. The refinement of the La position yielded the temperature dependence as plotted in Fig. 3.9. If we compare these curves with the curves in Fig. 3.7 and Fig. 3.8 it is obvious that the curve of rotation vs. temperature of the x = 0.25 sample is mimicked by the A site shift vs. temperature curve. Similarly, the curve of the JT order parameter vs.


44 50

100

150

200

250

300

0.030

0.030

x=0.16

0.028

0.028

A site shift [a.u.]

x=0.19 x=0.25 0.026

0.026

0.024

0.024

0.022

0.022

0.020

0.020 50

100


250

300

Figure 3.9: The temperature dependence of the La site shift. The lines are guides to the eyes.

temperature of the x = 0.16 sample looks like the A site shift vs. temperature curve, but a small change in slope is observed near Tc . This behaviour with three different gradients is most obvious in the La site shift curve of the La0.81 Ca0.19 MnO3 sample, compare with Fig. 3.5. The La site shift in LaMnO3 is 0.0490(2) at room temperature and 0.0217(3) at 798 K [12]. The latter value is comparable with the observed values near 300 K for x = 0.19 and x = 0.25.

3.5. Interpretation

3.5 3.5.1

45

Interpretation Rotation

From Fig. 3.6, we observe that LaMnO3 has a rotation parameter of 0.0810 [12]. The rotation parameter for CaMnO3 , 0.0752, is calculated from the data by Ref. [20]. These values are not in the same range as our observations. On first approximation, a decrease in tolerance factor is expected by Ca2+ doping, since the radius of Ca2+ is smaller than the radius of La3+ . However, by doping with Ca2+ , we introduce the same amount of Mn4+ . The smaller radius of Mn4+ with respect to Mn3+ , compensates the effect of Ca doping and a small increase in tolerance factor is obtained. A somewhat larger tolerance factor will yield a less rotated structure. The observed decreasing trend with increasing Ca content is in agreement with this argument. The rotation parameter is clearly sensitive to the ferromagnetic ordering in the x = 0.19 and x = 0.25 samples at Tc = 177 K and Tc = 225 K, respectively. The decrease in rotation parameter indicates a straightening of the Mn−O−Mn bond angles. If a constant volume of the MnO6 octahedra is assumed, the decrease in rotation yields an increase in total volume. An increase in molar volume, or an anomalous step in the lattice parameters is a common feature of ferromagnetic ordering, as observed for instance in pure nickel [21].

3.5.2

JT order parameter at low temperature

Below TJT the average Mn environment is distorted for samples with x < 0.20, and the eg orbitals are antiferrodistortively ordered in the d type fashion [15]. Due to the orbital ordering, the charge carriers are localised and the material behaves as an insulator. Kilian and Khaliullin discuss the effect of orbital disorder-order crossover on the metal-insulator transition. An incoherent process consists of an electron that is excited to an orbital that breaks the long range order. In case the incoherent processes are absent a large reduction of the holon band width is achieved, which can cause the metal-insulator transition. The incoherent processes are negligible if it costs too much energy for an electron to occupy an orbital, that breaks the long range orbital order. However, in their model the orbital excitation energy is not large enough to neglect incoherent processes. They argue that the reduction of the holon band width is thus too small to have an significant effect on the kinetic energy of the charge carriers, and therefore the disorder-order crossover cannot be responsible for the metal-insulator transition [24]. However the influence of the coherent JT distortions of the lattice is neglected in their model. An incoherent process not only costs the orbital excitation energy associated with the breaking of the long range interactions, but it also compromises the JT distortions. We emphasise that in La1−x Cax MnO3 the orbital ordering is associated with ordering of the large JT distortions. Thus an electron that is excited to a ”wrong” orbital, has to adjust the local oxygen co-ordination, such that the orbital and distortion are aligned. However, this frustrates the 3D Mn−O network of the perovskite structure. We have not observed any superlattice reflections. A possible charge ordering phase

46


either exists at lower temperatures, T < 90 K, or at a hole concentration closer to x = 1/8. We note that the idea of orbital polarons might lead to low temperature charge and orbital ordering. However this feature is inconsistent with P nma symmetry and is thus not observed in our study [24, 25]. In the phase diagram of La1−x Srx MnO3 , the CO phase borders the FMM phase, as observed by superlattice reflections in single crystal neutron experiments [3]. In contrast, for La1−x Cax MnO3 the CO phase is suppressed by the orbital ordered FMI phase. The value of the JT order parameter, 0.002, for the x = 0.25 sample is comparable with values calculated for AFeO3 , e.g. 0.0036 for LuFeO3 [17]. As there is no indication nor reason for a JT distortion in the orthoferrites, it is concluded that La 0.75 Ca0.25 MnO3 is not JT ordered. The JT parameter as a function of doping level can be investigated by looking at the values for T = 100 K. A continuous decrease of the JT order parameter is observed with increasing hole concentration. Furthermore, the JT ordering temperature is reduced with increased doping level. Both observations are in agreement with the observed increase in the conductivity with increasing doping level, x. The reduced JT order parameter suggests that with increased doping, not only the charge carrier density is enlarged but also the barrier is lowered, as the average distortion becomes smaller. Palstra et al. calculated the transport gap from resistivity and Seebeck measurements for La1−x Cax MnO3 [22]. They showed that the energy gap decreases with increasing doping. This is in correspondence with our observation that the magnitude of the ordered JT distortion decreases with increasing doping level.

3.5.3

Decreasing JT order parameter

Above TJT the parameter for JT ordering begins to decrease for samples with x < 0.20. We have to make a distinction between the two samples with respect to TJT /Tc . For La0.84 Ca0.16 MnO3 we find TJT > Tc , thus the O*-O’ transition takes place in the paramagnetic state, see Fig. 3.2. The conductivity in this regime is determined by polaronic hopping [23, 26]. The onset of JT orbital order will not effect the conductivity behaviour but only fix the charge carriers to the orbital order. For La0.81 Ca0.19 MnO3 compounds, TJT < Tc , the O*-O’ transition occurs in the ferromagnetic phase. Typically, the ferromagnetic phase is associated with the double exchange mechanism and therefore with metallic behaviour. Therefore, one expects equal Mn−O distances in the metallic, itinerant phase [10]. The observed absence of equal bond lengths indicates that the structure on average is not a fully itinerant phase, although the JT order parameter decreases. The low conductivity in the metallic regime agrees well with the interpretation of incomplete itineracy. However, the decrease in the JT order parameter signals the destruction of long range orbital ordering, although medium-range correlations remain. This orbital ordering melting is sufficient to render the material metallic, though the metallicity is not associated with the absence of Jahn-Teller distortions, only with the absence of long range orbital order.

3.6. Conclusion

47

The Bragg peaks signal this order because the time scale of diffraction is very small, ∼ 10−15 s. A decrease of the integrated intensity can thus be attributed to a decrease in phase coherence on length scales 100 − 1000 ˚ A. The observed decreases of the La site shift and the JT order parameter indicate that the long range orbital ordering is broken. Locally the distortions are still present, but ordered on smaller length scales, in good agreement with experiments probing the local distortions [27]. This implies that metallic behaviour and long range JT ordering can not coexist in the same phase, in contradiction to the interpretation of references [1, 5].

3.5.4

Paramagnetic state

Above Tc we observe no further change in the structure, except the continuous decrease of the La site shift due to the decreasing JT order parameter (x = 0.19) and the decreasing rotation parameter (x = 0.19 and x = 0.25). The magnetic ordering is broken, which decreases the ’bare’ electron kinetic energy and the conduction becomes semiconducting as the electron-phonon coupling is the leading term [28]. The absence of JT distortion in La0.75 Ca0.25 MnO3 is in agreement with the general perception of La1−x Cax MnO3 with 0.20 < x < 0.50 as a ferromagnetic metal. Upon crossing Tc there is no indication of a change in bond lengths, although a step in the rotation is observed. This step is associated with the volume increase of the ferromagnetic ordering. Single crystal diffraction does not allow any observations about polaron formation near Tc as this is a local phenomenon, and single crystal diffraction is sensible to long range order of electrons. The effect of the magnetic ordering on the structure is observed via the rotation. The magnetically ordered state allows metallic conduction, but for the La0.81 Ca0.19 MnO3 crystal the mobility is impeded by JT fluctuations. For the La0.84 Ca0.16 MnO3 sample the magnetic ordering is preceded by the JT orbital order, which excludes metallic behaviour. Eventually, the breaking of the magnetic ordering leads to a semiconducting state, with localised charge carriers due to the JT fluctuations. With increasing temperature the average structure will have less and less the signature of the JT ordered phase, for x < 0.20. For all samples the average structure will have a continuous decrease in the rotation.

3.6

Conclusion

The effect of introducing holes, for instance by Ca doping, in orbital ordered antiferromagnetic insulating LaMnO3 is described in the following way. When holes are introduced on Mn3+ sites that are JT distorted, the resulting Mn4+ ions still experience a JT distorted oxygen co-ordination. The reason is that the perovskite lattice consists of corner sharing oxygen octahedra. Therefore, the oxygen position is determined by the two Mn ions that are linked via this oxygen ion. Thus a Mn4+ ion co-ordinated by Mn3+ ions will still experience the JT distortion, albeit with a smaller amplitude.

48


With increasing Mn4+ concentration the total gain in lattice energy by the JT distortion of the Mn3+ ions will decrease as there are less and less Mn3+ ions. Consequently, the amplitude of the JT deformation of the lattice will also decrease with increasing Mn 4+ . The decreasing number of Mn3+ -Mn3+ interactions also reduces the average interaction strength and thereby the O*-O’ transition temperature, TJT . With increasing Mn4+ concentration, the magnetic ground state switches from antiferromagnetic to ferromagnetic as the holes create ”occupied-empty” superexchange interactions. The superexchange between these orbitals create a ferromagnetic coupling between the layers resulting in a ferromagnetic insulator at x > 0.10. As long as TJT is larger than Tc , the effect of the O*-O’ transition is reflected by a jump in the resistivity curves. Above TJT , the conductivity mechanism is polaronic hopping. Below TJT , the polarons are frozen in by the orbital ordering. The magnetic ordering has no effect on the orbital order and the conduction mechanism for x < 0.19. However, above x = 0.19 doping, the JT ordering transition is preceded by the ferromagnetic ordering. The ferromagnetic double exchange interaction allows a delocalisation of the charge carriers and metallic behaviour is observed. We have demonstrated that the ferromagnetic metallic phase is obtained, in a limited temperature range, by the suppression of the long range Jahn-Teller ordering. This contrasts with the common opinion that metallicity occurs if the charge carrier density exceeds a critical concentration. Furthermore, we have shown that we can study the Jahn-Teller ordering by observing the La site shift. The JT ordering is no longer long range above TJT , but on shorter length scales the JT distortions do not disappear. With increasing temperature there is a simultaneous reduction of the JT order parameter and the La site shift. The metallic state of La1−x Cax MnO3 is bounded by ferromagnetic ordering and the absence of orbital ordering.

references [1] H. Kawano, R. Kajimoto, M. Kubota and H. Yoshizawa, Phys. Rev. B 53, R14709 (1996). [2] A. P. Ramirez, J. Phys.: Condens. Matter 9, 8171 (1997). [3] Y. Yamada et al., Phys. Rev. Lett. 77, 904 (1996). [4] D. N. Argyriou et al., Phys. Rev. Lett. 76, 3826 (1996). [5] Y. Endoh et al., Phys. Rev. Lett. 82, 4328 (1999). [6] B. Dabrowski et al., Phys. Rev. B 60, 7006 (1999). [7] A. Urushibara et al., Phys. Rev. B 51, 14103 (1995). [8] B. B. Van Aken, A. Meetsma and T. T. M. Palstra, Phys. Rev. B submitted 14 March 2001 (2001), cond-mat/0103628.

3.6. Conclusion

49

[9] M. Uehara, B. Kim and S.-W. Cheong, (2000), personal communication. [10] C. Booth et al., Phys. Rev. Lett. 80, 853 (1998). [11] A. Vegas, M. Vallet-Regí, J. González-Calbet and M. Alario-Franco, Acta Crystallogr., Sect. B: Struct. Sci. 42, 167 (1986). [12] J. Rodríguez-Carvajal et al., Phys. Rev. B 57, R3189 (1998). [13] J. B. Goodenough, Magnetism and the Chemical Bond (Wiley, New York, 1963). [14] J. B. Goodenough, Prog. Solid State Chem. 5, 145 (1971). [15] T. Mizokawa, D. I. Khomskii and G. A. Sawatzky, Phys. Rev. B 60, 7309 (1999). [16] G. A. de Wijs, P. K. de Boer, R. A. de Groot and G. Kresse, Phys. Rev. B 59, 2684 (1999). [17] M. Marezio, J. Remeika and P. Dernier, Acta Crystallogr., Sect. B: Struct. Sci. 26, 2008 (1970). [18] J. Alonso, M. Martínez-Lope, M. Casais and M. Fernández-Díaz, Inorg. Chem. 39, 917 (2000). [19] Y. Murakami et al., Phys. Rev. Lett. 81, 582 (1998). [20] K. R. Poeppelmeier et al., J. Solid State Chem. 45, 71 (1982). [21] C. Williams, Phys. Rev. 46, 1011 (1934). [22] T. T. M. Palstra et al., Phys. Rev. B 56, 5104 (1997). [23] A. J. Millis, P. B. Littlewood and B. I. Shraiman, Phys. Rev. Lett. 74, 5144 (1995). [24] R. Kilian and G. Khaliullin, Phys. Rev. B 60, 13458 (1999). [25] T. Mizokawa, D. I. Khomskii and G. A. Sawatzky, Phys. Rev. Lett 63, 024403 (2000). [26] A. Lanzara et al., Phys. Rev. Lett. 81, 878 (1998). [27] S. Billinge et al., Phys. Rev. Lett. 77, 715 (1996). [28] A. J. Millis, Nature 392, 147 (1998).

50


Chapter 4 Structural view of hexagonal non-perovskite AMnO3 In the previous chapters, several aspects of the orthomanganites were discussed. They showed the importance of a thorough structural knowledge. Without such knowledge, a deep understanding of the physics behind the phenomena is not possible. Structure is also a major topic in the second half of the thesis. It is well known that manganites AMnO 3 , with A a lanthanide with radius smaller than that of holmium, have a hexagonal crystal structure as the thermodynamically stable state. This hexagonal crystal structure has no similarity with the typical perovskite structure, whatsoever. The next chapter, Chapter 5, discusses the structural ground state of samples near the critical tolerance factor as a function of the variance of the ionic radii and external pressure. Y1−x Gdx MnO3 samples were synthesised that showed anomalous coexistence of both phases. Surprisingly high temperature annealing does not destroy the coexistence, in contrast with the reported experiments on YMnO3 samples grown via soft chemistry routes. Chapter 6 covers experiments to find colossal magnetoresistance behaviour with T c ’s higher than 400 K. We hoped that tetravalent dopants would induce a larger spin state and therefore a higher transition temperature. Electronic band structure calculations showed that above ∼ 4.1 electrons these hexagonal manganites are no longer in a completely highspin state. This is witnessed by a decrease in magnetic moment with increasing number of electrons per manganese site. As mentioned before, the hexagonal-orthorhombic transition occurs at a critical tolerance factor. However, in related systems, samples with even smaller tolerance factors are well known to have the orthorhombic ground state. This paradox is extensively covered in Chapter 7. But first, in this chapter, the basics and details of the structure of hexagonal manganites are reported. Single crystals of AMnO3 , with A = Y, Er, Yb and Lu have been grown. We studied the crystal structure of these crystals by single crystal x-ray diffraction. Our results show some distinct differences with previous reports on LuMnO3 and YbMnO3 . YMnO3 attracts a lot of attention due to its ferroelectricity. The precise structure determination 51

Chapter 4. Structural view of hexagonal non-perovskite AMnO3

52

shows that the ferroelectric behaviour originates from the dipole moments of the A coordination and not, as is the common opinion, of the Mn co-ordination.

4.1

Introduction

In the search for new composition-properties relations ABO3 compounds have attracted a lot of attention. The perovskite materials, ABO3 , have been researched extensively because this structure forms the basis for interesting physical properties such as high T c superconductivity [1] and colossal magnetoresistance [2]. The hexagonal1) AMnO3 compounds [3] have a basically different structure than most ABO3 compounds, that are distorted perovskites. A schematic view is given in Fig. 4.1. Non-perovskite AMnO3 , with A = Y, Ho,...,Lu, attracted interest, initially due to their ferroelectric properties [4] and lately due to the possibility of coexistence of combined ferroelectric and ferromagnetic behaviour [5]. Nonetheless, all these properties arise due to the strong correlation of the 3d electrons with the O 2p orbitals. However, it is argued in Chapter 7 that the ferroelectricity is mostly due to the anomalous oxygen surrounding of the lanthanide position and the covalent interaction of the A 5d0 ion with the oxygen ions. Already in the 1960’s, structure determinations of these and related compounds, including atomic positions, have been reported in literature including YMnO3 [3], YAlO3 [6] and InGaO3 [7]. Isobe et al. reported the structure of YbMnO3 [8]. Their report gives no additional information on the structure and does not mention the ferroelectric behaviour at all. Mu˜ noz et al. used neutron powder diffraction to study the magnetic structure of YMnO3 and ScMnO3 [9]. Neutron powder diffraction is intrinsically insensitive to twinning and structural domains. Furthermore L Ã ukaszewicz and KarutKalicinska reported the high temperature phase as P 63 /mmc [10]. Remarkably the Figure 4.1: Sketch view of the crystal strucstructural transition is some 300 K higher ture of AMnO3 . The A cations are shown than the ferroelectric ordering temperature. as circles, the MnO5 are represented by trigNote that we use OX,ap and OX,eq to denote onal bipyramids. apical and equatorial positions, respectively, with respect to the cation X. We observe that the crystal structure at ambient temperature differs in several aspects from the previous reports, where the local electric dipole moments 1)

some perovskite ABO3 compounds, like Sr-doped LaMnO3 and LaCoO3 , can have a rhombohedralhexagonal structure. However, the hexagonal ABO3 we report here, have a profoundly different structure than the perovskite based ABO3 compounds.

4.2. Single crystal diffraction

53

were ascribed to the asymmetric Mn environment. We show that the local electric dipole moment is caused by the asymmetric co-ordination of the A ion. This supports the general argument that d0 -ness is the driving factor for ferroelectric behaviour, as extensively discussed by Hill [5] and others.

4.2

Single crystal diffraction

Single crystals of AMnO3 , A=Y, Yb, Er and Lu, were obtained using a flux method by weighing appropriate amounts of A2 O3 and MnO2 with Bi2 O3 in a 1:12 ratio [3]. The powders were thoroughly mixed and heated for 48 h at 1523 K in a Pt crucible. The separation of the crystals from the flux was performed by two methods [4]: 1. by increasing the temperature to 1723 K and evaporating the Bi2 O3 flux 2. by slowly cooling (50 K h−1 ) through the solidification temperature of the flux. The single crystals then segregated on top of the flux. Both methods were used and the results are equal within the precision of the structure determination. Only crystals prepared by slow cooling are reported here. Reflections have been recorded on two single crystal x-ray diffractometers. ErMnO 3 is measured on the Bruker SMART APEX diffractometer, using area detector scans with a CCD camera. The other crystals are measured on the Enraf-Nonius CAD-4F diffractometer, using ω/2θ scans. In Table 4.1 the lattice parameters of the studied compounds are shown. Y Er Yb Lu

a (˚ A) 6.1387 6.1121 6.0584 6.0380

˚3 ) c (˚ A) Vmol (A 11.4071 372.27 11.4200 369.47 11.3561 360.97 11.3610 358.70

Table 4.1: Lattice parameters and unit cell volume for AMnO3 . Yakel et al. determined the space group to be non-centrosymmetric P 63 cm [3]. In a non-centrosymmetric space group, the Bragg reflections h k l 2) and h k l are not symmetry equivalent. Since we have a hexagonal crystal, reflections h k l, k -h-k l and -h-k h l are equivalent2) . Therefore it is necessary to include Bragg reflections h k l and h k l to cover the whole asymmetric region of the reciprocal space [11, 12]. On the CAD4 the covered range is 0 < h < hmax , −kmax < k < 0 and −lmax < l < lmax . The APEX experiment included reflections from a whole sphere of reciprocal space. Although Yakel et al. recognised the importance and constraints of the non-centrosymmetry, their experimental set-up did not allow them to access negative l’s. Our rerefinement of LuMnO 3 , 2)

h, k and l can have any integer value.


54

including negative l’s is therefore better on principal grounds. The same line of arguing is applicable to the determination of the structure of YbMnO3 by Isobe et al. [8]. Again, the authors measured only positive values for l, thereby missing half of the asymmetric region [12]. The first sample, YMnO3 , was solved using the data reported by Yakel et al.. Later experiments used the values that we obtained for YMnO3 as initial solution. The final difference Fourier map showed a large peak, 3.1 e ˚ A−3 , at 0.23 ˚ A from the Y1 position and −3 ˚ ˚ a hole, 3.5 e A , at 0.01 A from the Y1 position. No other significant peaks were observed. The refinements on the other samples also showed these two peaks in the residual electron density. The Flack parameter of an initial refinement attempt on YMnO3 indiatom Y Er Yb Lu cated that these crystals were twinned. A(1)-z 0.2743 0.2746 0.2753 0.2746 Yakel et al. speculated on the exisA(2)-z 0.2335 0.2320 0.2326 0.2311 tence of domains with opposite po0.3352 0.3396 0.3333 0.3355 Mn-x lar directions, but could give no supO1-x 0.3083 0.3113 0.3030 0.3070 porting evidence for the existence of O2-x 0.3587 0.3593 0.3610 0.3614 those domains. The refinement on O2-z -0.1628 -0.1620 -0.1639 -0.1630 our model and data, without an inO3-z -0.0218 -0.0225 -0.0249 -0.0277 version twin, yielded a Flack paramO4-z 0.0186 0.0186 0.0211 0.0198 eter x = 0.47(3) and for the inverse structure x = 0.53(3). The R val- Table 4.2: Values for the refinable positions in ues are wR2 = 0.15, R = 0.047 and AMnO3 at room temperature. The z co-ordinate wR2 = 0.14, R = 0.047 respectively. of Mn is fixed at zero. An inversion twin was added to the structure model. The twin fraction refined to 47(2)%, with quality factors wR 2 = 0.113 and R = 0.0370. We expect a 50-50 distribution because this yields no net electrical polarisation [13]. We fixed the twin fraction at 50(-)%, which had no significant influence on any other parameter, with respect to the refinement with variable twin fraction. The results of the refinements are given in Table 4.2. Final R factors are wR 2 = 0.114 and R = 0.0372.3)

4.3

Crystal structure

In this section the hexagonal crystal structure is explained in terms of polyhedra and close packed layers. We first ignore the non-centrosymmetry. The structure can be constructed in two ways. The general physics approach is to start with the transition metal and its oxygen surrounding. The lanthanides are regarded ’just’ as space fillers. The other way to get a feeling for the structure is to think in close packed layers. 3)

More details of the data collection and refinement are given in the Appendices D, E, F and G and references [14, 15] and can be obtained via A. Meetsma: [email protected]

4.3. Crystal structure

55

First the physics approach. The Mn ions are surrounded by a trigonal bipyramid of oxygen ions. The bipyramids are linked by corner sharing the equatorial oxygen ions. Between these slabs of bipyramids, there is a layer of A ions. In Fig. 4.1 the layered nature is shown. The general atomic co-ordinates are given in table 4.3. In Fig. 4.2 two MnO layers are sketched. The top layer is only drawn in the right half x y z atom 1 of the figure. The lanthanide cations, A1 and A1 0 0 4 −δ 2 1 1 A2, are located exactly between two OMn,eq A2 +δ 3 3 4 1 ions, O3 and O4, respectively, of consecutive ∼0 Mn ∼3 0 1 1 layers. In the left part of Fig. 4.2, we observe +δ 0 ∼6 O1 3 1 1 that half of the OMn,eq triangles form trigo− δ 0 ∼ −6 O2 3 nal bipyramids around Mn ions. In the next 0 0 −δ O3 2 1 layer, the other half is filled. The corner sharδ O4 3 3 ing of the trigonal bipyramids is highlighted in Table 4.3: General atomic positions of the Fig. 4.3, which shows a cross-section through ambient temperature phase of hexagonal the Mn ions, along the ab plane. Each OMn,eq AMnO3 . δ indicates a shift of the order is shared by three bipyramids. These oxygen of 0.02 lattice parameter. ions make up a triangular lattice, as is indicated by the thin black lines in the figure.

Figure 4.2: Sketch view of hexagonal AMnO3 along the c axis, showing the complementary occupation of half of the O5 bipyramids in each MnO layer.

Figure 4.3: Cross-section at z ∼ 21 . O3, O4 and Mn are drawn as gray, open and closed circles. The unit cell, Mn−O3 and Mn−O4 bonds are shown as thick, dotted and dashed lines.

The second approach is via close packed layers. The standard notation used for fcc, ABCABC, or hcp, ABABAB is used here for the three ’positions’ of a close packed layer on a triangular lattice. Note that the in-plane bond lengths between the O ions and between the A ions is too large to truly regard h-AMnO3 as a close packed system. The h-AMnO3 structure consists of eightfold co-ordinated A ions in bicapped antiprisms. The stacking of the AO6 antiprism is expressed as ABC. In Fig. 4.2 the ABC stacking can be seen by going from the OMn,ap of the bottom layer, via the A ion, to the OMn,ap of the top layer, the

56


corresponding letters are plotted in Fig. 4.3 . The ’bicapping’ OA,ap are again located on B sites, both above C and below A. In this notation one A ion environment makes up a BABCB stack, or in chemical elements: OOAOO. The top OA,ap and the bottom OA,ap of the next layer are one and the same. Therefore, each B is also the end-member of the next stack, however with the opposite order i.e. BCBAB. This yields BcbaBabcBcbaBabcBcba, in elements: OoaoOoaoOoaoOoaoOoao.

4.4

From centrosymmetry to non-centrosymmetry

All h-AMnO3 compounds are reported to be ferroelectric with transition temperatures between 800 and 1000 K. L Ã ukaszewicz measured the centrosymmetric structure of YMnO3 at elevated temperatures. The main difference in symmetry between the high and low temperature structure is that in the high temperature (HT) phase all atoms are constrained to planes, parallel to the ab plane. Below the transition temperature the structure loses the mirror planes parallel to the ab plane and all inequivalent atoms get a refinable z position. The deviations from these planes are sketched in Fig. 4.4.

Figure 4.4: Sketch view of the surrounding oxygen polyhedra of the A ion. The left part shows the ferroelectric low temperature structure, the right part the centrosymmetric high temperature structure. The anomalous long bond in the low temperature structure is shown as a thin line. Yakel et al. refined the structure of h-LuMnO3 at room temperature. Although the authors are aware of the ferroelectric properties of these materials [4], the origin of the ferroelectric state or the presence of local dipole moments is not discussed. It was already argued that their measurement, and Isobe’s for that matter, are principally incorrect. By missing half of the reflections an incomplete data set is obtained. Their structure solution

4.4. From centrosymmetry to non-centrosymmetry

57

is nonetheless basically correct. However, the refined atomic positions are slightly wrong. These positions yield Mn−Oap bond lengths that are distinctly different, see Table 4.4. Later, it was assumed by the ferroelectrics community, for instance Cohen [16] and Hill [5], that the dipole moment is related to the Mn co-ordination. The anomalous A co-ordination was overlooked. Due to this misinterpretation, or misunderstanding of the structure, the ”d0 ”-ness condition for ferroelectric behaviour was wrongfully invalidated. Compound Reference YMnO3 Van Aken et al. [14] ErMnO3 Van Aken et al. [15] YbMnO3 Van Aken et al. LuMnO3 Van Aken et al. LuMnO3 Yakel et al. [3] YbMnO3 Isobe et al. [8] HT-YMnO3 L Ã ukaszewiczet al. [10]

Mn−O1 Mn−O2 Mn−O3 Mn−O4 1.863 1.862 2.073 2.052 1.854 1.886 2.092 2.030 1.867 1.868 2.039 2.034 1.882 1.859 2.050 2.019 1.93 1.84 1.98 2.06 1.866 1.924 1.992 2.040 1.879 1.879 2.084 2.084

Table 4.4: Manganese-oxygen bond lengths, determined by single crystal x-ray diffraction at room temperature, except the HT-YMnO3 entry which is taken at 1273 K. Note that for HT-YMnO3 , Mn−O1 and Mn−O2 as well as Mn−O3 and Mn−O4 are identical. The deviations from the mirror planes yield different bond lengths for A−O A,ap . One bond obtains a regular value ∼ 2.4 ˚ A while the other becomes about 1 ˚ A larger. The asymmetric A environment is the main reason for the ferroelectric behaviour. As we have two inequivalent lanthanide positions in P 63 cm, we have two inequivalent, although similar, dipole moments as a result of the movement of the OA,ap ions. This movement can also be expressed as a tilting of the MnO5 bipyramids. Two out of three OMn,eq positions in the triangular base of the bipyramid are constrained by symmetry, note OA,ap = OMn,eq . As two equivalent O ions move down, the third moves up. This yields, for the two layers in the unit cell, four upwards pointing local dipole moments, whereas the other two point downwards. YMnO3 ErMnO3 YbMnO3 LuMnO3 LuMnO3 YbMnO3 YMnO3

[14] [15]

[3] [8] [10]

A1-O1 A1-O2 A1-O3 2.281 2.316 2.326 2.312 2.281 2.320 2.231 2.294 2.269 2.234 2.294 2.244 2.18 2.35 2.42 2.255 2.263 2.354 2.298 2.298 2.298

A1-O3 A2-O1 A2-O2 A2-O4 3.378 2.275 2.300 2.451 3.390 2.306 2.244 2.437 3.409 2.257 2.270 2.401 3.436 2.227 2.277 2.401 3.26 2.19 2.31 2.36 3.425 2.267 2.273 2.536 2.848 2.298 2.298 2.298

A2-O4 3.253 3.273 3.277 3.280 3.32 3.243 2.848

Table 4.5: Lanthanide-oxygen bond lengths determined with single crystal x-ray diffraction at room temperature. The O1 and O2 bond lengths are all threefold present. In the HT structure both O1 and O2 and O3 and O4 are identical. The references are identical with those in Table 4.4.

58

4.5


Detailed structure analysis

We regarded the structure as layers of corner linked MnO5 trigonal bipyramids with the A ions between the layers (Section 4.3). The ferroelectric properties were discussed using AO7 polyhedra (Section 4.4). In this section, the link between the two approaches will be made, revealing that the trigonal bipyramids are a direct consequence of the large O−O bond lengths within the close packed layers. It is shown that the anomalous seven- or eightfold environment is a result of the apical Mn−O bond length.

*

;

*

;

A

C

B

B

C

A

B

B

C

A

Figure 4.5: Sketch view of the local environment, showing AO7 , left side, and MnO5 , right side. The arrow indicates the distance between two oxygen planes. The dashed line indicates the Mn−OM n,ap distance. The two possible stacks are indicated by the letters in the columns on the right. Conventionally, the holes between two close packed layers are tetrahedral sites, cf. the well-known spinel structure. In our loosely packed layers, two tetrahedra from adjacent layers join to form a trigonal bipyramidal site. In AMnO3 this occurs in the ooo stack of the oaoOoao sequence. Half of the bipyramidal holes are occupied by Mn. In Fig. 4.5 two neighbouring polyhedra are sketched, where the shared edge is shown. On the right side the letters indicating the close packed layers are given. We observe that the distance between the AB/CB, left/right column, and BC/BA is roughly one-twelfth of the unit cell height. The CB/AB and BC/BA distances are much larger. The OMn,ap ions are also the oxygen ions that make up the antiprisms. The Mn−OMn,ap bond length is thus identical to the distance between the antiprism oxygen layer and the OA,ap layer. This distance is indicated by the arrow in the figure. The Mn−OMn,ap bond length, dotted line, is constrained. Therefore, the steric hindrance of the Mn puts a lower limit to the CB/AB layer separation and increases the A−Oap bond length. Thus, the eightfold co-ordination is not uniform. The two A−OA,ap have slightly larger bond lengths, i.e. ∼ 2.7˚ A.

4.6. Conclusions

4.6

59

Conclusions

We conclude that hexagonal AMnO3 consists of MnO5 trigonal bipyramids, stacked in layers, alternated with layers of A ions. This yields a capped trigonal antiprism as coordination polyhedra for the A ion. In the ferroelectric phase, the capping is effectively removed on one side. This asymmetric co-ordination of the A ion is the origin of the local electric dipole moment.

references [1] J. G. Bednorz and K. A. M¨ uller, Z. Phys. B: Condens. Matter 64, 189 (1986). [2] S. Jin et al., Science 264, 413 (1994). [3] H. L. Yakel, W. Koehler, E. F. Bertaut and E. F. Forrat, Acta Crystallogr. 16, 957 (1963). [4] E. F. Bertaut, E. F. Forrat and P. Fang, C. R. Acad. Sci. 256, 1958 (1963). [5] N. A. Hill, J. Phys. Chem. B 104, 6694 (2000). [6] E. F. Bertaut and J. Mareschal, C. R. Acad. Sci. 257, 867 (1963). [7] R. D. Shannon and C. T. Prewitt, J. Inorg. Nucl. Chem. 30, 1389 (1968). [8] M. Isobe, N. Kimizuka, M. Nakamura and T. Mohri, Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 47, 423 (1991). [9] A. Mu˜ noz et al., Phys. Rev. B 62, 9498 (2000). [10] K. L Ã ukaszewicz and J. Karut-Kalicinska, Ferroelectrics 7, 81 (1974). [11] H. D. Flack and G. Bernardinelli, Acta Crystallogr., Sect. A: Found. Crystallogr. 55, 908 (1999). [12] H. D. Flack, 2001, private communication. [13] C. Rao and J. Gopalakrishnan, New directions in solid state chemistry, 2nd ed. (Cambridge University Press, 1997), page 385. [14] B. B. Van Aken, A. Meetsma and T. T. M. Palstra, Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 57, 230 (2001). [15] B. B. Van Aken, A. Meetsma and T. T. M. Palstra, Acta Crystallogr., Sect. E: Struct. Rep. Online 57, i38 (2001). [16] R. E. Cohen, J. Phys. Chem. Solids 61, 139 (2000).

60


Chapter 5 The hexagonal to orthorhombic structural phase transition AMnO3 compounds with A = a lanthanide with a larger ionic radius than Ho3+ have the orthorhombic structural ground state. If A = Y or a lanthanide with a smaller radius than Dy3+ , a hexagonal structure is found. In this chapter, the focus is on the boundary between the two structural states. The relative stability of the two phases depends among others on synthesis and annealing temperature, average ionic radius of the A ion and the pressure. One part of the boundary region is the ionic radius gap between rY 3+ and rDy3+ . A crossing of the boundary is observed during high pressure synthesis of YMnO3 . The influence of high temperature annealing, which prefers the hexagonal phase, and synthesis route, which enables low temperature synthesis of the orthorhombic phase, is already known. Here, another parameter that partially controls the transition is introduced, the disorder or the variance of the ionic radii on the A site. The variance σ 2 is given by, 2

σ =

n X 1

xi (ri − hrA i)2

(5.1)

It is shown that the transition in AMnO3 from the orthorhombic perovskite phase to the hexagonal phase is promoted by inducing disorder on the A site. The ionic radius gap between the orthorhombic (o-DyMnO3 ) and the hexagonal (h-YMnO3 ) phases is widened for disordered, mixed yttrium-gadolinium manganite samples. At the cost of the orthorhombic phase a two phase region emerges. The phase separation exhibits very unusual thermodynamical behaviour. We also show that high pressure synthesis favours the orthorhombic phase. YMnO3 is formed in the orthorhombic phase at 15 kbar. After a short introduction to both structures, including the effect of tolerance factor, the possibilities to create the unstable orthorhombic state are reviewed. Then the effect of cation disorder on the stable state of Y1−x Gdx MnO3 is discussed. The last part of this chapter is dedicated to the experiments on high pressure synthesis of o-YMnO3 . 61

62

5.1

Chapter 5. The hexagonal to orthorhombic structural phase transition

Introduction

In the search for new composition-properties relations ABO3 compounds have attracted a lot of attention. The perovskite materials, ABO3 , have been researched extensively because this structure forms the basis for interesting physical properties such as high T c superconductivity [1] and colossal magnetoresistance [2–4]. Non-perovskite AMnO 3 , with A = Y, Ho,...,Lu, attracted renewed interest, due to their ferroelectric properties [5]. These hexagonal AMnO3 [6, 7] have a basically different structure than most ABO3 compounds, that are distorted perovskites. Although each crystal structure is very stable, only slight variations in the constituents or synthesising conditions are sufficient to transform the structure, with large changes in co-ordination, density and electronic properties. The transition from the orthorhombic perovskite (o) to the hexagonal (h) phase is investigated by changing the average ionic radius of the A site and by high pressure synthesis. The effect of the ionic radius on the transition is studied by partially replacing Y by Gd ions in YMnO3 . The resulting phase diagram leads us to discuss the effect of disorder, in terms of the ionic radius variance, on the stability of the hexagonal and orthorhombic phases. The basic building block of the perovskite is an oxygen octahedron with a transition metal, B, in its centre, see Fig. 2.1. The A ions, usually lanthanides or alkaline earth metal ions, occupy the holes between the octahedra, that form a 3D corner shared network. In this picture B is sixfold and A is twelvefold co-ordinated. Most perovskites have a distorted structure, derived from this building block. The distortions have various origins, including a ferroelectric transition for B a d0 transition metal ion like Ti4+ [8]. The most common distortion however originates from the relatively small radius of the A ions compared with the holes between the octahedra. This results in a cooperative rotation [9] of the octahedra known as the GdFeO3 rotation [10, 11]. While the structure is interesting in its own right, it also has large effects on the physical properties. It is well documented that the physical properties strongly depend on the magnitude of the structural distortions. An overview for the manganites is given in Ref.’s [12, 13]. The magnitude of the GdFeO3 rotation strongly depends on the tolerance factor t, see Eq. (2.1). The tolerance factor gives the relation between the radii of ions A, B and O in a ideal cubic perovskite. For t = 1 the size of the lanthanide is exactly right to compose the cubic perovskite system. For Mn3+ , rM n3+ = 0.645 ˚ A and rO2− = 1.42 ˚ A ˚ this yields a ionic radius rA3+ = 1.50 A, where the largest lanthanide, La, has a radius of 1.215 ˚ A [14]. The corresponding tolerance factor, t = 0.90, indicates a large distortion for LaMnO3 . With increasing atomic number, the lanthanide radius decreases and thereby the distortion increases. For the manganites, the tolerance factor is conventionally regarded as the factor signalling the boundary between the hexagonal and orthorhombic structures. The orthorhombic perovskite phase is stable for t > 0.855, corresponding to rA > rDy [15]. For t < 0.855, rA 6 rHo , the hexagonal phase prevails [6]. Yttrium, although not in the lanthanide series, behaves chemically identical and its radius falls between dysprosium and holmium. An overview on the ionic radii and tolerance factors of some relevant compounds is given in Table 5.1.

5.1. Introduction

63 A3+ ion La Gd Dy Y Lu

ionic radius tolerance factor (˚ A) 1.215 0.902 1.109 0.866 1.083 0.857 1.075 0.854 1.032 0.840

Table 5.1: Ionic radii and tolerance factors for relevant AMnO3 compounds. The high temperature phase of the hexagonal AMnO3 consists of eightfold co-ordinated A ions in bicapped antiprisms. Trigonal bipyramidal holes are formed between two layers of face-sharing antiprisms by the edges of the capping oxygen ions with the antiprisms. The capping oxygen ions of two adjacent layers are located on the same ab plane. Half of the bipyramidal holes are occupied by Mn. The apical oxygen ions of the MnO5 bipyramid are also the oxygen ions that make up the antiprism. The two polyhedra are sketched in Fig. 5.1, where the shared edge is shown. The Mn−Oap distance is thus equal to the distance between the antiprism oxygen layer and the capping oxygen layer. The steric hindrance of the Mn restricts this layer separation and therefore increases the A−O ap bond length. Thus, the eightfold co-ordination is not uniform. The two apical oxygen ions have slightly larger bond lengths. Furthermore, the structure is unstable against a ferroelectric distortion at lower temperatures. The apical oxygen ions move in such a way that one bond becomes ’normally’ short, while the other becomes about 1 ˚ A larger.

Figure 5.1: Sketch view of the local environment, showing AO7 , left side, and MnO5 , right side. Atoms marked with ”*” and with ”x” are identical, the thick line indicates the shared edge. Although the hexagonal phase of YMnO3 at ambient conditions is the thermodynamically stable phase, there are several ways to obtain orthorhombic YMnO3 . Already in

64

Chapter 5. The hexagonal to orthorhombic structural phase transition A3+ ion Pressure Temperature (kbar) (◦ C) Y 34 650 Y 45 900 35 1000 Y Ho 45 950 35 1000 Ho Er 42 675 42 780 Tm Yb 42 700 40 1000 Yb Lu 42 750

Reference Waintal et al. [19] Waintal et al. [19] Wood et al. [20] Waintal et al. [19, 21] Wood et al. [20] Waintal et al. [19, 21] Waintal et al. [19, 21] Waintal et al. [19, 21] Wood et al. [20] Waintal et al. [19, 21]

Table 5.2: A literature overview of high pressure experiment. the 1960’s Yakel et al. reported ”In the case of YMnO3 two distinct and separable crystal habits were observed, one plate-like, (our hexagonal crystals are platelets) the other more prismatic.” [6]. Using thin film growth, an appropriate substrate will force the coherent growth of the orthorhombic phase [16]. Another way to obtain o-YMnO3 is to reduce the reaction temperature. The thermally promoted diffusion of the cations is replaced by dissolving the metal oxides, for instance in citric acid. A sol-gel pyrolysis of the organic precursors yields a ”green” product, which can be sintered at relatively low temperatures. Depending on the sintering temperature or the oxygen pressure, the orthorhombic phase is obtained in larger or smaller fractions. A high temperature anneal of either the ”green” product or the o-YMnO3 always returns the hexagonal phase [17]. Waintal et al. showed that high pressure synthesis can produce the distorted perovskite phase for HoMnO3 [18]. A more elaborate study by Waintal and Chenavas gave critical transition temperatures and pressures for the whole lanthanide series. Synthesis of YMnO 3 will yield the orthorhombic phase at 34 kbar and 923 K [19]. High pressure synthesis favours the orthorhombic phase, because it has a higher density. In Table 5.2 an overview of high pressure experiments that yielded the orthorhombic phase is given.

5.2

Experimental

Polycrystalline ceramic samples of AMnO3 , where A is a mixture of Y and Gd, have been synthesised using regular solid state synthesis at ambient pressure. Starting materials were Y2 O3 , Gd2 O3 and MnO2 . Stoichiometric amounts corresponding to formulae which range from pure YMnO3 to pure GdMnO3 were weighted and wet-mixed using acetone as liquid medium. The pressed pellets were sintered for 24 hours at 1250◦ C and for 24 hours at 1400◦ C. High pressure experiments were carried out both on the mixture of oxides and on as-

5.3. High pressure synthesis

65

prepared samples. X-ray powder diffraction patterns were identical for both methods. The high pressure high temperature piston cylinder apparatus is a Depth of the Earth Quickpress 3.0, with an experimental range up to 25 kbar and 2100◦ C [22]. The lower pressure limit is ∼ 1 to 2 kbar. The sample environment is a complex set-up, including a graphite resistance furnace and the pressure medium. Care has to be taken to prevent contamination from the graphite resistance furnace or any of the other materials, e.g. Al2 O3 or NaCl, in the sample assembly. Therefore, a small amount of powder ∼ 0.5 g was encapsulated in a Pt capsule. The capsule consisted of a tube (diameter 4 mm and height 6 mm) and two pre-shaped lids, which were welded together using a small welding apparatus. Recovery of the pellet from the sample assembly is improved by the Pt container [23]. X-ray diffraction patterns were recorded using a Bruker-AXS D8 powder diffractometer, with primary and secondary monochromator, using Cu Kα radiation. Patterns were analysed for phase determination using the evaluation software EVA [24], the Powder Diffraction File [25] and the Inorganic Crystal Structure Database [26]. Patterns of noncontaminated samples, containing only the hexagonal and orthorhombic phases, were used in the Rietveld refinement using TOPAS R [27]. Rietveld refinements included lattice parameters, zero point correction and the ratio between the two phases. Atomic positions were assumed to be constant using the positions determined by single crystal x-ray diffraction on YMnO3 [7]. The ratio Y:Gd was fixed at the nominal composition.

5.3

High pressure synthesis

We applied high pressure and high temperature to convert or synthesise some of the conventionally hexagonal samples in the orthorhombic state. Pressure generally stabilises the most dense phase. The density of the orthorhombic and hexagonal phase are roughly 5.6×103 and 5.1×103 kg m−3 , respectively. Therefore, pressure favours the orthorhombic structure. First, we consider samples with σ 2 = 0. YMnO3 is still hexagonal at 5 kbar, but the orthorhombic phase is found using a pressure of 15 kbar. The pressure-ionic radius phase diagram is shown in Fig. 5.2. The necessary pressure for the h-o transition, less than 15 kbar, is much less than the 34 kbar, reported previously in the literature [19]. The h-o transition phase line has been sketched in Fig. 5.2 by using midpoints. Extrapolating the pressure dependence of the h-o transition yields a critical pressure of . 27 kbar for HoMnO3 . The error bar on this value, ∼ 10 kbar, is large because of the sparse data points. We also carried out high pressure experiments on the Y1−x Gdx MnO3 compounds. The necessary pressure to induce the orthorhombic phase from the phase mixture decreased with increasing hrA i. The x = 0.06 sample, which is hexagonal at ambient pressure, yields the orthorhombic phase after high pressure synthesis at 10 kbar. The x = 0.19 and x = 0.25 samples showed the two phases after standard solid synthesis. These samples turned orthorhombic after high pressure synthesis at 10 kbar and 5 kbar respectively. The x = 0.5 sample is already orthorhombic at ambient pressure synthesis.


pressure (kbar)

20

tolerance factor t (-) 0.854 0.856 0.858 0.860 0.862

15 10 5

orthorhombic hexagonal mixed calculated limit

orthorhombic hexagonal

66

mixed 0 1.07 1.075 1.08 1.085 1.09 1.095 1.10 average radius (Å) Figure 5.2: Pressure versus average radius phase diagram. Undoped samples are shown with open symbols, doped Y1−x Gdx MnO3 samples with closed symbols. We never observed mixed samples after high pressure synthesis. Schematic phase boundaries are drawn.

5.4

Y1−x GdxMnO3; the influence of disorder

In Fig. 5.3, we present a phase diagram of Y1−x Gdx MnO3 as a function of hrA i against the variance σ 2 of the samples given in Table 5.3. The phase diagram can be divided in three regions. Low hrA i compounds, hrA i < 1.078 ˚ A, are hexagonal. Large hrA i and small σ 2 compounds are orthorhombic. The intermediate region shows both phases. Data for HoMnO3 and DyMnO3 have been taken from Ref. [6]. x 0 0.06 0.19 0.25 0.31 0.38 0.5 1

hrA i (˚ A) 1.075 1.077 1.081 1.084 1.086 1.088 1.092 1.109

t 0.854 0.855 0.857 0.857 0.858 0.859 0.860 0.866

σ 2 (10−6 ˚ A2 ) 0 68 176 217 248 271 289 0

Table 5.3: Ionic radii, tolerance factors and variance of the studied Y 1−x Gdx MnO3 samples. By changing the value of x we substitute Y by Gd, whereby hrA i increases linearly. The tolerance factor of orthorhombic DyMnO3 is equal to that of Y1−x Gdx MnO3 , with

5.4. Y1−x Gdx MnO3 ; the influence of disorder

67

x = 0.23. Thus for x & 0.23 we expect to observe the orthorhombic phase. For smaller x and t the hexagonal phase is expected. For x = 0 and x = 0.06 we indeed found the hexagonal structure. However, for 0.19 6 x 6 0.38 we do not observe a sharp transition to the orthorhombic structure, but a mixture of the hexagonal and orthorhombic phases is observed. Only for x = 0.5 an (almost) pure orthorhombic compound is found. The anomalous behaviour of the mixed Y,Gd samples is best illustrated by focussing on the sample with x = 0.25, which has an almost identical tolerance factor as DyMnO3 . Where the latter sample is orthorhombic, the former segregates into two phases. The only difference between the two compounds is that one is undoped, σ 2 = 0 and the other has a mixed lanthanide composition, σ 2 > 0.

0.854

tolerance factor t (-) 0.856 0.858 0.860

0.862

variance σ2 (10-6 Å2)

350 300

mixed

250

orthorhombic

200 150 hexagonal 100 50 0

Ho Y

1.07

Dy

hexagonal mixed orthorhombic hexagonal calculated limit

1.075 1.08 1.085 1.09 average radius (Å)

1.095 1.10

Figure 5.3: Phase diagram of Y1−x Gdx MnO3 as a function of rA and σ 2 . Diamonds, triangles and squares indicate hexagonal, mixed and orthorhombic phases. The drawn lines are estimates of the phase boundaries as explained in the text. The lattice parameters and the relative amounts of orthorhombic and hexagonal fractions are determined by Rietveld refinement of the powder diffraction data. The lattice parameter a is plotted in Fig. 5.4. The lattice parameter c is independent of hr A i as shown in Table 4.1 and discussed in Section 7.2.2. We can rule out segregation of Y and Gd, since the continuous increase in the lattice parameter a of the hexagonal phase with increasing Gd concentration indicates perfect mixing of the A ions. A linear increase in a with hr A i is also observed for the single A cation h-AMnO3 series [6, 7, 28, 29]. Fig. 5.5 shows that the fraction of the orthorhombic phase increases linearly with the Gd concentration. This allows us to apply the lever rule on the h-o transition x − xhexa yortho = (5.2) x − xortho yhexa


68

Lattice parameter a (A)

6.24 6.2

(Y,Gd)MnO3 AMnO3

6.16

Trendline

6.12 6.08 6.04 6 1.02

1.04

1.06 Ionic radius (A)

1.08

1.1

Figure 5.4: Lattice parameter a of the hexagonal phase as a function of the Gd content x. where xhexa and xortho are the boundary values for the respective phases and yortho /yhexa the ratio of the two fractions. From the observed ratios yortho /yhexa as a function of x, the boundary values are derived. The boundary values derived from all five mixed phase samples are plotted in Fig. 5.3 as inverted triangles. We construct a preliminary phase diagram by assuming that the h-o transition at 2 σ = 0 occurs halfway between hexagonal YMnO3 and orthorhombic DyMnO3 . The phase boundaries are drawn in Fig. 5.3 as straight lines through the two calculated boundary values and the assumed σ 2 = 0 midpoint. This phase diagram can be described as follows. The phase line associated with the upper t limit of the pure hexagonal phase does not depend on the variance. Slightly increasing σ 2 and t results in the appearance of a two phase region, consisting of both the hexagonal and the orthorhombic phase. With increasing tolerance factor, the fraction of the orthorhombic phase increases until the lower boundary limit for the orthorhombic phase is crossed. This limit strongly depends on σ 2 . The lower limit for the orthorhombic phase increases from hrA i = 1.078 ˚ A at σ 2 = 0 to hrA i = 1.093 ˚ A 2 2 ˚ at σ = σmax . Note that hrA i = 1.093 A corresponds with the ionic radius of terbium, the second smallest lanthanide to form the perovskite structure. We have shown the dependence of the h-o transition on the average radius hrA i and 2 σ . In the next section, the effect of high pressure experiments on the h-o transition will be discussed.

5.5

Discussion of the disorder

We note the following observations of the two-phase region:

5.5. Discussion of the disorder

69

tolerance factor t (-) 0.856 0.86

fraction (%)

100 80

+H[D

R'\

0.864

RUWKRUKRPELF

JRQDO

60 40

,

20 0

orthorhombic hexagonal o-DyMnO3 Y1-xGdxMnO3

0

0.2 0.4 0.6 0.8 Gd3+ fraction x (-)

1

Figure 5.5: Relative amounts of hexagonal, triangles, and orthorhombic, squares, fractions as a function of the Gd content x. An open square is plotted for DyMnO 3 at the corresponding value of the tolerance factor. 1. The phase mixture is only observed after ambient pressure synthesis for samples with σ 2 6= 0. 2. We do not observe the mixed phase for any of the experiments at high pressure (>5 kbar). We cannot exclude the presence of the mixed phase at lower pressures, but our experimental set-up is not well-suited for those pressures. 3. The lattice parameters of both phases in the two phase region indicate no segregation into Y-rich and Gd-rich phases, see Fig. 5.4, which is unconventional. 4. Literature reports that synthesis via organic precursors can result in a mixture of hexagonal and orthorhombic phases for AMnO3 , σ 2 = 0, compounds [17]. These observations lead to the following conclusions. For σ 2 = 0 compounds either the hexagonal or the orthorhombic structure is stable. Whereas low temperature synthesis may yield mixed phase samples, a high temperature annealing will convert the unstable phase and realises a pure single phased sample. Either the hexagonal or the orthorhombic phase will be stable depending on the tolerance factor. However for σ 2 6= 0 mixed phase samples can be obtained for a broad range of tolerance factors. Even a high temperature annealing retains the phase segregated state. Surprisingly, the phase segregation is not accompanied by the existence of two limiting compositions, e.g. Y1−x Gdx MnO3 with x = 0.1 and x = 0.5. The continuous increase of the lattice parameters of both the hexagonal and the orthorhombic phase throughout the two phase region indicates that the composition of the hexagonal and the orthorhombic state are the same. We have no explanation for this unconventional form of phase segregation.


70

5.6

Conclusions

We have constructed phase diagrams for the hexagonal and orthorhombic phases of AMnO3 , including the effects of average ionic radius, hydrostatic pressure and variance. For compounds with σ 2 6= 0 a phase separation in the orthorhombic phase and the hexagonal phase is found. The mixed region exists only at low pressures. We have shown that, at ambient pressure, this region expands towards higher values of the average radius with increasing variance. The upper limit for the pure hexagonal phase is not affected by an increase in the variance. We speculate that disorder, introduced by a large variance or soft chemical synthesis routes, allows the occurrence of the phase separation in the absence of other driving forces. Suppressing the disorder by applying external pressure or annealing at high temperatures prevents the existence of the phase separation. Pressure favours the denser, orthorhombic phase, whereas thermal annealing promotes the hexagonal phase.

references [1] J. G. Bednorz and K. A. M¨ uller, Z. Phys. B: Condens. Matter 64, 189 (1986). [2] K.-i. Chahara, T. Ohno, M. Kasai and Y. Kozono, Appl. Phys. Lett. 63, 1990 (1993). [3] R. von Helmolt et al., Phys. Rev. Lett. 71, 2331 (1993). [4] S. Jin et al., Science 264, 413 (1994). [5] E. F. Bertaut, E. F. Forrat and P. Fang, C. R. Acad. Sci. 256, 1958 (1963). [6] H. L. Yakel, W. Koehler, E. F. Bertaut and E. F. Forrat, Acta Crystallogr. 16, 957 (1963). [7] B. B. Van Aken, A. Meetsma and T. T. M. Palstra, Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 57, 230 (2001). [8] A. von Hippel, R. Breckenridge, F. G. Chesley and L. Tisza, Ind. Eng. Chem. 38, 1097 (1946). [9] A. M. Glazer, Acta Crystallogr. B28, 3384 (1972). [10] M. O’Keefe and B. G. Hyde, Acta Crystallogr., Sect. B: Struct. Sci. 33, 3802 (1977). [11] P. M. Woodward, Acta Crystallogr., Sect. B: Struct. Sci. 53, 32 (1997). [12] A. P. Ramirez, J. Phys.: Condens. Matter 9, 8171 (1997). [13] J. M. D. Coey, M. Viret and S. Von Molnar, Adv. Phys. 48, 167 (1999). [14] R. D. Shannon and C. T. Prewitt, Acta Crystallogr., Sect. A: Found. Crystallogr. 32, 751 (1976).

5.6. Conclusions

71

[15] H. L. Yakel, Acta Crystallogr. 8, 394 (1955). [16] P. A. Salvador, T.-D. Doan, B. Mercey and B. Raveau, Chem. Mater. 10, 2595 (1998). [17] H. W. Brinks, H. Fjellv˚ ag and A. Kjekshus, J. Solid State Chem. 129, 334 (1997). [18] A. Waintal et al., Solid State Commun. 4, 125 (1966). [19] A. Waintal and J. Chenavas, C. R. Acad. Sci. 264, 168 (1967). [20] V. Wood, A. Austin, E. Collings and K. Brog, J. Phys. Chem. Solids 34, 859 (1973). [21] A. Waintal and J. Chenavas, Mater. Res. Bull. 2, 819 (1967). [22] Quickpress 3.0 piston cylinder apparatus, operations manual (Depths of the Earth Company, 738 S. Perry lane, Tempe, Az, USA). [23] J.-W. G. Bos, M.Sc. thesis. More information www.chem.rug.nl/ssc/projects/report20010124.pdf (2001).

available

at

[24] EVA 4.0, Bruker AXS, software program, 1998. [25] Powder Diffraction File, NIST, Database, 1998. [26] Inorganic Crystal Structure Database, Fachinformationszentrum Karlsruhe, Germany, 2001. [27] TOPAS 2.0, Bruker AXS, Software program, 2000. [28] B. B. Van Aken, A. Meetsma and T. T. M. Palstra, Acta Crystallogr., Sect. E: Struct. Rep. Online 57, i38 (2001). [29] B. B. Van Aken, A. Meetsma and T. T. M. Palstra, submitted to Acta Crystallogr., Sect. E: Struct. Rep. Online (2001).

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Chapter 6 Asymmetry of electron and hole doping in YMnO3 Originally, this chapter was planned in the part of the present thesis on the orthorhombic manganites. The intention was to add electrons1 to LaMnO3 , creating a mixed 3d4 -3d5 state. The larger magnetic interaction, Si · Sj , in such a system, compared with a mixed 3d4 -3d3 state, would lead to a higher Tc and thus to a higher metal-insulator transition temperature, but the important electron-phonon coupling on the Mn3+ 3d4 sites would be maintained. The limited stock of solely tetravalent elements in the periodic table of elements and the drawback of powdering and firing radioactive metal oxides, ThO 2 , pushed the present chapter to the part of this thesis covering the hexagonal manganites. Hexagonal YMnO3 doped with tetravalent Zr ions is synthesised to study the electronic and magnetic properties of Y1−x Zrx MnO3 . Zr substitution creates a mixed Mn3+ -Mn2+ system, instead of the conventional Mn3+ -Mn4+ of colossal magnetoresistance orthomanganites. The YMnO3 system displays a pronounced asymmetry for electron and hole doping. Hole doping results in a conducting state, whereas electron doping retains the insulating state. This asymmetry is a consequence of the crystal field splitting of the Mn ions in trigonal bipyramidal co-ordination.

6.1

Introduction

The colossal magnetoresistance compounds based on doped LaMnO3 exhibit metal-insulator transitions that are concurrent with ferromagnetic ordering. The electronic properties are determined by a competition between localisation, caused by electron-phonon interaction and on-site Coulomb repulsion, and itinerancy caused by double exchange [1]. The electronphonon coupling is most apparent from the Jahn-Teller activity of the Mn3+ d4 state, which leads to structural distortions that can identify the orbital occupation. Interestingly, there is an asymmetry between A2+ doping of LaMnO3 , d4 →d3 , leading to metallicity [2–8], and 1

Using LaMnO3 as parent insulator, we refer to hole doping as the mixed valent state 3d 4 -3d3 , and to electron doping as the mixed valent state 3d4 -3d5 .

73

74

Chapter 6. Asymmetry of electron and hole doping in YMnO3

A3+ doping of CaMnO3 , d3 →d4 , which remains in an insulating, charge ordered state [9]. The origin of the asymmetry is based on the balance between Jahn-Teller distortion, on-site Coulomb repulsion and double exchange. [10] This chapter reports on the asymmetry of hole and electron doping in the electronic properties of hexagonal YMnO3 . In this compound hole doping by Ca2+ , d4 →d3 , results in a conducting state [11], whereas electron doping by Zr4+ , d4 →d5 , retains the insulating state. We will demonstrate that this asymmetry can be understood in terms of the orbital occupation dictated by the crystallographic structure. Hole doping results in partial occupation of the xy and x2 -y 2 orbitals, which have good overlap, whereas electron doping partially fills the 3z 2 -r2 orbitals, which have poor overlap. The influence of doping by tetravalent ions in the manganese perovskites has little been studied. The group of Raveau has reported successful Th doping of AMnO3 , with A = Ca2+ , Sr2+ and Ba2+ [12,13]. Typically, the ionic radius of tetravalent ions is incompatible with that of the trivalent rare earth ions that form the perovskite structure. Therefore, polyvalent elements such as Pb or Ce do not adopt the tetravalent state in LaMnO3 [14]. Nevertheless, tetravalent doping would be very significant because it leads to a mixed valence system d4 -d5 , see Fig. 6.1, instead of the conventional d4 -d3 system. The higher spin value of d5 could lead to higher magnetic ordering temperatures, while preserving the strong electron-phonon interaction of the Jahn-Teller active Mn3+ d4 ions.

Mn4+ 3d3

Mn3+ 3d4

Mn2+ 3d5

Figure 6.1: The crystal field splitting in an octahedral environment. Hole and electron 1) doping are shown in the middle and left part, respectively the middle and right part. The 3d4 ion is Jahn-Teller active. Both hole and electron doping will retain this d 4 ion. We have found that a large ionic size mismatch, such as between La3+ and Zr4+ , yielding a large variance, results in phase separation. In order to stabilise AMnO3 , with the A site partially substituted with tetravalent ions, small rare earth ions are required to minimise the variance of the ionic radii, cf. Eq. (5.1). In Table 6.1 an overview on some relevant radii is given. Therefore, we chose Y3+ , being somewhat larger than Zr4+ . While YMnO3 can be synthesised in the orthorhombic P nma structure [15–17], we focus here on the hexagonal structure, which is thermodynamically stable for AMnO3 with A a small rare earth ion [18]. The hexagonal structure consists of MnO5 trigonal bipyramids. The bases of the pyramids

6.2. Electron doping

75 Ion Sr2+ La3+ Ca2+ Y3+ Th4+ Zr4+ Mn2+ Mn3+ Mn4+

Radius ˚ A [22] 1.31 1.216 1.18 1.075 1.09 0.89 0.830 0.645 0.530

Table 6.1: Overview of relevant ionic radii for the electron doping of AMnO 3 . A ions have an assumed co-ordination number of nine, Mn ions have a co-ordination number of six. are corner linked to form a triangular lattice in the ab basal plane. Between these MnO 3 sheets, the Y ion is located above the linking oxygen ions. Each consecutive layer of MnO 3 is rotated by 180◦ along the c axis. YMnO3 is of current technological interest, because of its ferroelectric properties with Tc ∼ 900 K [19]. Its layered crystal structure is compatible with thin film growth techniques [20, 21]. The ferroelectric component is perpendicular to the layers and can thus be modulated by an external electrical field.

6.2

Electron doping

Electron doping of YMnO3 with Zr results in a mixed valence state of Mn3+ -Mn2+ instead of the conventional Mn3+ -Mn4+ of the colossal magnetoresistance materials. This results in a larger spin state for the Mn, which is expected to enhance Tc . We note that the Mn3+ -Mn2+ mixed valence state preserves the double exchange mechanism between d4 and d5 and the strong coupling to the lattice through the Jahn-Teller active d4 (Mn3+ ) ion. We attempted to stabilise this phase by using tetravalent dopants instead of the conventional divalent alkaline earth ions. A number of tetravalent ions adopt a divalent state in the manganite perovskite, such as Pb and Ce [14]. Although Th substitutes Ca in CaMnO3 with oxidation state Th4+ [12, 13], our attempts to synthesise (La,Th)MnO3 were unsuccessful. The powder x-ray diffraction patterns showed finger print patterns that could only be indexed as Lax Thy Oz compounds, using the Powder Diffraction File [23]. Sintering temperatures were limited to 1073 K, due to the radioactive hazards. Therefore, we chose Zr as tetravalent dopant. Although the tolerance factor, t cf. Eq. (2.1), based on the radii of La3+ , Mn3+ and Zr4+ , is within the existence range of the orthorhombic structure, doping of LaMnO 3 with Zr was unsuccessful. The pellets were well sintered but white impurities were visible. Xray powder diffraction showed the presence of ZrO2 precipitates. Apparently the tolerance factor alone does not account for the stability regime of the perovskites. It is known that both the average ionic radius and the size difference, or variance σ 2 , control the

76


properties [24, 25] of perovskites. From these doping experiments, we conclude that not only the average value of the ionic radii but also the variance control the stability and existence range. This hypothesis is substantiated by our experiments on Y1−x Gdx MnO3 , see Chapter 5, where the orthorhombic phase is suppressed with respect to the hexagonal phase, for samples with σ 2 > 0 [26]. In order to reduce the variance of the ionic radii a much smaller lanthanide was necessary, to enable Zr substitution on the lanthanide site. It is known that the perovskite structure is stable down to a tolerance factor of t = 0.857, for samples with σ 2 = 0 [18]. The hexagonal structure is stable under standard synthesis conditions for samples with t < 0.854. We chose to synthesise and dope YMnO3 with Zr to ensure that our compounds would be hexagonal for all Zr doping levels. Using the values from Tabel 6.1, the Y1−x Zrx MnO3 samples up to x = 0.5 yield a tolerance factor range between 0.854 and 0.787.

6.3

Experimental

The YMnO3 -ZrMnO3 solid state solutions were prepared by mixing pure, dehydrated Y2 O3 , ZrO2 and MnO2 in the appropriate stoichiometric amounts. The oxides were repeatedly ground, pressed to pellets and heated to 1073-1673 K until no change in the diffraction patterns could be seen. Resistivity measurements were done in a standard four-contact set-up, using a Keithley 236 instrument. This limits the measurable range to 10 GΩ for two-point resistance. Magnetisation was measured using a Quantum Design MPMS magnetometer. Diffraction patterns of powder samples were obtained on a Philips PW1820 BraggBrentano diffractometer with secondary monochromator, using either Cu Kα or Mo Kα radiation. The patterns were analysed with the gsas software package [27]. The Rietveld refinement included profile parameters and sample height correction. Single crystals growth of YMnO3 is reported in Chapter 4. Single crystals have a typical size of 0.5 × 0.5 × 0.05 mm3 or up to 0.57 mg. The platelet shaped crystals have their crystallographic ab plane parallel to the plates. The single crystals were glued to a clean, glass rod to fix their orientation with respect to the external magnetic field. The perpendicular and parallel settings of the c axis were achieved by orienting the planes of the platelets parallel and perpendicular to the rod, respectively.

6.4

Magnetisation

In the literature YMnO3 is reported to order antiferromagnetically at ∼ 80 K, but no temperature dependent properties are reported [28]. Our magnetisation data on ceramic YMnO3 are dominated by a ferromagneticlike ordering at 42 K. No sign of the antiferromagnetic ordering at ∼ 80 K is observed, although a negative Weiss temperature, indicating antiferromagnetic interactions, is obtained from a fit of the susceptibility. In Fig. 6.2, we show the temperature dependence of the magnetisation of YMnO3 single crystals. An

6.4. Magnetisation

77

antiferromagnetic ordering is observed at 75 K for the basal plane both parallel and perpendicular to the applied magnetic field. The susceptibility, χ, for H⊥ is higher than for Hk , where ⊥ and k refer to orientations with respect to the ab plane. The antiferromagnetic ordering cannot be observed in our ceramic samples, because of the few percent impurity phase of the ferrimagnetic spinel Mn3 O4 with Tc ∼ 42 K [29]. The high temperature data for the ceramic YMnO3 show a linear dependence between the inverse susceptibility and the temperature. A fit to the Curie-Weiss law,√χ = C/(T − θ), yields a Weiss temperature θ = −254 K and an effective moment P = 8C = 4.5µB , somewhat smaller than the spin-only value expected for Mn3+ ions, 4.90 µB .

-3

χ (10 emu/mol)

7

YMnO 3 single crystal

6 5 H//c H//ab

4

0

100 200 Temperature (K)

300

Figure 6.2: Temperature dependence of the dc magnetic susceptibility of single crystalline YMnO3 with the external field perpendicular ( +) and parallel ( o) to the ab plane. Fig. 6.2 shows the antiferromagnetic ordering in single crystals of YMnO 3 . From earlier neutron diffraction experiments, it is known that the spins are oriented in the ab plane. This agrees with the anisotropy of χ with χ⊥ > χk . In the case of H⊥ , the ab plane is perpendicular to the field. The planar orientation of the spins always yields 90 ◦ angles between the applied magnetic field and the magnetic moments. In the case of Hk , the ab plane has one direction parallel and the other, orthonormal, direction perpendicular to the applied magnetic field. Due to the triangular orientation of the spins a part of the local magnetic moments is perpendicular to the applied field. We observe that χk does not go to zero for T →0, as expected for a conventional antiferromagnet, but remains finite. The finite value of χk can be ascribed to the in-plane response of the triangular frustrated magnetic structure as observed by neutron diffraction [30]. Due to the triangular spin structure of these compounds, χk always probes the part of the spins perpendicular to the applied magnetic field, and therefore does not go to zero for T →0. The measurement of the magnetisation of powder samples shows ferromagnetic ordering at 42 K. However, the value of the magnetic moment is too low to suggest a ferromagnetic or ferrimagnetic ordering of all Mn moments in ceramic YMnO3 . This behaviour is often seen in powder samples of YMnO3 [29, 31]. It was concluded that the magnetic transition


78

originates from Mn3 O4 impurities. Mn3 O4 is ferrimagnetic with a spin of S = 2 (or 4 µB ) per formula unit. The value of the magnetic moment suggests that the ceramic YMnO3 sample has a Mn3 O4 impurity of 4 at. %. The Mn−O bonds in the ab plane form a trigonal network. Each oxygen ion links three Mn ions, and each Mn ion is surrounded, in plane, by three oxygen ions. The superexchange interaction between the Mn ions is antiferromagnetic. However, two neighbouring Mn ions share one other Mn ion as nearest neighbour. This results in a frustrated configuration in the planes. The coupling between the layers is much weaker as the superexchange occurs via two oxygen ions. The large difference between the Weiss temperature θ = -254 K and TN = 75 K is attributed to the pseudo-two-dimensional character of this compound and to the frustration. The Weiss temperature signals strong antiferromagnetic coupling and the TN is a measure for the long range magnetic order.

6.5

X-ray diffraction

Ground samples of Y1−x Zrx MnO3 were analysed with powder x-ray diffraction. We show in fig. 6.3 the refined lattice parameters versus the nominal doping level. The lattice parameters a and c both decrease gradually with increasing Zr concentration, but the slope changes significantly above x = 0.3. Rietveld refinement [32] using the software package gsas [27] of the XRD patterns was carried out to investigate both the doping dependencies of the atomic co-ordinates and possible mixed site occupancy. The refinement of the fractional co-ordinates of the ions yielded no dependence on the substitution within the error bars. Models involving mixed site occupancy show that for up to x = 0.3 no unwanted mixing is present. However, the refinements of the samples with x = 0.4 and x = 0.5 improved significantly, resulting in 40% and 50% of Zr on the Mn site, respectively. 11.45 Y1-xZrxMnO 3

6.14

6.13 11.35 a c

6.12

11.30

6.11 0.0

0.1

c (Å)

a (Å)

11.40

0.2

0.3

0.4

0.5

11.25

x

Figure 6.3: Lattice parameters of h-Y1-x Zrx MnO3 versus the Zr doping level, x. Error bars are smaller than the symbol size. For x< 0.3 no mixed Mn-Zr site occupancy is observed. Increasing the amount of Zr4+ substitution for Y3+ in YMnO3 results in a clear decrease

6.6. Electronic structure

79

of the lattice parameters. This means that Zr is incorporated in the crystal structure. For the samples with x < 0.3, no traces of other Zr containing oxides could be found with either powder x-ray diffraction or energy dispersive spectroscopy. The refinement of the occupation of the Mn site shows that Zr has not replaced Mn in the lattice. Furthermore, substituting Mn with Zr would most likely increase the lattice parameters, as Zr 4+ is larger than Mn2+ , cf. Table 6.1. Therefore, we conclude that we introduced tetravalent zirconium in the hexagonal form of YMnO3 . The crystal structure of the single crystals was determined by x-ray diffraction [33]. A schematic view of the structure, showing the pseudo layered nature of these crystals is shown in Fig. 6.4. Details of the structure are reported in Chapter 4.

(a) ab plane

(b) c axis

Figure 6.4: Sketch of the hexagonal structure of YMnO3 . (a) is a cross-section of the ab plane, showing one MnO layer. (b) is a cross-section along the c axis. O and La ions are represented by open and grey circles, respectively. The Mn ions are represented by their d orbitals. The fully occupied xy and x2 -y2 orbitals and the empty 3z2 -r2 orbitals are shown in (a) and (b), respectively. Note the very poor overlap between two consecutive MnO layers.

6.6

Electronic structure

In contrast to Ca doping of h-YMnO3 [11], we observe upon Zr doping no measurable increase in the conductivity. All samples had two-point resistances of the order of 1 GΩ or higher at room temperature, near the limit of our measurable range. In order to explain the different effect of electron and hole doping for the electronic conductivity, we calculated the crystal field splitting of the Mn 3d orbitals. We assume a simplified structure: Mn surrounded by a perfect equidistant trigonal bipyramid of oxygen ligands. We found a splitting of the 3d orbitals in three states as shown in Fig. 6.5. Since the crystal field in


80

the trigonal bipyramid does not contain off-diagonal terms, the splitting is according to the absolute value of the magnetic quantum number. Consequently, the eg orbitals x2 -y 2 and 3z 2 -r2 are not degenerate as in the orthorhombic perovskites, but x2 -y 2 is degenerate with xy. The orbitals are filled assuming strong Hund’s rule coupling. Both the xz and yz orbitals, which are directed between the oxygen ions, and the in-plane orbitals xy and x2 -y 2 are singly occupied in YMnO3 , Mn3+ 3d4 , whereas the orbital pointing to the two apical oxygen ions is empty.

]

[\[ \

[]\] 0Q G

0Q G

0Q G

Figure 6.5: The crystal field splitting in an trigonal bipyramidal environment. The lowest two orbitals are xz, yz. Hole doping, e.g. Y1−x Cax MnO3 , and electron1) doping, Y1−x Zrx MnO3 , are shown in the middle and left part, respectively the middle and right part. The 3d3 ion is Jahn-Teller active. Crystal field splitting of d levels can be interpreted as the result of a covalent interaction between metal d states and anion p states. Since the metal d states are usually higher in energy, the states of major d character form the antibonding states. The p-d interaction increases with increasing energy of the mixed pd state and therefore the amount of anion p admixture also increases with increasing energy. Thus in a highly symmetrical structure the d bands derived from the crystal field split d states show a larger bandwidth the higher they are in energy. In YMnO3 , the situation is more complicated. The lowest d band is quite localised, while the second band shows more dispersion. The highest d state (of z 2 character) is fairly localised again, contrary to the usual situation. In this structure, the weak O−O interaction in the z direction limits the bandwidth, rather than the Mn−O interaction. As a consequence, doping the d4 system with holes has a large effect on the conductivity [11] since the charge carriers are introduced in the dispersive x2 -y 2 , xy band. However, electron doping leads to occupation of either localised majority z 2 states and/or localised minority xz, yz states. The fate of the electrons introduced by Zr substitution can be determined by investigating the size of the magnetic moment as a function of Zr concentration (Fig. 6.6). The

6.7. Conclusion

81

sample with x = 0.1 shows an increase in the magnetic moment of 0.1 µB , indicating that the extra electrons occupy the majority 3z 2 -r2 states. An increase in doping to x = 0.2 leads to a decrease in the magnetic moment. Thus with increased doping, minority xz and yz states are occupied. The sample with x = 0.3 shows a further reduction of magnetic moment. In Fig. 6.6 the calculated values for the magnetic moment are reported using the LSW method in a virtual crystal approximation. Since the size of the magnetic moment in these systems is not expected to be very dependent on the type of magnetic ordering, a simple ferromagnetic structure was assumed. The calculations show a similar trend but the decrease in magnetic moment is less than observed experimentally. The point at x = 0.33 doping refers to a calculation not employing the virtual crystal approximation but replacing 1/3 of the Y by Zr. Since the value of the magnetic moment obtained in this calculation follows the trend of the values for smaller doping, the virtual crystal approximation is not responsible for the deviation between theoretical and experimental results. 4.7

peff [µB]

4.6

4.5 Measured Calculated 4.4 0.0

0.1

0.2

0.3

0.4

x

Figure 6.6: Magnetic moment as a function of the Zr concentration. In this simplified picture, we do not have a strong electron-phonon coupling via the Jahn-Teller effect on the d4 ions, as they have completely filled subbands. Furthermore, the d4 -d5 mixed valence system has no degenerate partially filled orbitals, so electronphonon coupling via a Jahn-Teller like distortion cannot occur. In contrast, the d 3 ion, with the equidistant, trigonal bipyramidal environment, does have a degeneracy that can be lifted by a structural deformation of the bipyramid. This warrants a direct comparison of h-(Y,Ca)MnO3 with the orthorhombic manganites.

6.7

Conclusion

We successfully doped hexagonal YMnO3 with tetravalent Zr ions, thereby creating a mixed Mn3+ and Mn2+ system. This system displays a pronounced asymmetry for electron and hole doping. Hole doping results in a conducting state because of partial occupation of the

82


dispersive xy and x2 -y 2 band. Both majority and minority bands are partially occupied by electron doping. However, this remains an insulating state because of the poor overlap of the 3z 2 -r2 orbitals and the low mixing of the xz, yz band with the O 2p orbitals.

references [1] A. J. Millis, P. B. Littlewood and B. I. Shraiman, Phys. Rev. Lett. 74, 5144 (1995). [2] G. H. Jonker and J. H. van Santen, Physica 16, 337 (1950). [3] J. H. van Santen and G. H. Jonker, Physica 16, 599 (1950). [4] R. von Helmolt et al., Phys. Rev. Lett. 71, 2331 (1993). [5] K.-i. Chahara, T. Ohno, M. Kasai and Y. Kozono, Appl. Phys. Lett. 63, 1990 (1993). [6] S. Jin et al., Science 264, 413 (1994). [7] A. Urushibara et al., Phys. Rev. B 51, 14103 (1995). [8] P. Schiffer, A. P. Ramirez, W. Bao and S.-W. Cheong, Phys. Rev. Lett. 75, 3336 (1995). [9] J. Hejtmánek et al., Phys. Rev. B 60, 14057 (1999). [10] J. van den Brink and D. Khomskii, Phys. Rev. Lett 82, 1016 (1999). [11] C. Moure et al., J. Mater. Sci. 34, 2565 (1999). [12] M. Hervieu et al., Eur. Phys. J. B 10, 397 (1999). [13] A. Maignan et al., Phys. Rev. B 60, 15214 (1999). [14] R. Kusters et al., Physica B 155, 362 (1989). [15] H. W. Brinks, H. Fjellv˚ ag and A. Kjekshus, J. Solid State Chem. 129, 334 (1997). [16] P. A. Salvador, T.-D. Doan, B. Mercey and B. Raveau, Chem. Mater. 10, 259 (1998). [17] A. Waintal and J. Chenavas, Mater. Res. Bull. 2, 819 (1967). [18] H. L. Yakel, W. Koehler, E. F. Bertaut and E. F. Forrat, Acta Crystallogr. 16, 957 (1963). [19] G. Smolenskii and I. Chupis, Usp. Fiz. Nauk 136-138, 415 (1982) [Sov. Phys. Usp. 25, 475 (1982)]. [20] K.-J. Choi, W.-C. Shin, J.-H. Yang and S.-G. Yoon, Appl. Phys. Lett. 75, 722 (1999).

6.7. Conclusion

83

[21] T. Yoshimura, N. Fujimura, D. Ito and T. Ito, J. Appl. Phys. 87, 3444 (2000). [22] R. D. Shannon and C. T. Prewitt, Acta Crystallogr., Sect. A: Found. Crystallogr. 32, 751 (1976). [23] Powder Diffraction File, NIST, Database, 1998. [24] L. M. Rodríguez-Martínez and J. P. Attfield, Phys. Rev. B 54, R15622 (1996). [25] F. Damay, C. Martin, A. Maignan and B. Raveau, J. Appl. Phys. 82, 6181 (1997). [26] J.-W. G. Bos, B. B. Van Aken and T. T. M. Palstra, submitted to Chem. Mater. (2001), cond-mat/0106335. [27] A. Larson and R. Von Dreele, General Structure Analysis System (GSAS), Los Alamos National Laboratory Report LAUR 86-748, 1994. [28] W. Koehler, H. L. Yakel, E. Wollan and J. Cable, Phys. Lett. 9, 93 (1964). [29] E. F. Bertaut, R. Pauthenet and M. Mercier, Phys. Lett. 18, 13 (1965). [30] E. F. Bertaut, E. F. Forrat and P. Fang, C. R. Acad. Sci. 256, 1958 (1963). [31] E. F. Bertaut, R. Pauthenet and M. Mercier, Phys. Lett. 7, 110 (1963). [32] H. M. Rietveld, J. Appl. Crystallogr. 2, 65 (1969). [33] B. B. Van Aken, A. Meetsma and T. T. M. Palstra, Acta Crystallogr., Sect. C: Cryst. Struct. Commun. C57, 230 (2001).

84


Chapter 7 Origin of the hexagonal phase In Chapter 4 the structure of the hexagonal phase is discussed in great detail. In this chapter we will focus on the origin of the hexagonal phase by comparing AMnO3 compounds with AFeO3 and AVO3 . The tolerance factor, t, is a parameter that indicates to what extent the orthorhombic structure is distorted or wants to distort. V3+ , Mn3+ and Fe3+ have very similar ionic radii in octahedral co-ordination: 0.640, 0.645 and 0.645 ˚ A, respectively. A similar amount of distortion is therefore expected for orthovanadates, orthomanganites and orthoferrites with the same lanthanide. The boundary between hexagonal manganites and orthomanganites is commonly drawn at a critical ionic radius, rc = 1.078 ˚ A or critical tolerance factor, tc = 0.855. In other words, the transition occurs above a certain amount of distortion. However, no transition to the hexagonal phase is observed for o-AVO3 or o-AFeO3 , which have the same amount of distortion. So there must be another important parameter controlling this transition. Even in the manganites the tolerance factor is not the only limiting factor, as Chapter 5 shows by the effect of Gd substitution on YMnO3 samples. The main question that will be addressed in this chapter is ”why do we observe a transition from the orthorhombic phase? Why towards the hexagonal phase? And why only for the manganites?”. The degeneracy of the Mn3+ could be one of the reasons that a transition to a hexagonal structure takes place below a critical value of t. Note that the hexagonal crystal structure is not formed by the octahedral building block, but by trigonal bipyramids, MnO 5 , in which Mn3+ is non-degenerate. The role of the degeneracy is emphasised by the absence of an orthorhombic-hexagonal transition in non-degenerate perovskites with even smaller tolerance factors.

7.1

Introduction

Typically, transition metal oxides, ABO3 , have the perovskite type crystal structure. Nonetheless, there are many varieties within the perovskite structure and some, AMnO 3 with small A site ions, do not form perovskites at all. Physical properties for most of the 85

Chapter 7. Origin of the hexagonal phase

86

ABO3 compounds manifest strong correlation between the cation and oxygen electrons. Some changes in the structure are a sign of a transition in the electronic or magnetic properties. From simple AB systems we know that if the ratio between rA and rB changes, a transition to another way of stacking the atoms is observed, this is known as the radiusratio rule [1]. Generally, for AMnO3 and AFeO3 , the structure is of the GdFeO3 type [2, 3], due to the relatively small radius of the A ions compared with the oxygen ions. However for the smallest A ions a non-perovskite crystal structure is found, but only for the manganites [4]. In this chapter the relation between o-AMnO3 and o-AFeO3 on the one hand and hexagonal AMnO3 on the other hand is investigated. We will show that the Jahn-Teller activity of octahedrally surrounded Mn3+ determines the transition from perovskite to hexagonal in the manganites. Absence of such a Jahn-Teller energy term in the ferrites will therefore not support an early transition to the hexagonal phase. We speculate that for increasingly smaller ionic radii first the orthovanadates and then also the orthoferrites will show a structural phase transition from the orthorhombic to the hexagonal phase, unless the hexagonal phase is surpassed by other ABO3 or (A,B)2 O3 phases. The structure of the perovskites is well known [5–8]. Key features are the large JT distortion, the rotation of the Mn octahedra and the A site shift. The P nma structure can be deconvoluted in a rotation and a distortion of the octahedra. The reason for the La site shift is the covalent bond between La and O [3, 9, 10]. This promotes the lowering of some La−O distances at the cost of increasing other distances. The tolerance factor [11] is a measure of the distortion of the structure, or better rotation of the octahedra. It is commonly accepted already since the 60’s that for t < 0.85, i.e. rA < rHo , the perovskite structure is no longer stable and a transition to the hexagonal1) phase occurs [4]. Although the fact that the transition occurs is well known, the question why is never answered. Moreover, the tolerance factors for YMnO 3 , YFeO3 and YVO3 are very similar but only the manganites show the transition. In the following section a detailed analyses of the transition and the question why only the manganites transform are covered. But first we have a close look at both phases.

7.2

Of radii and shells

7.2.1

Orthorhombic P nma

The orthorhombic distortion in the perovskites originates from the small volume of the A ions with respect to the volume of the holes between the octahedra in the undistorted cubic symmetry. Therefore a large dependence of the distortion on the lanthanide size is expected. A smaller radius of the A site, rA , is adjusted by increasing the rotation, which decreases most A−O distances. These A−O distances should be proportional to rA + rO . 1)

Some perovskite ABO3 compounds, like Sr-doped LaMnO3 and LaCoO3 , can have a rhombohedralhexagonal structure. However, the hexagonal ABO3 we report here, have a profoundly different structure than the perovskite based ABO3 compounds.

7.2. Of radii and shells

87

The transition to the hexagonal phase in the manganites is conventionally attributed to tolerance factors smaller than some critical value. The tolerance factor expresses the ratio of the radii of the A ion and the B ion. Fig. 7.1 and Eq. (2.1) stress the simplicity of t. For a perfect cubic system the edge of the cube is given by the radius of the oxygen plus the radius of√the B ion. The face diagonal is formed by the A ion and the oxygen ion. Thus the ratio is 2 and the tolerance factor is 1. Usually the A ion is too small to form a perfect cube, we find tolerance factor ranging from 0.85 to 0.98. Note that reported values depend strongly on the used radii and co-ordination number. diagonal t= √ 2(edge)

(7.1)

Figure 7.1: Sketch view of the cubic perovskite. The face diagonal (dashed line) and edge (dotted) are indicated for comparison with Eq. (7.1). AFeO3 is a typical perovskite compound. The whole lanthanide series can be used on the A site and single crystals have been grown and studied [2]. The lattice parameters versus the lanthanide radius are plotted in Fig. 7.2. One would expect that with decreasing lanthanide ionic radius, the volume of the unit cell decreases gradually and uniformly. Second, the various parameters indicating the deviation from the cubic structure should increase. As La is usually regarded as the prototypical lanthanide, we will consider the magnitude of rA with respect to rLa . √ √ The lattice parameters of LaFeO3 , rLa = 1.215 ˚ A, obey closely the 2 x 2 x 2 relationship. Therefore, it is almost cubic and twinning is observed [7]. The twinning is probably identical to the twins observed in La1−x Cax MnO3 , which we discussed in Chapter 2. Clearly, the lattice parameters b and c decrease with decreasing rA , with reductions, from LaFeO3 to LuFeO3 , of -8% and -5%, respectively. In sharp contrast, the lattice parameter a increases 1% for GdFeO3 and decreases thereafter to change only to -0.4% at LuFeO3 . This behaviour can be understood by considering the entire crystal structure.


5.60

7.90

5.55

7.85

Lattice parameter b (A)

Lattice parameter a and c (A)

88

5.50 5.45

a c

5.40 5.35 5.30 5.25 5.20 1.00

1.05

1.10

1.15

ionic radius (A)

1.20

1.25

7.80 7.75 7.70 7.65 7.60 7.55 1.00

1.05

1.10

1.15

1.20

1.25

ionic radius (A)

Figure 7.2: Lattice parameters a’, b’ and c’ of AFeO3 as a function of rA [2]. The volume of the unit cell exhibits a small kink at rA = 1.109, which corresponds to GdFeO3 . We will use the conventions introduced by Glazer [12]. Glazer considers the perovskite structure as a fixed sequence of rotations of octahedra in a double cubic unit cell, which contains eight octahedra. The conventional P nma unit cell can be obtained from the double cubic unit cell by the transformations a0 = 21 (a00 − c00 ),2) b0 = b00 and c0 = 21 (a00 + c00 ). The lattice parameters will be influenced by the buckling and tilting of the octahedra. Due to these rotations the lattice parameters generally decrease. Remember that the GdFeO 3 rotation is there in the first place to decrease the volume around the lanthanide ion. Now we focus on the steady decrease of lattice parameter c0 and the near constant values for lattice parameter a0 . The rotation around the b0 axis is ignored. The effect of the equal rotation, a− b+ a− , of the octahedra around the a00 and c00 axes is that both a00 and c00 are reduced. In P nma the rotation sequence is transformed to an a− b+ c0 rotation sequence. Therefore, only lattice parameter c0 will decrease. Thus in first approximation no change in lattice parameter a0 is expected. But second order effects, like the influence of the tilting or deviations from rigid MnO6 octahedra, could have the effect on a0 as is seen in Fig. 7.2. Up to now, we viewed the structure as consisting of rigid MnO6 octahedra and spheres of A ions. But the A−O interactions can also play a role, cf. the A site shift in Chapter 3. We will now consider the importance of the A−O environment in AFeO3 , where the MnO6 octahedra are not distorted. The rotation increases upon smaller rA . We applied a simple shell picture to study the oxygen environment of the lanthanide ions. In an undistorted cubic perovskite, the A ions substitute 25% of the oxygen ions of a perfect fcc lattice. Consequently, the A ions are surrounded by perfect oxygen dodecahedra. Due to the distortion into the orthorhombic P nma structure, by rotating the MnO6 octahedra, the dodecahedra are deformed. A 3D view of the environment is very hard to picture. Therefore, the 2)

a0 , a00 and c00 are vectors. No difference in notation for a scalar or a vector is applied.


89

Density of bond lengts (a.u.)

environment is mapped on one variable, namely the distance from the A ion, as shown in Fig. 7.3. The figure shows a convolution of all A−O bond lengths. Every bond length is depicted by a Gaussian peak of width 0.1 ˚ A and has unit area. This figure shows that we can distinguish three A−O bond length ranges. The ranges are 2-3 ˚ A containing 8 bonds, ˚ ˚ 3-4 A with 4 bonds and 4-5 A with 8 bonds. The first 12 A−O bond lengths originate from the original dodecahedron. 40 30

PrFeO3 GdFeO3

20

LuFeO3 10 0 2

3

4

5

radius (A)

Figure 7.3: Sketched distribution of the A−O bond lengths of AFeO3 . Grey, dashed and black lines indicate PrFeO3 , GdFeO3 and LuFeO3 , respectively. The closest eight bond lengths decrease with decreasing rA , while the next four bond lengths more or less increase. Bond length data has been taken from Ref. [2]. The influence of rA on the co-ordination of the A site is elucidated in Fig. 7.3, by observing the changes from PrFeO3 via GdFeO3 to LuFeO3 . The spread of the first 12 bond lengths increases from 1.1 ˚ A to 1.5 ˚ A. The increased width of the bond length distribution indicates an increased deformation of the dodecahedra. The first part of the first co-ordination shell, including eight A−O bond lengths, moves to shorter distances and becomes only slightly broadened. The broadening is best observed by the increased splitting in the bond length peaks of the last four bond lengths. Furthermore, as also observed by Marezio [2], the next four oxygen bond lengths do not decrease with decreasing rA . On the contrary, the whole second part of the first shell moves to slightly larger distances. Moreover, the three largest bond lengths in this part of the first shell become significantly larger. This indicates a pronounced increase in the difference in distance within the first co-ordination shell. The first co-ordination shell originates from the original 12-fold coordination of the A ions. But as the difference gets larger and larger, we should regard the two parts of the first shell as distinct shells. This large spread in A−O distances caused several authors to speculate on the co-ordination number of the A site. But any choice would be arbitrary in this distorted structure. Till now, we used the atomic positions and lattice parameters of the unit cell to calculate


90

the A−O bond lengths and to illustrate the distortions of the dodecahedron. Now, we take a close look at distinct features in these positions themselves. In Fig. 7.4 the rotation of the octahedra and zA are plotted versus rA . The rotation is expressed by xO2 − zO2 as explained in Chapter 3. We observe an increase in the rotation of the octahedra with decreasing rA . Furthermore, the parameter for the JT distortion, xO2 + zO2 − 12 , is zero within the accuracy of the positions. The rotation of the octahedra will also affect the position of the A ion, as the A ions can increase their covalent interactions by decreasing the distance to the closest three oxygen ions. The ratio of zA and xA is constant for all AFeO3 . In the figure the A site shift is plotted by the z component of its position. The A site shift enhances the differentiation of the A−O distances. The combined effect of the rotation and the A site shift is that most A−O distances become smaller and some become larger, which is seen in Fig. 7.3. Furthermore, the AFeO3 series shows that the increase of rotation and increase of A site shift is uniform, see Fig. 7.4.b.

0.12

0.10

0.08

rotation z-position

0.06

rotation (a.u.)

z-position (-) and rotation (a.u.)

0.12

0.10

0.08

0.04 0.06 0.02 1.00

1.05 1.10 1.15 1.20 ionic radius (A)

(a)

0.03 0.04 0.05 0.06 0.07 z-position (-)

(b)

Figure 7.4: (a) The rotation and zA versus the ionic radius in AFeO3 . (b) The rotation versus zA in AFeO3 . The parameters show good correlation indicating their intimate relation. Data has been taken from Ref. [2]. The initial strong increase in rotation and site shift with rA becomes less for the smaller lanthanides. In this region, the rotation and tilting are hindered, as the distortion of the AOn polyhedra becomes very large. The smaller increase in rotation also moderates the A site shift. For these large distortions the A site will effectively not have a ”8+4” coordination, but a more or less 8 co-ordination. This makes the whole structure unstable


91

and a transition to a less strained structure will occur, with a truly decreased co-ordination for the A site. This is in agreement with the ratio-rule, as the ratio-rule states that the co-ordination decreases as the difference in ionic radius increases, cf. the transition from the CsCl structure to the rock salt structure [1]. A similar dependence on rA is observed in the AMnO3 compounds. In Fig. 3.6 the values for the rotation and the A site shift has been plotted for AMnO3 compounds. Data has been taken from Ref. [13]. Note that Alonso et al. used neutron powder diffraction to obtain their data, whereas Marezio et al. used single crystal x-ray diffraction. If we compare the values for AFeO3 and AMnO3 , we observe that the rotation and the site shift for Mn compounds is slightly larger. Two arguments for the larger distortions can be given. The first reason is a possible difference in ionic radius for Mn3+ and Fe3+ . Normally, a continuous decrease in ionic radius with increasing atomic number is expected, although Shannon and Prewitt report exactly the same value, 0.645 ˚ A, for Mn3+ and Fe3+ [14]. 4+ 4+ This is illustrated by the radii from Ti till Mn , which decrease continuously. In case the determination of the ionic radii by Shannon and Prewitt is not exact and Mn3+ has a larger radius than Fe3+ , then we expect that for the same lanthanide radius the site shift and rotation in the orthomanganites is larger than in the orthoferrites, since the orthomanganites have a smaller tolerance factor. Secondly, the rotation and site shift might be enhanced in the orthomanganites by the JT character of the Mn ions. Although the numbers differ slightly, the overall picture is the same and an almost identical linear relation between the rotation and the site shift is observed: the proportionality constants are very similar, i.e. the rotation over shift parameter ratio is almost the same ∼ 1.25 (-).

7.2.2

Hexagonal P 63 cm manganites

In the previous section, the decrease in the ’relative’ co-ordination number of the A ion, in the orthorhombic perovskite structure, with decreasing ionic radius is discussed. Hexagonal AMnO3 also has a roughly eightfold co-ordination number for the A site. In this structure, the eightfold co-ordination with oxygen ions forms bicapped antiprisms as shown in Fig. 4.4. In Fig. 7.5, the distribution of A−O bond lengths for hexagonal AMnO3 is shown. Note that there are two inequivalent A sites in the hexagonal structure. For clarity, the distribution of bond lengths around only one A site is shown, the other inequivalent A position has a very similar surrounding, but the bond lengths differ somewhat. Two distinct differences with respect to Fig. 7.3 are observed. To start, the first shell is much narrower. This can be explained by the fact that the total co-ordination number is lower in the hexagonal phase than in the orthorhombic phase. As the total volume around each lanthanide is constant, the volume per neighbouring oxygen is increased and therefore the steric hindrance in the hexagonal phase is less than in the orthorhombic phase. As a direct result, the first seven bond lengths have the smallest possible distance. The second difference is the known difference in density. A decrease in density means a reduction in the number of surrounding oxygen ions, which is reflected in the fact that the orthorhombic orthoferrites have 12 oxygen ions within 3.7 ˚ A, while hexagonal manganites have only eight oxygen ions within the same distance.


density of bond lengths (a.u.)

92

120 100

YMnO3 80

LuMnO3

60

HT-YMnO3

40 20 0 2

3

4

5

radius (A)

Figure 7.5: Sketched distribution of the A−O bond lengths of hexagonal AMnO 3 . Grey, dashed and black lines indicate LuMnO3 [15], high temperature YMnO3 [16] and room temperature YMnO3 [17], respectively. The first peak, up to 2.5 ˚ A contains seven bond lengths, six for HT-YMnO3 .

We now focus on the influence of ionic radius on the distribution of the bond lengths, specifically on the two apical A−O bond lengths. In Fig. 7.5 we observe that although the seven shortest bond lengths decrease with decreasing rA , the eighth bond length, the anomalous ’long’ bond, increases. In Section 4.5 the restricted Mn−Oap bond length and the stacking of the O−A−O layers was discussed. It was argued that the stacking resembles closed packing, but the intralayer distances are too large. In Table 4.1 we observe that the c axis hardly changes with ionic radius, while the a axis decreases linearly with decreasing ionic radius. This can be understood from the constraint applied by the restricted Mn−O bond length and the extra space in the ’widely spaced’ close packed layers. Substituting the A ion with another ion with smaller radius cannot result in a decrease in the c direction as the stacking in this direction is dictated by the minimal Mn−Oap bond lengths. The substitution will affect the intralayer distance, giving rise to the observed reduction in the a axis length. We observe a decrease in the apical ’short’ bond, while having a constant c axis length. This must be accompanied with a similar increase in the apical ’long’ bond, as the total height of the stacking stays constant. In Fig.7.5 the bond length distribution of the centrosymmetric high temperature (HT) phase is also included using the data from Ref. [16]. Clearly the transition from two identical A−Oap distances, 2.8 ˚ A in the high temperature phase to one short, 2.4 ˚ A, and one long bond, 3.4 ˚ A, is illustrated.

7.3. Ferroelectricity and covalency

7.3

93

Ferroelectricity and covalency

Ferroelectrics crystal are crystals with parallel alignments of local dipole moments, which results in an external dipole moment, after application of an external electric field. Usually the net external moment is zero, due to domain formation of opposite polar directions [4,18]. Commonly, ferroelectric crystals are divided in two groups, one with a displacive transition and the other with a order-disorder transition. Above the ferroelectric transition temperature the external dipole moment of each domain is zero. For the displacive transition crystals, the atomic displacements in this paraelectic state are zero. In the order-disorder ferroelectrics the displacements have a multiwell configuration of sites and the transition is similar to the ordering of local magnetic moments. The paraelectric state is of course the disordered state of the multiwells. The origin of ferroelectric behaviour can be investigated by an accurate determination of the crystal structure. It is reflected in asymmetric bond lengths around the metal ions. A wrong structure determination could lead to wrong conclusions, as, for instance, an inversion twinned non-centrosymmetric structure mimics centrosymmetry and centrosymmetry does not allow ferroelectric behaviour. For the hexagonal AMnO3 compounds, Yakel was the first to report the structure, which we redetermined. The hexagonal YMnO 3 community usually refers to the structure determination by Yakel et al. [4]. Unfortunately, they report a distinct difference in the two apical Mn−O bond lengths. This could be due to the experimental set-up that did not allow them to measure Friedel pairs. In Table 7.1 the values for the bond lengths are given. The local dipole moment, derived from Yakel’s determination of the Mn−O1 and Mn−O2 bond lengths, is in contradiction with the common opinion that one needs a d0 ion for ferroelectric behaviour, cf. the review by Hill [19] and the article by Cohen [20]. Several conditions for ferroelectric materials are given there. It is argued that the d0 -ness of Ti4+ , Nb5+ etc. is not a requirement for the occurrence of ferroelectricity because YMnO3 is ferroelectric. There, it is widely accepted that the dipole moment originates from the Mn co-ordination and Mn3+ is in the d4 configuration.

YMnO3 ErMnO3 YbMnO3 LuMnO3 LuMnO3 YbMnO3 YMnO3

Van Aken Van Aken Van Aken Van Aken Yakel Isobe L Ã ukaszewicz

[17] [21] [15] [15] [4] [22] [16]

Mn−O1 1.863 1.854 1.867 1.882 1.93 1.866 2.084

Mn−O2 1.862 1.886 1.868 1.859 1.84 1.924 2.084

Mn−O3 2.073 2.092 2.039 2.050 1.98 1.992 1.879

Mn−O4 2.052 2.030 2.034 2.019 2.06 2.040 1.879

Table 7.1: Manganese-oxygen bond lengths A measure for the local dipole moment3) is given by calculating the distance between 3)

The charge is ignored here as we only have A3+ and Mn3+ . The distance is expressed as ”average oxygen position” minus the cation position.


94

the (weighted) centre of gravity of the surrounding O ions and the position of the metal ion. In the following paragraphs, estimates of the centres of the O ions are given for both the Mn and the A sites. In Table 7.2 the oxygen positions around one Mn site are given. O3 and O4 are the equatorial oxygen ions. Their average position is ( 31 , 0, 4 zeq ∼ 0) with zeq = z3 +2×z . The two apical oxygen positions, O1 and O2, average out to 3 1 2 2 (xap ∼ 3 , 0, zap ∼ 0) with xap = x1 +x and zap = z1 +z . The values observed by us, given 2 2 in Table 4.2, yield a very small dipole moment in-plane, -0.0018 ˚ A, and a similar moment ˚ perpendicular to the plane, +0.0028 A. However, if we take the values as determined by Yakel, we find a significant dipole moment along the c axis, 0.0062 ˚ A and 0.0137 ˚ A inplane. By summing over the entire unit cell, the total dipole moment per unit cell can be calculated from the local dipole moment. A unit cell contains six Mn ions. They have all the same environment, although the environments are rotated over 60◦ around the c axis with respect to each other. This will intrinsically cancel the dipole moment in-plane. The new structure determination shows that there is very little difference between the two apical distances and therefore hardly any local dipole moment. x position O3 0 2 O4 3 1 O4 3 O1 x1 ∼ 0.31 O2 x2 ∼ 0.35 Mn ∼ 0.33

y 0 1 3 − 13

0 0 0

z z3 ∼ −0.02 z4 ∼ 0.02 z4 z1 ∼ 0.16 z2 ∼ −0.16 0

Table 7.2: Global positions of Mn and the five co-ordinating oxygen ions in fractional co-ordinates. Now we perform the same calculation for one of the two A positions, see Table 7.3. O1 and O2 are the ’close packed’ oxygen ions. Their average position is (0, 0, z1 ∼ 0.16) and (0, 0, z2 ∼ 0.33), respectively. The midpoint between these two averages is rather near the A1 position, there might only be a small component along the z direction. The two apical oxygen positions, O3, average out to (0, 0, z3 + 41 ). Depending on the sign of z3 and zA1 this will give a large contribution or hardly any contribution to the local dipole moment. In the latter case the local dipole moment that is derived will be rather small. In the former case a large dipole moment on the A1 position is calculated and with opposite values for A2 and O4 a similar dipole moment at the A2 position. Using the values, obtained by single crystal diffraction and refinement for LuMnO3 and other LnMnO3 compounds, a large moment perpendicular to the ab plane is found, -0.0308 ˚ A, i.e. more than 10 times larger than the moment due to the Mn co-ordination. We therefore attribute the ferroelectric behaviour in AMnO3 to the anomalous surrounding of the A ion. Normally, it is expected to have symmetrical environments for the lanthanide ion sites. If the signs are equal, the A−Oap bond lengths stay identical, whereas if they are opposite, one A−O bond length increases and the other decreases. Why does the structure not make the signs of z3 and zA1 equal such that all local dipole moments are zero? Note

7.4. Discussion

95 position x O1 x1 O1 0 O1 -x1 O2 x2 O2 0 O2 -x2 O3 0 O3 0 A1 0

y z 0 z1 ∼ 0.16 x1 z1 -x1 z1 0 z2 ∼ 0.33 x2 z2 -x2 z2 0 z3 ∼ 0.00 0 z3 + 21 0 zY 1

Table 7.3: Oxygen positions around A1 in fractional co-ordinates. that an external dipole moment should be reduced by a domain structure of opposite moments. The external field and the domain structure increases the total energy with respect to a non-ferroelectric phase. To explain why the ferroelectric phase in spite of the external field wins the competition from the non-ferroelectric phase, we have to take into account the covalency to explain the anomalous surrounding. The reason why covalent interactions favour anomalous environments is explained in Chapter 3, where we saw the A ion moving towards the closest three oxygen ions to lower its energy. In the P 6 3 cm space group symmetry a similar shift is allowed for the eightfold environment. Making the signs opposites allows a lowering of the covalency energy, which makes the ferroelectric distortion favourable with respect to the first option, the non-ferroelectric phase.

7.4

Discussion

Now we address the question why the hexagonal phase is only observed in the manganites, or stronger phrased: Why does this phase exist at all? There are several approaches to these questions: 1. the structure of A2 O3 and Mn2 O3 2. the increased distortion of AMnO3 with decreasing rA 3. the differences between AMnO3 and AFeO3

7.4.1

A2 O3 and Mn2 O3

The first approach starts with the end-member materials. Both A2 O3 and Mn2 O3 have the bixbyite structure. The bixbyite structure is a very common A2 O3 structure. The oxygen ions are close packed, the A ions are octahedrally co-ordinated. Since both compounds have the same structure, one would expect a solid solution phase, in first approximation. However if we take into account a large difference in radii, cation ordering is expected. The


96

large cation will have a loose packing, whereas the environment of the smaller cation is very dense, making the structure unstable with increasing radius ratio, rrMAn . Therefore a new, not bixbyite related crystal structure can occur. From the radius-ratio rule we know that the co-ordination number increases with decreasing difference in radius. The co-ordination of the A site should increase, while that of the Mn site should decrease. From this point of view it is not strange that the hexagonal phase, the mixing of A2 O3 and Mn2 O3 , yields an increased co-ordination of A (to 7 or 8) and that the co-ordination of Mn decreases from 6 to 5. Also Fe2 O3 and even the larger lanthanides A2 O3 compounds have the bixbyite structure. However, AFeO3 and ”large lanthanide” AMnO3 are only known in the orthorhombic structure. Although this first approach is a neat way to describe the solid state reaction, between A2 O3 and Mn2 O3 into the hexagonal phase, it does not support the transition to the orthomanganite phase. There the Mn co-ordination number is again 6. It also does not explain why Fe2 O3 never yields the hexagonal phase in combination with A2 O3 .

7.4.2

Distortion vs ionic radius

The second approach considers the dependence of the distortion of the orthomanganite structure on rA . If we follow the structural changes with decreasing rA , we observe that the GdFeO3 rotation increases monotonously. The Fe−O distances stay constant. If we consider the lanthanide oxygen bond lengths we observe a more varied behaviour as is discussed in Fig. 7.3. To summarise, the distance distribution broadens and splits in a 8+4 like co-ordination. The shortest 6 bond lengths of the first 8 become even shorter, whereas the longer bonds of the 8 start to increase after an initial decrease. The 4 long bonds only increase with decreasing rA . If we assume that the stability of the structure is determined by the deviation of the bond lengths from the ideal 2.4 ˚ A, it is clear that the stability decreases if the deviations increase. Then, the 4 longest bonds will continuously decrease their contribution to the stability. In this scenario it is feasible that at a certain amount of distortion the stability of a real eightfold co-ordination is identical to that of the distorted perovskite with the 8+4 co-ordination. Note that the 4 long bonds even slightly increase the shorter bonds. So there is good reason to assume that for small rrMAn ratio, that is large distortion, the structure reaches the end of its stability range. In the most extreme case, when this ratio equals one, the bixbyite structure will prevail. Another argument is found by observing the dependence of the lattice parameters and unit cell volume on the ionic radius. In Fig. 7.2 the lattice parameters of AFeO 3 are plotted. The unit cell volume is of course given by V = a × b × c. With decreasing radius the unit cell volume decreases, but below rA ∼ 1.09 the gradient becomes smaller. This is an indication that the volume of the unit cell cannot continue to shrink with the same pace as the decreasing radii of the lanthanides. These arguments make it feasible that there is a limited phase stability for the perovskite structure. It even suggests that below a certain rrMAn ratio this would lead to a real eightfold co-ordination, which is evidently found for the hexagonal manganites. Nevertheless, this

7.4. Discussion

97

does not discriminate the behaviour of the orthomanganites from the orthoferrites.

7.4.3

3d series

As already suggested in the two previous approaches, there is very little difference between the various transition metal oxides from a structural chemistry point of view. However, the phenomena observed in orthotitanates, orthovanadates, orthomanganites, orthoferrites and orthocobaltates can be very different. The main reason for that is the number of 3d electrons that changes with the elements and with the oxidation state. Let’s consider ABO3 compounds, with A a relatively large ion and B a small transition metal, i.e. the bixbyite structure is not stable. In the whole known ABO3 range, the hexagonal phase is the only non-perovskite phase. Several distortions within the perovskite structure are known. For instance off-centre cations, e.g. SrTiO3 , and distorted octahedra, e.g. YVO3 , are observed. In the orthomanganites, on the other hand, the Jahn-Teller distortion leaves the Mn 3+ in the centre, but deforms the octahedra. the reason for the JT distortion is the degeneracy of the 3d4 t2g 3 eg 1 . The degeneracy has to be lifted, dictated by the Jahn-Teller theorem. The degeneracy can be lifted by a local distortion of the octahedra or by long range lattice distortions. In LaMnO3 this leads to a long range order of the eg orbitals, giving alternatively long and short Mn−O bonds in plane. Of course, the lifting of the degeneracy, i.e. the local distortion, requires energy for the lattice distortion. AFeO3 has Fe3+ 3d5 with total occupation of the majority spin. The absence of the hexagonal structure in the orthoferrites series and the very small difference in GdFeO 3 rotation compared with AMnO3 suggests that for similar radii the o-AFeO3 structure has a lower energy than the o-AMnO3 structure and that the JT activity of the Mn3+ 3d4 ion is an important factor. In the hexagonal phase Mn3+ is no longer JT active, as the crystal field of the trigonal bipyramid (Fig. 6.5 is intrinsically different from the octahedral crystal field, see Fig. 6.1. The lattice energies for hypothetical h-AFeO3 and h-AMnO3 are therefore very similar. Note that it is assumed that h-AFeO3 is completely high spin. The results of band structure 4.1 4+ the minority is also calculations on Y1−x Zrx Mn3+ 1−x Mnx O3 showed that above Mn 3d partially filled. Considering the increase in distortion with decreasing rA and the extra JT distortion for Mn3+ , it is easy to understand that when the radius gets below a critical value the transition to the hexagonal phase takes place. Furthermore, the same rA yields still an orthorhombic orthoferrite, since there is no degeneracy that needs to be lifted, by an increased distortion.

7.4.4

AVO3 and AFeO3

To elucidate the occurrence of the transition in the manganites and not (yet) in the orthoferrites and orthovanadates, in Fig. 7.6 the lattice energy against the ionic radius is


98

sketched. In the orthorhombic phase, the distortion increases with decreasing rA and it is assumed that the lattice energy depends linearly on the distortion.

Lattice energy (a.u.)

20 15

tolerance factor t (-) 0.825 0.845 0.865 0.885 0.905

rY

10

o-AMnO3 o-AVO3 o-AFeO3 h-ABO3

5 0 0.95 1.00 1.05 1.10 1.15 1.20 1.25 average radius (Å)

Figure 7.6: Schematic view of the lattice energy vs. the average A site radius. The gradient of the curves is a measure of the increase of the GdFeO3 rotations with decreasing rA . The offset for the curves of the perovskite phases is a measure for the increased distortion due to JT active Mn3+ and V3+ . The lattice energy of the hexagonal phase is assumed to be independent of the A site radius. 3d2 , 3d4 and 3d5 are non-degenerate in a trigonal bipyramidal crystal field.

The lattice energy of the orthomanganites is higher than that of the orthoferrites, due to the extra distortion to lift the JT degeneracy. The orthovanadates have also a JT active electron configuration, but the energy associated with a t2g degeneracy is much lower than that for eg , which is reflected in the much smaller distortions of the VO6 octahedra [23,24]. Therefore the lattice energy is lower than for the orthomanganites, but higher than for the orthoferrites. The energy of the (hypothetical) hexagonal phase is assumed to be identical for all three materials and does not depend on the ionic radius. Near rA = rY the lattice energy of the orthomanganites and the hexagonal phase are equal. Below the critical ionic radius rc,M n the hexagonal phase is stable. Due to the lower contribution of the V3+ t2g degeneracy to the lattice energy, the hexagonal-orthorhombic transition in the orthovanadates will occur at lower radius than for the orthomanganites, rc,M n > rc,V . The perovskite structure is stable up to a larger GdFeO3 rotation compared with the manganites. As the orthomanganites have a larger, A site radius independent, contribution from the JT distortion, a larger GdFeO3 is necessary in the orthovanadates. In the orthoferrites, there is no electronic contribution at all. Therefore the transition in the orthoferrites will occur at an even lower critical ionic radius, r c,M n > rc,V > rc,F e . The perovskite orthoferrite is stable with a very large GdFeO3 rotation.

7.5. Conclusion

7.5

99

Conclusion

We conclude that with decreasing average ionic radius on the A site the distortions of the GdFeO3 type increase, both in the orthoferrites and -manganites. Upon a certain critical amount of distortion, the perovskite structure becomes unstable and a transition to a less dense, but also less strained structure occurs. This transition is accelerated in the manganites as the perovskite structure also accommodates the distortion of the JT active Mn3+ . It is expected that the orthovanadates will show a hexagonal-orthorhombic transition at a somewhat smaller radius than LuVO3 .

references [1] P. W. Atkins, Physical Chemistry, 5th ed. (Oxford University Press, Walton street, Oxford, UK, 1993), Chap. 21, p. 741. [2] M. Marezio, J. Remeika and P. Dernier, Acta Crystallogr., Sect. B: Struct. Sci. 26, 2008 (1970). [3] T. Mizokawa, D. I. Khomskii and G. A. Sawatzky, Phys. Rev. B 60, 7309 (1999). [4] H. L. Yakel, W. Koehler, E. F. Bertaut and E. F. Forrat, Acta Crystallogr. 16, 957 (1963). [5] H. L. Yakel, Acta Crystallogr. 8, 394 (1955). [6] S. Quezel-Ambrunaz, Bull. Soc. Fr. Min. Cristallogr. 91, 339 (1968). [7] M. Marezio, Mater. Res. Bull. 6, 23 (1971). [8] J. Rodríguez-Carvajal et al., Phys. Rev. B 57, R3189 (1998). [9] J. B. Goodenough, Magnetism and the Chemical Bond (Wiley, New York, 1963). [10] J. B. Goodenough, Prog. Solid State Chem. 5, 145 (1971). [11] V. M. Goldschmidt, Skr. Norske Videnskap. Akad. No.2 (1926). [12] A. M. Glazer, Acta Crystallogr., Sect. B: Struct. Sci. 28, 3384 (1972). [13] J. Alonso, M. Martínez-Lope, M. Casais and M. Fernández-Daz, Inorg. Chem. 39, 917 (2000). [14] R. D. Shannon and C. T. Prewitt, Acta Crystallogr., Sect. A: Found. Crystallogr. 32, 751 (1976). [15] B. B. Van Aken, A. Meetsma and T. T. M. Palstra, submitted to Acta Crystallogr., Sect. E: Struct. Rep. Online (2001).

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[16] K. L Ã ukaszewicz and J. Karut-Kalicinska, Ferroelectrics 7, 81 (1974). [17] B. B. Van Aken, A. Meetsma and T. T. M. Palstra, Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 57, 230 (2001). [18] C. Rao and J. Gopalakrishnan, New directions in solid state chemistry, 2nd ed. (Cambridge University Press, 1997), page 385. [19] N. A. Hill, J. Phys. Chem. B 104, 6694 (2000). [20] R. E. Cohen, J. Phys. Chem. Solids 61, 139 (2000). [21] B. B. Van Aken, A. Meetsma and T. T. M. Palstra, Acta Crystallogr., Sect. E: Struct. Rep. Online 57, i38 (2001). [22] M. Isobe, N. Kimizuka, M. Nakamura and T. Mohri, Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 47, 423 (1991). [23] P. Bordet et al., J. Solid State Chem. 106, 253 (1993). [24] Y. Ren et al., Phys. Rev. B 62, 6577 (2000).

Appendix A La0.84Ca0.16MnO3 Formula Formula weight Crystal system Space group, no a b c reflections Formula Z Space group Z ρcalc F(000) µ(Mo Kα) Color, habit Approx. crystal dimensions

La0.84 Ca0.16 MnO3 226.03 g mol−1 orthorhombic P nma, 62 5.5257 ˚ A 1) 7.7377 ˚ A 5.5305 ˚ A 2282 4 8 6.341 g cm−3 399.9 electrons 203.6 cm−1 black, platelet 0. × 0. × 0.0 mm3

Table A.1: Crystal data and details of the structure determination of La 0.84 Ca0.16 MnO3

101

Appendix A. La0.84 Ca0.16 MnO3

102

0.71073 ˚ A Graphite Bruker APEX CCD area-detector 100-300 K (100 K results given here) φ scans & ω scans 38.5◦ h:-9→9 & k:-12→13 & l:0→9 733 706 0.072

λ(Mo Kα) Monochromator Diffractometer Temperature Measurement method θ range Index ranges Unique data Data (Fo ≥ 4σ(Fo ) Rsig

Table A.2: Data collection of La0.84 Ca0.16 MnO3 732 31 0.0408 0.1086 1.116 4.7 and -3.4 e ˚ A−3 0.0429 0.887 0.011(2)

Number of reflections Number of refined parameters R1 Final agreement factor W R2 Goodness of Fit Residual electron density Weighting scheme a Weighting scheme b Isotropic secondary extinction

Table A.3: Refinement of La0.84 Ca0.16 MnO3 atom La2) Mn O1 O2

x 0.02949(13) 0.00000(-) 0.4916(10) 0.2870(7)

y 0.25000(-) 0.00000(-) 0.25000(-) 0.0361(4)

z 0.49462(5) 0.00000(-) 0.5682(7) 0.2257(6)

Ueq (˚ A2 ) 0.0051(2) 0.0046(3) 0.0085(9) 0.0086(6)

Table A.4: Final fractional atomic co-ordinates of La0.84 Ca0.16 MnO3 U11 La 0.0063(2) Mn 0.0063(7) O1 0.008(2) O2 0.0075(11)

U22 0.0048(2) 0.0037(5) 0.008(2) 0.0077(11)

U33 0.0041(3) 0.0038(6) 0.009(2) 0.0106(14)

U23 0.0000(-) -0.0002(2) 0.0000(-) -0.0011(10)

U13 U12 -0.00090(8) 0.0000(-) 0.0001(4) 0.0003(3) 0.0002(15) 0.0000(-) -0.0007(8) -0.0004(13)

Table A.5: Anisotropic parameters (˚ A2 ) of La0.84 Ca0.16 MnO3

Appendix B La0.81Ca0.19MnO3 Formula Formula weight Crystal system Space group, no a b c reflections Formula Z Space group Z ρcalc F(000) µ(Mo Kα) Color, habit Approx. crystal dimensions

La1−x Cax MnO3 220.61 g mol−1 orthorhombic P nma, 62 5.497 ˚ A 1) 7.774 ˚ A 5.497 ˚ A 6822 4 8 6.240(8) g cm−3 392.2 electrons 197 cm−1 black, platelet 0.2 × 0.1 × 0.02 mm3

Table B.1: Crystal data and details of the structure determination of La 0.81 Ca0.19 MnO3

103

Appendix B. La0.81 Ca0.19 MnO3

104


0.71073 ˚ A Graphite Bruker APEX CCD area-detector 90-300 K (90 K results given here) φ scans & ω scans 38.5◦ h:-9→9 & k:-13→13 & l:-9→9 6350 4263 0.0185

Table B.2: Data collection of La0.81 Ca0.19 MnO3 Number of reflections Number of refined parameters R1 Final agreement factor W R2 Goodness of Fit Residual electron density Weighting scheme a Weighting scheme b Isotropic secondary extinction

6350 35 0.068 0.260 1.205 7.5(10) and -8.2(10) e ˚ A−3 0.144 0.256 0.033(3)

Table B.3: Refinement of La0.81 Ca0.19 MnO3 atom La2) Mn O1 O2

x 0.02535(8) 0.00000(-) 0.4886(4) 0.2830(3)

y z 0.25000(-) 0.49496(3) 0.00000(-) 0.00000(-) 0.25000(-) 0.5651(4) 0.0354(3) 0.2232(3)

Ueq (˚ A2 ) 0.0094 0.0088 0.0136 0.0141

Table B.4: Final fractional atomic co-ordinates of La0.81 Ca0.19 MnO3 U11 La 0.0096(2) Mn 0.0073(4) O1 0.0083(11) O2 0.0118(8)

U22 0.0095(2) 0.0100(4) 0.0123(9) 0.0130(7)

U33 0.0092(2) 0.0092(5) 0.0202(14) 0.0175(8)

U23 U13 0.0000(-) -0.00103(4) -0.0002(1) 0.00015(10) 0.0000(-) 0.0010(8) 0.0017(6) 0.0016(6)

U12 0.0000(-) 0.00034(17) 0.0000(-) -0.0014(5)

Table B.5: Anisotropic parameters (˚ A2 ) of La0.81 Ca0.19 MnO3

Appendix C La0.75Ca0.25MnO3 Formula Formula weight Crystal system Space group, no a b c reflections Formula Z Space group Z ρcalc F(000) µ(Mo Kα) Color, habit Approx. crystal dimensions

La0.75 Ca0.25 MnO3 g mol−1 orthorhombic P nma, 62 5.477 ˚ A 1) 7.746 ˚ A 5.477 ˚ A 8330 4 8 6.132 g cm−3 383.1 electrons 189.3 cm−1 black, platelet 0.1 × 0.08 × 0.02 mm3

Table C.1: Crystal data and details of the structure determination of La 0.75 Ca0.25 MnO3

105

Appendix C. La0.75 Ca0.25 MnO3

106


0.71073 ˚ A Graphite Bruker APEX CCD area-detector 100-300 K (100 K results given here) φ scans & ω scans 49.9◦ h:-11→11 & k:-16→16 & l:-11→11 8330 5953 0.0875

Table C.2: Data collection of La0.75 Ca0.25 MnO3 Number of reflections Number of refined parameters R1 Final agreement factor W R2 Goodness of Fit Residual electron density Weighting scheme a Weighting scheme b Isotropic secondary extinction

8330 35 0.0872 0.2894 1.070 7.5(10) and -8.2(10) e ˚ A−3 0.1854 0.0 0.013(3)

Table C.3: Refinement of La0.75 Ca0.25 MnO3 atom La2) Mn O1 O2

x 0.02124(8) 0.00000(-) 0.4906(4) 0.2787(3)

y 0.25000(-) 0.00000(-) 0.25000(-) 0.0335(3)

z 0.49553(4) 0.00000(-) 0.5629(6) 0.2235(3)

Ueq (˚ A2 ) 0.00442(7) 0.0038(2) 0.0066(5) 0.0080(3)

Table C.4: Final fractional atomic co-ordinates of La0.75 Ca0.25 MnO3 U11 La 0.00457(12) Mn 0.0020(3) O1 0.0049(12) O2 0.0063(7)

U22 0.00367(13) 0.0034(3) 0.0065(11) 0.0096(8)

U33 0.00501(12) 0.0058(3) 0.0084(10) 0.0082(6)

U23 0.0000(-) 0.00002(11) 0.0000(-) 0.0021(5)

U13 -0.00090(4) 0.00000(8) 0.0006(5) -0.0001(5)

Table C.5: Anisotropic parameters (˚ A2 ) of La0.75 Ca0.25 MnO3

U12 0.0000(-) 0.00017(10) 0.0000(-) -0.0001(6)

Appendix D YMnO3 Formula Formula weight Crystal system Space group, no a c reflections Formula Z Space group Z ρcalc F(000) µ(Mo Kα) Color, habit Approx. crystal dimensions

YMnO3 191.85 g mol−1 hexagonal P 63 cm, 185 6.1387(3) ˚ A 11.4071(9) ˚ A 3385 6 12 5.135 g cm−3 528 electrons 280.7 cm−1 black, platelet 0.15 × 0.15 × 0.024 mm3

Table D.1: Crystal data and details of the structure determination of YMnO 3 λ(Mo Kα) Monochromator Diffractometer Temperature Measurement method θ range Index ranges Unique data Data (Fo ≥ 4σ(Fo ) Rsig

0.71073 ˚ A Graphite Enraf-Nonius CAD-4F 293(2) ω / 2θ scans 40.0◦ h:0→11& k:-11→0 & l:-20→20 865 658 0.0405

Table D.2: Data collection of YMnO3 107

Appendix D. YMnO3

108

Number of reflections Number of refined parameters Constraints R1 Final agreement factor W R2 Goodness of Fit Residual electron density Weighting scheme a Weighting scheme b Isotropic secondary extinction

865 32 zM n = 0 0.0372 0.1065 1.117 3.1(4) and -1.2(4) e ˚ A−3 0.072 0.0 0.025(3)

Table D.3: Refinement of YMnO3

Y1 Y2 Mn O1 O2 O3 O4

U11 0.0035(3) 0.0021(2) 0.0073(3) 0.008(3) 0.005(2) 0.004(2) 0.008(2)

U22 0.0035(3) 0.0021(2) 0.0060(3) 0.010(2) 0.0038(15) 0.004(2) 0.008(2)

U33 0.0044(4) 0.0081(3) 0.0047(3) 0.0052(16) 0.0060(14) 0.008(4) 0.011(3)

U23 0.0000(-) 0.0000(-) 0.0006(2) -0.0012(14) 0.0003(12) 0.0000(-) 0.0000(-)

U13 U12 0.0000(-) 0.00175(17) 0.0000(-) 0.00107(11) 0.0000(-) 0.0037(6) 0.0000(-) 0.0040(13) 0.0000(-) 0.0023(10) 0.0000(-) 0.002(1) 0.0000(-) 0.0039(10)

Table D.4: Anisotropic parameters (˚ A2 )

Appendix E ErMnO3 Formula Formula weight Crystal system Space group, no a c reflections Formula Z Space group Z ρcalc F(000) µ(Mo Kα) Color, habit Approx. crystal dimensions

ErMnO3 270.2 g mol−1 hexagonal P 63 cm, 185 6.1121(5) ˚ A 11.420(1) ˚ A 7178 6 12 7.286 g cm−3 702 electrons 386.8 cm−1 black, platelet 0.11 × 0.10 × 0.08 mm3

Table E.1: Crystal data and details of the structure determination of ErMnO 3 λ(Mo Kα) Monochromator Diffractometer Temperature Measurement method θ range Index ranges Unique data Data (Fo ≥ 4σ(Fo ) Rsig

0.71073 ˚ A Graphite Bruker APEX CCD area-detector 293(1) φ scans & ω scans 38.5◦ h:-6→10 & k:-10→8 & l:-18→19 759 569 0.0363

Table E.2: Data collection of ErMnO3 109

Appendix E. ErMnO3

110


759 32 zM n = 0 0.034 0.0787 1.032 3.9(9) and -6.4(9) e ˚ A−3 0.0457 0.0 0.022(1)

Table E.3: Refinement of ErMnO3

Er1 Er2 Mn O1 O2 O3 O4

U11 0.0090(2) 0.0093(3) 0.0122(8) 0.030(5) 0.018(5) 0.010(4) 0.013(4)

U22 0.0090(2) 0.0093(3) 0.0105(5) 0.008(2) 0.012(3) 0.010(4) 0.013(4)

U33 0.0088(2) 0.0067(3) 0.0048(3) 0.004(3) 0.008(3) 0.009(7) 0.008(4)

U23 0.0000(-) 0.0000(-) 0.0015(4) -0.001(2) 0.001(2) 0.0000(-) 0.0000(-)

U13 0.0000(-) 0.0000(-) 0.0000(-) 0.0000(-) 0.0000(-) 0.0000(-) 0.0000(-)

Table E.4: Anisotropic parameters (˚ A2 ) of ErMnO3

U12 0.0045(1) 0.0046(2) 0.0061(4) 0.015(3) 0.009(2) 0.005(2) 0.007(2)

Appendix F YbMnO3 Formula Formula weight Crystal system Space group, no a c reflections Formula Z Space group Z ρcalc F(000) µ(Mo Kα) Color, habit Approx. crystal dimensions

YbMnO3 275.9 g mol−1 hexagonal P 63 cm, 185 6.0584(6) ˚ A 11.3561(7) ˚ A 3264 6 12 7.617 g cm−3 714 electrons 435.8 cm−1 black, platelet 0.15 × 0.10 × 0.013 mm3

Table F.1: Crystal data and details of the structure determination of YbMnO 3 λ(Mo Kα) Monochromator Diffractometer Temperature Measurement method θ range Index ranges Unique data Data (Fo ≥ 4σ(Fo ) Rsig

0.71073 ˚ A Graphite Enraf-Nonius CAD-4F 295 K ω/2θ scans 39.9◦ h:-10→0 & k:0→10 & l:-20→20 835 636 0.0246

Table F.2: Data collection: YbMnO3 111

Appendix F. YbMnO3

112


835 32 zM n = 0 0.0295 0.0722 1.080 2.5(10) and -7.3(10) e ˚ A−3 0.0494 0.0 0.0121(7)

Table F.3: Refinement of YbMnO3

Yb1 Yb2 Mn O1 O2 O3 O4

U11 0.0047(2) 0.0035(1) 0.0069(4) 0.005(1) 0.014(2) 0.003(2) 0.009(3)

U22 0.0047(2) 0.0035(1) 0.0048(4) 0.017(2) 0.000(2) 0.003(2) 0.009(3)

U33 0.0035(2) 0.0071(2) 0.0039(2) 0.004(2) 0.003(2) 0.005(6) 0.000(3)

U23 U13 0.0000(-) 0.0000(-) 0.0000(-) 0.0000(-) 0.0002(3) 0.0000(-) -0.002(2) 0.0000(-) 0.000(2) 0.0000(-) 0.0000(-) 0.0000(-) 0.0000(-) 0.0000(-)

Table F.4: Anisotropic parameters (˚ A2 ) of YbMnO3

U12 0.00233(10) 0.00177(6) 0.0024(6) 0.0009(9) 0.0000(9) 0.0020(10) 0.0047(13)

Appendix G LuMnO3 Formula Formula weight Crystal system Space group, no a c reflections Formula Z Space group Z ρcalc F(000) µ(Mo Kα) Color, habit Approx. crystal dimensions

LuMnO3 277.9 g mol−1 hexagonal P 63 cm, 185 6.038(1) ˚ A 11.361(1) ˚ A 4711 6 12 7.719 g cm−3 720 electrons 460.3 cm−1 black, platelet 0.12 × 0.10 × 0.004 mm3

Table G.1: Crystal data and details of the structure determination of LuMnO 3 λ(Mo Kα) Monochromator Diffractometer Temperature Measurement method θ range Index ranges Unique data Data (Fo ≥ 4σ(Fo ) Rsig

0.71073 ˚ A Graphite Enraf-Nonius CAD-4F 295 K ω/2θ scans 40.0◦ h:-10→9 & k:0→10 & l:-20→20 833 610 0.0480

Table G.2: Data collection: LuMnO3 113

Appendix G. LuMnO3

114


833 32 zM n = 0 0.0266 0.0653 1.047 2.0(4) and -5.65(4) e ˚ A−3 0.0293 0.0 0.024(2)

Table G.3: Refinement of LuMnO3

Lu1 Lu2 Mn O1 O2 O3 O4

U11 0.0044(2) 0.0041(1) 0.0053(14) 0.007(3) 0.006(3) 0.004(2) 0.009(3)

U22 0.0044(2) 0.0041(1) 0.0053(6) 0.007(3) 0.006(3) 0.004(2) 0.009(3)

U33 0.0043(2) 0.0056(2) 0.0023(3) 0.004(2) 0.007(2) 0.002(5) 0.005(4)

U23 0.0000(-) 0.0000(-) -0.0005(3) 0.0015(17) -0.0018(17) 0.0000(-) 0.0000(-)

U13 0.0000(-) 0.0000(-) 0.0000(-) 0.0000(-) 0.0000(-) 0.0000(-) 0.0000(-)

Table G.4: Anisotropic parameters (˚ A2 ) of LuMnO3

U12 0.0022(1) 0.00206(6) 0.0016(7) 0.005(3) 0.002(3) 0.002(1) 0.005(1)

Samenvatting Materialen kunnen onderverdeeld worden in talrijke categorien, afhankelijk van bijvoorbeeld oorsprong, gebruik of morfologie. Het aantal toepassingen en eigenschappen, en te vormen combinaties, lijkt bijna onbeperkt. Een mooi voorbeeld van een kleine, doch diverse groep van materialen zijn de perovskieten, een groep oxides met gelijksoortige kristalstructuur, vernoemd naar het mineraal perovskiet, CaTiO3 . Fysici, scheikundigen en materiaalwetenschappers hebben een grote interesse in deze materialen, vanwege de grote variëteit aan fysische eigenschappen, waaronder ferroelektriciteit (titanaten en niobaten), metaalisolator overgangen (nikkelaten) en supergeleiding (cupraten). Maar nog steeds worden er nieuwe en onuitgebuite mogelijkheden van combinaties van eigenschappen ontdekt. Deze grote variëteit is duidelijk te zien in het fasediagram van het LaMnO3 -CaMnO3 , waarin slechts de La:Ca verhouding gevarieerd wordt. Een van de meest in het oog springende eigenschappen van manganaten LaMnO3 CaMnO3 is het effect van een magnetische overgang op de elektrische geleiding. Jonker en Van Santen vonden al in 1950 dat de weerstand halfgeleidend is boven de magnetische ordeningstemperatuur, Tc , en metallisch daaronder. Het gevolg is een maximum in de weerstandscurve tegen temperatuur. In 1993 kwam een belangrijke ontdekking. In dunne films werd een daling van de weerstand onder invloed van een extern magnetisch veld waargenomen door Chahara et al. en Von Helmolt et al. Deze daling was ”slechts” 50% van de oorspronkelijke weerstand. Een jaar later bleek dat het mogelijk is om de weerstand met enige grootte-ordes te verlagen. De term Colossal Magnetoresistance (CMR), (Kolossale Magnetoweerstand), was geboren. De nieuwe term lijkt op de term Giant Magnetoresistance (GMR), (reusachtige Magnetoweerstand) die al gebruikt werd voor de weerstandsverandering in ferromagnetische / non-magnetische multilagen. GMR wordt veroorzaakt door spin gepolariseerd transport door grensvlakken en komt alleen voor bij temperaturen beneden Tc , terwijl CMR zijn origine vindt in magnetische ordening en beperkt wordt tot temperaturen rond Tc . De ontdekking van CMR leidde tot vele artikelen beginnend met ”The discovery of colossal magnetoresistance initiated a lot of research.” en uiteindelijk ook tot dit proefschrift. Een van de aandachtspunten van dit proefschrift is het fasegebied rond de 20% CaMnO3 , waar een overgang plaats vindt van ferromagnetisch isolerend naar ferromagnetisch metallisch gedrag. Deze ferromagnetische isolator is op zich al een vreemde fase, aangezien ferromagnetisme in het algemeen met metallisch gedrag geassocieerd wordt. Daarnaast is er nog de orbitaalordening in LaMnO3 , die ook niet meer waargenomen wordt boven 115

116

Samenvatting

20% doping. De precieze concentratie-afhankelijkheid van de orbitaalordening is niet bekend. Tevens zijn er tegenstrijdige meningen over de invloed van de orbitaalordening op de elektronische eigenschappen te vinden in de literatuur. De nadruk in dit proefschrift ligt op de structurele respons, veroorzaakt door fenomenen met een elektronische oorsprong, zoals Jahn-Teller vervormingen, ferroelektriciteit en orbitaalordening. Aangezien de metaal-zuurstof bindingslengten en -hoeken de uitwisselingsinteracties bepalen, is een diepe kennis van de structuur noodzakelijk om de fysica achter de fenomenen te begrijpen. De elektronische en magnetische eigenschappen van de hier onderzochte materialen zijn sterk aan elkaar, en ook aan het kristalrooster gekoppeld. Hierdoor kunnen de meeste eigenschappen en overgangen niet beschreven worden met een één elektron model. Deze verbindingen maken dan ook deel uit van de ”sterk gecorreleerde elektron systemen”. De sterke koppeling tussen de elektronen en het onderliggende rooster heeft tot gevolg dat een kleine verandering van de chemische samenstelling, zoals de verhouding tussen drieen tweewaardige ionen op de A-positie (zie volgende alinea) of de gemiddelde straal van de ionen op de A-positie, grote veranderingen teweeg kan brengen in de fysische eigenschappen. Een zelfde verandering kan ook optreden door externe effecten als een magneetveld, hydrostatische druk of een verandering van de temperatuur. Een van de interessantste vragen is waarom het ene materiaal een goede geleider is, terwijl het andere gelokaliseerde en geordende ladingsdragers heeft. De perovskiet kristalstructuur kan gezien worden als een driedimensioneel netwerk van hoekgeschakelde MnO6 octaëders, waarbij het Mn ion in het midden van de octaëder zit. Acht octaëders vormen een kubus, met in het midden van deze opgespannen kubus de A-positie. In de kubische variant is de A-positie twaalfvoudig omringd. Maar typisch is de ionstraal van het A-ion kleiner dan de ruimte waarin het ligt. Deze ruimte kan verkleind worden door de octaëders ten opzichte van elkaar te draaien. Van de vele mogelijkheden zijn er twee ”standaard” in de manganaten. De ene levert een rhombische ruimtegroep op, de ander een orthorhombische, Pnma. De twaalf A-O bindingsafstanden zijn dan ongelijk geworden. De overgangsmetalen hebben als gevolg van hun oxidatietoestand de elektronische structuur [Ar] 3dn , waarbij n een geheel getal is tussen 0 en 10. Deze maximaal tien 3d orbitalen worden door een octaëdrische omringing van O anionen opgesplitst in twee banden: de lager in energie liggende t2g band met drie orbitalen en de hogere eg band met twee orbitalen. Mn3+ heeft vier 3d elektronen. De eerste drie elektronen zullen dus in de t2g band komen, het vierde elektron in één van de twee eg orbitalen. Een theorema, van Jahn en Teller, zegt nu dat deze ontaarding tot een instabiele toestand leidt en dat door een kristalroostervervorming de ontaarding opgeheven zal worden. Deze Jahn-Teller vervorming van de octaëders ordent zich in LaMnO3 zodat in een vlak, de naastebuur eg orbitalen loodrecht op elkaar liggen. Deze vervorming en ordening van de octaëders is toegestaan binnen de ruimtegroep P nma. In CaMnO3 hebben we geen vierde elektron en dus geen vervorming. Juist deze vervorming koppelt sterk met de elektronen, waardoor er een keur van magnetische en elektronische fasen kan ontstaan. Het gedrag van de manganaten is een goed voorbeeld van de interactie tussen chemi-sche

Samenvatting

117

samenstelling, experimentele condities en fysische eigenschappen. LaMnO3 en CaMnO3 zijn beide antiferromagnetische isolatoren. In eerste instantie verwacht men van het mengkristal van LaMnO3 -CaMnO3 geen spectaculaire effecten. Echter, in het fasediagram vinden we ook ferromagnetisme, metalliciteit en verscheidene ladings- en spinordeningen. De oorzaak uit zich in het verschil in kristalstructuur. Hoewel beide verbindingen de perovskiet kristalstructuur hebben, bestaat LaMnO3 uit vervormde MnO6 octaders, terwijl deze in CaMnO3 perfect zijn. De oorzaak van de vervorming is de kristalveldopsplitsing van 3d orbitalen in een octadrische omringing. In het fasediagram van LaMnO3 -CaMnO3 vinden we onder andere een ferromagnetisch metaal tussen 20 en 50% CaMnO3 . Bij nog grotere concentratie CaMnO3 treden er verscheidene ordeningen van lading en spin op. Het ferromagnetische metaal wordt uitgelegd aan de hand van het principe van double exchange (dubbel uitwisseling). De antiferromagnetische isolatoren aan de uiteinden van het fasediagram worden verklaard met het superexchange (superuitwisseling) model. Een heel ander aspect is het effect van de gemiddelde ionstraal van de A-positie. In eerste instantie neemt de orthorhombische vervorming toe met afnemende ionstraal tot aan de straal van Y. Echter, voor YMnO3 wordt een fundamenteel andere kristalstructuur gevonden. De kleine lanthaniden vormen hexagonale manganaten. De twee meest in het oog springende veranderingen ten opzichte van de orthorhombische manganaten zijn het pseudotweedimensionale karakter van de structuur en de anomale vijfvoudige, trigonale bipyramidale omringing van het Mn ion door de anionen. Deze bipyramides zijn hoekgeschakeld tot trigonale roosters, maar er is geen directe Mn−O−Mn verbinding tussen de lagen. De A ionen bevinden zich daartussen. Ook hier zijn de fysische eigenschappen interessant, doordat er een combinatie van ferroelektriciteit en magnetisme optreedt. Dat is tegenstrijdig met het algemene beeld dat ferroelektriciteit veroorzaakt wordt door ”d0 ”-ionen, zoals Ti4+ en Nb5+ , en magnetisme door atomen of ionen met d-elektronen, zoals Mn, Fe en Ni. Het eerste deel (hoofdstukken 2 en 3) van het proefschrift behandelt de orthorhombische manganaten, het tweede deel (hoofdstukken 4 tot 7) verschillende aspecten van de hexagonale fase. Bovendien wordt er in hoofdstuk 5 en 7 ook gekeken naar de overgang en verschillen tussen de twee fasen. Hoofdstuk 2 is getiteld ”Tweeling model voor orthorhombische manganaten”. Tweelingen zijn aan elkaar grenzende kristallen met een specifieke kristaloriëntatierelatie. Deze speciale oriëntatierelatie is veroorzaakt door, in dit geval, een structurele overgang, die gepaard gaat met een verlaging van de symmetrie. In de orthorhombische manganaten vindt deze structurele overgang plaats uitgaand van de kubische symmetrie. De overgang gaat gepaard met van de roosterparameter in de y-richting, algemeen √ een verdubbeling √ aangeduid met 2 × 2 × 2 eenheidscel. Uit symmetrie overwegingen kan de orthorhombische fase ook ontstaan met een verdubbeling langs een van de andere kubusrichtingen. Een van de grote valkuilen is dat deze ”speciale” oriëntaties leiden tot een rooster dat lijkt op een 2 × 2 × 2 eenheidscel. We presenteren een methode om de structuur toch te kunnen afleiden uit éénkristaldiffractie. Deze methode wordt gebruikt in Hoofdstuk 3 ”Jahn-Teller ordening versus ferromag-

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netisch metaal”, waarin LaMnO3 -CaMnO3 in de omgeving van 20% doping onderzocht wordt. Er wordt gebruik gemaakt van drie éénkristallen met 16%, 19% en 25% CaMnO 3 . De kristalstructuur is onderzocht met éénkristaldiffractie tussen de 100 en 300 K. Uit de posities van de ionen worden twee parameters gedistilleerd. Een parameter beschrijft de draaiing van de octaders, de ander beschrijft de vervorming van de octaëders. Tevens blijkt dat de positie van het A-ion afhankelijk is van zowel de draaiing als de vervorming van de octaders. Het blijkt dat het opheffen van de lange afstand orbitaalordening een voorwaarde is voor het ontstaan van een metallische grondtoestand. Niet het overschrijden van een kritische ladingsdragerconcentratie maar de onderdrukking van de orbitaalordening genereert de metallische grondtoestand. In Hoofdstuk 4 ”Structureel overzicht van hexagonale niet-perovskiet AMnO3 ” wordt een inleiding in de hexagonale structuur gegeven. De structuur kan beschreven worden in termen van polyeders, maar ook als een dichtst gepakte stapeling van O en A ionen. Er wordt ingegaan op het ferroelektrische gedrag, dat zijn origine vindt in de achtvoudige omringing en het bijbehorende lokaal dipool moment van het A ion. Hoofdstuk 5 ”De hexagonale naar orthorhombische overgang” gaat in op de overgang tussen de orthorhombische en de hexagonale fasen. Het is bekend dat hoge druk synthese de orthorhombische fase kan opleveren voor YMnO3 . Dit kan al bij lagere druk dan voorheen gerapporteerd. Verder wordt er gekeken naar het YMnO3 -GdMnO3 fasediagram. GdMnO3 is stabiel in de orthorhombische structuur. In plaats van een kritische concentratie waarbij de stabiele fase omgaat van de hexagonale fase naar orthorhombische fase, bestaat er een breed gebied waarin beide fasen stabiel naast elkaar bestaan, terwijl de orthorhombische fase verwacht wordt op basis van de ionstraal. Wat dit tweefasengebied bijzonder maakt is dat uit de roosterparameters een continue verandering van de concentratie GdMnO3 afgeleid kan worden, overeenkomstig de nominale concentratie. Er treedt dus geen chemische fasescheiding op. De elektronische eigenschappen van de hexagonale fase zijn het onderwerp van Hoofdstuk 6 ”Asymmetrie van elektronen gatdoping in YMnO3 ”. Het CMR effect is het prominentst rond de magnetische overgang. Voor praktische toepassingen is dus een hoge overgangstemperatuur gewenst. Deze temperatuur wordt mede bepaald door de grootte van het lokale magnetisch moment en kan dus verhoogd worden door de spin per atoom te vergroten. Het idee is om dit toe te passen in de manganaten. Mn3+ heeft vier 3d elektronen en een spin van S = 2, Mn4+ heeft nog maar drie 3d elektronen. Het ligt dus voor de hand om Mn2+ te onderzoeken dat vijf 3d elektronen heeft. Dit betekent dat we de A positie deels door vierwaardige elementen moeten gaan bezetten, bijvoorbeeld LaMnO3 -PbMnO3 . Het blijkt dat we alleen succes krijgen door het systeem YMnO3 -ZrMnO3 te onderzoeken. Door het tweedimensionale karakter van deze structuur worden de extra elektronen gelokaliseerd, ze hebben geen interactie met andere Mn posities. Verder nemen we een afname van het magnetisch moment waar, wat verklaard wordt met een bandenstructuur berekening die laat zien dat de opsplitsing tussen de meerderheidsspin en minderheidsspin banden van dezelfde grootte is als de breedte van de meerderheidsspin band. Uit de literatuur blijkt dat YMnO3 -CaMnO3 wel een sterke toename van de geleiding laat zien. Het verschil tussen elektron doping (Zr) en gaten doping (Ca) wordt veroorzaakt door de kristalveldopsplits-

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ing. In een trigonale bipyramidale omringing is de opsplitsing in drie banden, de onderste twee bestaan ieder uit twee orbitalen. Ongedoopt YMnO3 heeft dus volledig bezette banden. Elektronen doping introduceert ladingsdragers in de bovenste band, maar deze heeft een zeer zwakke interactie met andere Mn orbitalen. Gaten doping daarentegen brengt ladingsdragers in de middelste band met een grote overlap met andere Mn orbitalen. Het laatste hoofdstuk ”Oorsprong van de hexagonale fase” behandelt het paradoxale voorkomen van de hexagonale fase in de manganaten. Het paradoxale aan deze structuur is dat hij alleen voorkomt met Mn als overgangsmetaal ion. Andere overgangsmetalen, met name ijzer en vanadium, vormen voor alle lanthaniden stabiele orthorhombische perovskiet kristallen. In het algemeen wordt de tolerantiefactor, die de orthorhombische vervorming kwantiseert, gezien als de drijvende kracht achter de hexagonaal-orthorhombisch overgang. Wordt de tolerantiefactor te klein, dan is de perovskiet fase niet stabiel meer. Maar de tolerantiefactoren voor LuFeO3 en LuVO3 zijn kleiner dan die voor YMnO3 . Volgens het kritische tolerantiefactor principe zouden deze Lu verbindingen dus ook hexagonaal moeten zijn. De reden voor AMnO3 om al tussen Dy en Y de overgang te hebben, is dat in de manganaten naast de vervorming door de lanthanide ionstraal een extra vervorming door de orbitaalordening aanwezig is. De extra vervorming verhoogt de kritische tolerantiefactor, waardoor al bij grotere lanthanide ionstraal de hexagonale fase gevormd wordt.

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List of publications • Hexagonal YMnO3 , B.B. Van Aken, A. Meetsma and T.T.M. Palstra, Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 57, 230 (2001). • Asymmetry of electron and hole doping of YMnO3 , B.B. Van Aken, J.-W.G. Bos, R.A. de Groot and T.T.M. Palstra, Phys. Rev. B 57, 125127 (2001). • Hexagonal ErMnO3 , B.B. Van Aken, A. Meetsma and T.T.M. Palstra, Acta Crystallogr., Sect. E: Struct. Rep. Online 57, i38 (2001). • La-site shift as probe for Jahn-Teller effect, B.B. Van Aken, A. Meetsma and T.T.M. Palstra, submitted to Phys. Rev. Lett. (2001) cond-mat/0105197. • Twin model for orthorhombic perovskites, B.B. Van Aken, A. Meetsma and T.T.M. Palstra, submitted to Phys. Rev. B (2001) cond-mat/0103628. • Pressure dependence of orthorhombic - hexagonal transition in LnMnO3 , J.-W.G. Bos, B.B. Van Aken and T.T.M. Palstra, submitted to Chem. Mater (2001) condmat/0106335. • Structural view of hexagonal non-perovskite AMnO3 , B.B. Van Aken, A. Meetsma and T.T.M. Palstra, cond-mat/0106298.

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Nawoord In dit hoofdstuk mag ik complimentjes, veren voor in je hoed en plakplaatjes uitdelen aan een ieder die een bijdrage geleverd heeft aan de totstandkoming van dit proefschrift. We onderscheiden als belangrijkste de kopgroep. Hierin zitten de mensen zonder wie ik dit proefschrift niet had kunnen schrijven. De achtervolgingsgroep bestaat voornamelijk uit diegenen die ”slechts” een bijdrage geleverd hebben, opdat het proefschrift bevat wat het bevat. Zonder hen had ik ook een dissertatie geschreven, maar was het een andere richting opgegaan of had het niet de huidige kwaliteit gehaald. In het peleton zitten de resterende mensen. De meeste hebben geen wetenschappelijke bijdrage geleverd aan mijn onderzoek. Toch zal een groot deel van degenen die dit nawoord lezen, zich zelf al dan niet met naam en toenaam terug vinden in deze groep. Al was het maar omdat het aantal Nederlands sprekende wetenschappers in ons vakgebied behoorlijk klein is. En er is natuurlijk een bezemwagen. Tijdens de laatste twee jaar van mijn studie, bleef mijn blik vooruit meestal hangen op de pijl die wees naar een baan als AIO, zodat ik bij mijn eerste bezoek aan de ”wetenschappelijke vergadering” van de stichting FOM (Fundamenteel Onderzoek der Materie) genteresseerd rond keek naar mogelijke promotieplaatsen. De eerste lezing werd gegeven door Prof.Dr. T.T.M. Palstra van de Rijksuniversiteit Groningen. In het begin dacht ik het wel te kunnen volgen, maar bij het concept polaron haakte ik af. Daarna kwam er een lezing over strepen door Dr. J. Zaanen. Ondanks zijn uitbundige manier van presenteren, had ik al wel door dat de vaste stof fysica niet mijn pakkie-an was. Wel zag ik op het prikbord nog een aankondiging voor AIO-plaatsen op het gebied van de overgangsmetaal oxiden. En als ijzerboer trok deze mededeling even mijn aandacht. Een paar maanden later trof ik dezelfde advertentie aan op het prikbord bij de koffiemachine op de tweede verdieping van het lab in Delft. Het contact met Thom Palstra was snel gelegd en halverwege mijn bezoek aan Groningen kwam ik tot de conclusie dat ik zijn verhaal al eens eerder gehoord had. Een lezing over mijn afstudeeronderzoek maakte deel uit van de sollicatie. Zenuwachtig als ik was voelde ik enige transpiratie opkomen tijdens mijn lezing. ”Interessant onderzoek. Maar je moet wel wat aan je temperatuur veranderen, als je hier wilt werken.” was dan ook een teleurstellende opmerking, totdat ik begreep dat het over het onderzoek zelf ging. 123

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Nawoord De 15 graden tussen mijn hoogste en laagste meettemperatuur vallen natuurlijk in het niet bij het 400 Kelvin bereik van de MPMS en de PPMS. De oorspronkelijke twijfel of ik wel genoeg bagage had voor dit onderwerp, werd weggenomen met het vertrouwen dat Thom in mij uitsprak door mij een promotiepositie aan te bieden. Dit proefschrift getuigt van de onterechte twijfel mijnerzijds, en het terechte vertrouwen van Thom’s kant. Thom heeft mij veel vrijheid gegeven bij het onderzoek doen. Al heb ik sterk de indruk dat de meeste richtingen eerder uit de lucht vielen dan dat een van ons er persoonlijk invloed op heeft kunnen uitoefenen. Toch betekent die vrijheid niet dat ik mocht doen wat ik wou. Een nieuw experiment moest altijd een doel hebben. En nieuwsgierigheid telde niet. Een aantal in mijn ogen veelbelovende onderzoeksvragen werd afgedaan met ”jaren zeventig onderzoek”. Namelijk een goed probleem hoort ”oneindig” moeilijk te zijn. Groot was dan ook mijn vreugde als het inderdaad veel moeilijker bleek te zijn, dan ik het mij voorgesteld had. Ik hoop dat ik deze manier van wetenschap bedrijven overgenomen heb. Enthousiasme en nieuwsgierigheid zijn natuurlijk van belang, maar ik heb geleerd dat je je altijd moet afvragen wat jouw experiment bijdraagt aan het grote geheel. Twee mensen die ook heel belangrijk geweest zijn voor het tot stand komen van dit proefschrift zijn mijn ouders, Gerda en Frank. Zij hebben mij altijd gestimuleerd, zowel in materiële als in geestelijke zin, met mijn studie en algemene ontwikkeling. Als ik twijfelde of ik weer iets naast mijn studie zou doen, dan was het antwoord altijd positief MITS de studie maar afgemaakt zou worden. Tevens zou het een stuk lastiger geweest zijn zonder het doorzettingsvermogen en ruimtelijk inzicht dat ik meegekregen heb. Een belangrijk deel van mijn promotieonderzoek bestaat uit éénkristaldiffractie experimenten. En wie éénkristaldiffractie zegt, bedoelt Auke Meetsma. Samen met Auke heb ik vele uren gediscussieerd over tweelingen, ruimtegroepen en verfijningen, waarbij we schrokken van ons eigen stemgeluid. Het is prettig en goed samenwerken met Auke, wat zich vertaalt in soms lange wachtrijen. Hiervoor had ik de ideale oplossing door weken aaneen, een CAD4 of de APEX bezet te houden. Hierdoor konden anderen niet meten. Niet meten = geen structuren oplossen = geen wachtrijen. Auke en ik hebben op deze manier gevonden dat de ferroelectriciteit in hexagonaal YMnO3 verbindingen zijn origine vindt in de anomale zevenvoudige omringing van het yttrium ion. Gemiddeld eens per week kwam Rob de Groot bij ons in de kelder. Zijn aanwezigheid is direct merkbaar aan de tabakslucht en de verhalen over de vroege wetenschap tijdens de koffiepauzes. Er wordt wel eens van mensen gezegd dat ze van alles een probleem kunnen maken. Rob is meer de persoon die voor alles een oplossing weet of je in ieder geval op het rechte pad zet. Neem bijvoorbeeld de afname van het magnetisch moment met toenemende Zr concentratie. Dit was voor mij een grote puzzel, Rob kijkt er na, gebruikt wat jargon en na wat rekenwerk ligt de verklaring

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klaar: De magnetische opsplitsing is kleiner waardoor het Mn niet volledig high spin is, zie ook Hoofdstuk 6. Een jaar lang mocht ik Gabi Maris begeleiden bij haar Master’s studie. Gabi en ik hebben kennis gemaakt met het grootste nadeel van chemie. Het verschil met de oude alchimisten is nog niet zo groot, zeker niet met de experimentele vaste stof synthese. Onze gezamenlijke pogingen om double layered perovskieten te groeien bleken vruchteloos, wat we ook bij elkaar mengden, roerden en bakten. Het afstudeeronderzoek van Jan-Willem Bos werd ook door mij begeleid. Terwijl hij met olie, grafiet en andere dingen zijn handen vuil maakte, keek ik op een afstand toe. Dit is ook veiliger met hoge druk experimenten. Blijkbaar beviel onze samenwerking zo goed dat hij besloot om op stage te gaan in Japan, iets wat hij op zijn afscheidsborrel nogmaals benadrukte. Ik had gehoopt dat hij daar een verklaring zou vinden voor het disorder-doping fasediagram van Y1−x Gdx MnO3 , zoals we dat in Hoofdstuk 5 presenteren. Het leven in de kelder zou een stuk rustiger geweest zijn zonder de kelderbewoners Christine, Jacob, Montu, Graeme, Coen, Ronald, Jasper, Anne en Amir. Geen commentaar op mijn muziekkeuze, geen langsvliegend boorgruis, geen stuiterende knikkers, geen mobiele telefoons, geen apel telefonic pentru Gabi (telefoon voor Gabi). Maar ook koffiedrinken in je eentje, iets wat ik nog steeds triester vind dan bierdrinken in je eentje. Niemand om je PC frustaties mee te delen. Alleen een rondje door het bos wandelen in Lunteren. No vegetable side dishes en niemand om Auke’s courgettes mee te delen. Hetzelfde geldt natuurlijk ook voor de gelukkigen die geen werkplek six feet under hebben hier in het lab, waaronder Karina, Wilma, (misschien iets te veel boswandelingen) Diana D, Diana R, Peter en Mark. Frans van der Horst wordt bedankt voor het gebruik van de poeder Röntgendiffractometer; Henk Bron, Coen van Dijk worden bedankt voor de electronenmicroscopie; Fop ten Broek voor het gebruik van het radiochemie lab; Ron Smith is acknowledged for the support at ISIS. Jan Spoelstra en Dirk Wieringa voor alle inspanningen om de CAD4’s, APEX en de koeling draaiende te houden. Interessante, hevige en vaak constructieve discussies binnen en buiten het lab worden zeer gewaardeerd. Ik dank: Gerrit Wiegers, Graeme Blake, Jan de Boer, Ilya Elfimov, George Sawatzky, Dirk van der Marel, Dana Tomuta, Jan Aarts, John Mydosh, Paul Attfield, Peter Littlewood, Andy Mackenzie, Juan Rodríguez-Carvajal, Martine Hennion, Ramanathan ’Sury’ Suryanarayanan, Art Ramirez, Pengcheng Dai, Takashi Mizokawa, Sang-Wook Cheong, Ravi Narasimhan, Nai-Chang Yeh, Montu Saxena and Neil Mathur. In het bijzonder wil ik hier de mensen bedanken die mijn manuscript gelezen, bekritiseerd en gecorrigeerd hebben waaronder de leescommissie: Tjipke Hibma, Daniel Khomskii en Lou-Fé Feiner. Antoine, Sabine en Clara worden bedankt voor hun bijdrage aan de Nederlandse samenvatting, wat niet mijn sterkste kant is. Nederlands bedoel ik. Studeren en promoveren houdt meer in dan alleen leren, studeren en op de meest

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Nawoord ongelukkige tijdstippen en plaatsen experimenten doen. Velen hebben dan ook hun best gedaan om de mens Bas zoveel mogelijk mens te laten zijn. Waarvan akte. Mijn eerste looppogingen deed ik aan de hand van mijn moeder en later achter mijn vader aan. Maar hardlopen heb ik echter pas leren waarderen bij De Delvers, alwaar ik nu een van de jongere Young Old Boys ben. Echte klassiekers, rondjes Hoogkérk en brugzitten zal ik niet vergeten dankzij de mannen van loopgoeroe Pov. Mijn leven is verrijkt met de transfer van Jong en Wild naar Tou eem (Team Dirk), waar ik van de echte basisgroepmentaliteit heb mogen proeven, alsmede van tapenades, Kriek en de smaak van gezelligheid. Hoogtepunten zijn de rondjes Punt en IJsselmeer. De meeste mensen verschillen met mij van mening over wat nu ”ver” is. De afgelopen jaren heb ik echter geleerd dat verre vrienden heel wat waard zijn. Behalve als ze met je huissleutel op pad zijn, die kan je beter bij de goede buur laten. Clara, Plunk, Panda, (oud)-LMAK-ers, Antoine, Rolf en Simone zullen wel begrijpen wat ik bedoel. Net als Jet, Jaco, Piet, Annemie, Roland en Adèle, maar dat is dan ook (bijna) familie. En dan is er nog iemand die er voor zorgt dat ik regelmatig tot aan mijn knien in de drek staat, dat ik eind December ga skin terwijl het vreselijk vriest, dat mijn oren tot driemaal toe vervellen (in Schotland, sic), dat ik meer treinreizen plan, maak en mis dan de gemiddelde NS-er en dat ik in het weekeinde vroeger op sta dan door de week: Sabine. Want zij gelooft in mij.