Structural and magnetic phase transitions in ...

JOURNAL OF APPLIED PHYSICS 115, 034102 (2014)

Structural and magnetic phase transitions in Bi12xNdxFe12xMnxO3 multiferroics ~ o1 V. A. Khomchenko,1,a) L. C. J. Pereira,2 and J. A. Paixa 1

CEMDRX/Department of Physics, University of Coimbra, P-3004-516 Coimbra, Portugal Unidade de Ci^ encias Quımicas e Radiofarmac^ euticas, IST/CTN, Instituto Superior T ecnico, Universidade T ecnica de Lisboa/CFMCUL, P-2686-953 Sacav em, Portugal

2

(Received 14 November 2013; accepted 6 January 2014; published online 15 January 2014) Crystal structure, local ferroelectric and magnetic properties of the Bi1xNdxFe1xMnxO3 (0.05 x 0.25) ferromanganites have been studied at room temperature to reveal effect of the simultaneous Ln/Mn substitution on the multiferroic behavior of the BiFeO3 perovskite. The substitution tends to suppress polar displacements in initial rhombohedral phase to give rise to an intermediate PbZrO3-like antiferroelectric ionic arrangement at x ¼ 0.11. Further increase of the Nd/Mn concentration stabilizes nonpolar structure specific to NdMnO3. Magnetic state of the Bi1xNdxFe1xMnxO3 compounds has been found to be structurally driven. The ferroelectric compounds demonstrate a dominant antiferromagnetic behavior. Magnetic field is able to modify the antiferromagnetic ordering to stabilize a weak ferromagnetic state. A threshold field inducing the metamagnetic transformation decreases with increasing the substituent’s content. However, a critical Nd/Mn concentration that would yield weak ferromagnetism at H ¼ 0 exceeds the upper limit of the compositional range of the ferroelectric phase existence, so the purely weak C 2014 AIP Publishing LLC. ferromagnetic state is realized in nonpolar solid solutions only. V [http://dx.doi.org/10.1063/1.4862433]

I. INTRODUCTION

Modern solid-state technology moves away from the applications based on a single property (electric, magnetic, or mechanical) to be concentrated on those using coupled response phenomena (magnetoresistance, magnetostriction, piezoelectric effect, etc.). This tendency underlies great interest in the materials possessing ferroelectric polarization and magnetic ordering in the same phase.1–4 Indeed, coupling between the corresponding order parameters gives rise to a magnetoelectric effect (induction of magnetization by an electric field or electric polarization by a magnetic field), which might be used in advanced electronic devices. However, contradiction between conventional origins of the cation off-centering in ferroelectrics and the formation of magnetic ordering5 makes multiferroic materials relatively rare. Despite the persistent attempts to develop novel singlephase magnetic ferroelectrics, BiFeO3 remains the only thermodynamically stable compound demonstrating a simultaneous spin and electric dipole order far above the room temperature (TAFM 640 K, TFE 1100 K).6 Nevertheless, a complex cycloidal-type antiferromagnetic structure characteristic of this material7 seriously limits its practical applicability to motivate further research in this field. Recent investigations have shown that the magnetic state of bismuth ferrite can be effectively changed via a chemical substitution/epitaxial strain,8–12 thus indicating principal ways towards improved magnetoelectric functionality.

a)

Author to whom correspondence should be addressed. Electronic mail: [email protected]. Telephone: þ351 239 410 637. Fax: þ351 239 829 158

0021-8979/2014/115(3)/034102/6/$30.00

Bismuth ferrite crystallizes in a rhombohedral structure (space group R3c)13,14 compatible with the spontaneous polarization (Ps 100 lC/cm2)15,16 directed along the [001]hex axis. Lanthanide (Ln) A-site doping changes the polar atomic arrangement and gives rise to a ferroelectric to antiferroelectric (R3c!Pnam) structural phase transformation. The threshold concentration inducing the polar-nonpolar transition in the Bi1xLnxFeO3 series depends on ionic radius of the substituting element and varies from x ¼ 0.18 (for Ln ¼ La) to x ¼ 0.115 (for Ln ¼ Tb).17–21 This transformation removes the magnetic modulation in Fe sublattice and stabilizes a canted antiferromagnetic structure with the spontaneous magnetization Ms 0.3 emu/g.17–21 In contrast to lanthanides, most of 3d transition metals can hardly be accommodated in crystal lattice of bismuth ferrite. Manganese, however, possesses relatively high solid solubility limit in BiFe1xMnxO3 (x 0.3 for the ambient-pressure synthesis).22 The BiFe1xMnxO3 compounds maintain the initial crystal and magnetic structures in the entire concentration range of the solid solutions realization.22,23 The relatively weak impact of the Mn doping on the multiferroic properties of BiFeO3 is due to the closeness of ionic radii of the host and substituting elements. The latter can be naturally used for a fine tuning of the ferroelectric and magnetic behavior of bismuth ferrite via combined Ln/Mn substitution.24–30 Indeed, a Mn doping-driven decoupling of the antiferromagnetic-weak ferromagnetic (AFM-wFM) and ferroelectric-antiferroelectric (FE-AFE) transitions resulting in the appearance of a weak ferromagnetic polar phase uncommon for the Bi1xLnxFeO3 (Ln ¼ Pr, Nd)19–21 and BiFe1xMnxO3 (Refs. 22 and 23) perovskites has been recently found in the Bi0.89Pr0.11Fe1xMnxO3 (Ref. 25) and

115, 034102-1

C 2014 AIP Publishing LLC V

034102-2

~o Khomchenko, Pereira, and Paixa

Bi0.92Nd0.08Fe1xMnxO3 (Ref. 27) series. Investigation of influence of Mn doping on the crystal structure of the lanthanide-modified compounds possessing fixed A-sublattice compositions and representing both polar and nonpolar phases of the Bi1xLnxFeO3 perovskites has shown that, despite the opposite effect of the A-site Ln and B-site Mn doping on the Goldschmidt tolerance factor determining the degree of distortion in perovskites, structural phase evolution in the Bi1xLnxFeO3 and (Bi, Ln)Fe1xMnxO3 series tends to follow the same scenario.24–28 To contribute to better understanding of this behavior and complete analysis of the magnetic/ferroelectric effects induced in BiFeO3 through the combined Nd/Mn doping26,27 (the latter is important from the viewpoint of searching for the conditions favoring stabilization of a polar weak ferromagnetic state in the co-doped materials), we performed synthesis and investigation of the crystal structure and multiferroic properties of the simultaneously substituted Bi1xNdxFe1xMnxO3 (0.05 x 0.25) perovskites (the chosen compositional range contains characteristic concentrations inducing the structural and magnetic phase transformations in this system). II. EXPERIMENTAL

Polycrystalline samples of Bi1xNdxFe1xMnxO3 (0.05 x 0.25) were prepared by a conventional solid-state reaction method using the high-purity oxides Bi2O3, Nd2O3, Fe2O3, and Mn2O3. The reagents were taken in stoichiometric cation ratio, mixed and pressed into pellets. The synthesis was carried out in air in a temperature range from 910 C (x ¼ 0.05) to 960 C (x ¼ 0.25) for 30 h. X-ray diffraction (XRD) patterns were collected at room temperature using a Bruker D8 Advance diffractometer with Cu Ka radiation. The data were analyzed by the Rietveld method using the FullProf program.31 Local ferroelectric properties were investigated with piezoresponse force microscopy (PFM) using a commercial setup NTEGRA Prima (NT-MDT). The NSG30 probes with a resonance frequency around 300 kHz were used. Domain visualization was performed under an applied ac voltage with an amplitude Vac ¼ 5 V and frequency f ¼ 100 kHz. Local piezoelectric hysteresis loops were measured inside individual grains by applying the consecutive voltage pulses and measuring the piezoelectric response as a function of the voltage. Magnetic measurements were performed with a superconducting quantum interference device (SQUID) magnetometer (S700X, Cryogenic Ltd).

J. Appl. Phys. 115, 034102 (2014)

in Glazer’s notation32,33) and polar anion/cation displacements along the h111ic direction of the parent cubic subcell (inset in Fig. 1(a)). The angle between the corner-linked octahedra, as defined in Ref. 34, gradually decreases from h 160 for x ¼ 0 (Ref. 14) to h ¼ 159.0(3) for x ¼ 0.1, thus suggesting enhancement of lattice deformation with increasing the Nd/Mn content. Further increase of the substituent’s concentration destabilizes the rhombohedral lattice, so a two-phase structural state (with 29(1)% of the R3c phase) is observed for the x ¼ 0.11 samples. In the concentration range of the rhombohedral phase (co)existence, the compositional dependence of polar ionic displacements (Fig. 2) follows the trend typical of both pure35 and doped9,10 bismuth ferrite upon approaching a heating-induced ferroelectric to paraelectric transition. The ionic component of spontaneous polarization evaluated from the polar shifts36,37 decreases from Pi 64 lC/cm2 for x ¼ 0.05 to Pi 47 lC/cm2 for x ¼ 0.11 (Fig. 2). These values are reasonably smaller than that characteristic of pure bismuth ferrite (Pi 72 lC/cm2).14 Ferroelectricity in BiFeO3 is driven by the stereochemically active Bi3þ cations containing a highly polarizable lone pair of valence electrons.6 Accordingly, the substitution-induced decrease of polarization observed in the Bi1xNdxFe1xMnxO3 series should be mainly associated with a change of the average A-site polarizability.38 Nevertheless, the B-sublattice modification can also contribute to the resulting polarization drop.

III. RESULTS AND DISCUSSION A. Substitution-induced structural phase transitions

The X-ray diffraction patterns obtained for the Bi1xNdxFe1xMnxO3 (x 0.1) samples were successfully fitted using a single-phase rhombohedral model (space group R3c) specific to pure BiFeO3 (Refs. 13 and 14) (Fig. 1(a)). With respect to an ideal perovskite (those crystal structure has a Pm 3m symmetry), lattice distortions in the low-doped compounds are determined by the combination of antiphase tilting of the adjacent oxygen octahedra (aaa tilt system

FIG. 1. Observed, calculated, and difference XRD patterns for the Bi1xNdxFe1xMnxO3 compounds: (a) x ¼ 0.05 [S.G. R3c; a ¼ b ¼ 5.5738(1) ˚ , c ¼ 13.8162(3) A ˚ ], (b) y ¼ 0.12 [S.G. Pnam; a ¼ 5.5870(1) A ˚, A ˚ , c ¼ 15.6075(3) A ˚ ], (c) y ¼ 0.2 [S.G. Pnma; a ¼ 5.5729(1) b ¼ 11.2229(2) A ˚ , b ¼ 7.8293(2) A ˚ , c ¼ 5.5337(1) A ˚ ]. The allowed Bragg reflections are indiA cated by ticks. The insets show schematic views of the corresponding crystal structures.

034102-3


FIG. 2. The compositional dependences of the ionic polarization (blue circles) and polar displacements of the hBi/Ndi3þ (white bars) and hOi2 (green bars) ions (the latter is taken in the setting with the hFe/Mni3þ ions fixed in the centrosymmetric position) for the rhombohedral phase of the Bi1xNdxFe1xMnxO3 system.

Indeed, Mn doping-driven decrease of the room-temperature polarization has been recently reported for the Bi0.92Nd0.08Fe1xMnxO3 series with the fixed A-sublattice composition.27 In BiFe1xMnxO3 (x 0.3) system, the B-site substitution-induced lattice instability shows itself in decrease of the ferroelectric Curie temperature (5 C per 1% Mn).22 The major doping-induced phase of the Bi0.89Nd0.11 Fe0.89Mn0.11O3 compound is isostructural with the intermediate antiferroelectric phase typical of the Bi1xLnxFeO3 (Ln ¼ La-Tb) systems.17–21 The corresponding structure (also characteristic of the single-phase x ¼ 0.12, 0.13, and 0.15 samples investigated in this work) can be described in terms of the modulated (aacþ)/(aac) octahedral tilting superimposed on the PbZrO3-like39 antipolar displacements of the A-site cations along the [110/1 10]c directions of the parent cubic subcell (Fig. 1(b)). Similar to the behavior observed for the antiferroelectric Bi0.825Nd0.175Fe1xMnxO3 (x 0.3) perovskites with increasing the Mn concentration,26 gradual decrease of intensity of the diffraction peaks originating from both the antipolar displacements and the complex cþ/c modulation takes place in the Bi1xNdxFe1xMnxO3 (0.11 x 0.15) series with increasing the Nd/Mn content. Further increase of the dopants concentration stabilizes the orthorhombic structure (abþa octahedral tilted framework; space group Pnma) characteristic of the NdMnO3 manganite40 (Fig. 1(c)). In accordance with a change of the average ionic radius in the A and B sublattices of the samples under study ˚ , rNd3þ ¼ 1:27A ˚ , rMn3þ rFe3þ ¼ 0:645A ˚ (rBi3þ ¼ 1:365A (Ref. 41)), the primitive cell volume decreases with increasing the Nd/Mn concentration (Fig. 3). A discontinuous change (DVp/Vp 0.55%) indicative of the first-order phase transition is observed across the R3c-Pnam phase boundary (Fig. 3). A very similar behavior is expected for the Pnam-Pnma phase transition. Indeed, in Bi0.825Nd0.175Fe1xMnxO3 series, this structural transformation is accompanied by a step-like contraction of the primitive cell volume by 0.5%.26

J. Appl. Phys. 115, 034102 (2014)

FIG. 3. The compositional dependence of the primitive cell volume for Bi1xNdxFe1xMnxO3 series at room temperature. The dashed lines separate concentration ranges of the distinct structural phases.

The structural phase evolution characteristic of the Bi1xNdxFe1xMnxO3 perovskites is generally similar to that observed in the Bi1xLnxFeO3 (Ln ¼ Pr, Nd, Sm, Eu, Gd, Tb) systems.19–21 In the Mn-free series, the evolution could be qualitatively understood in terms of the substitution-driven change of the cation spacing.42 Indeed, the doping replacing the Bi3þ with a smaller ion (rBi3þ > rLn3þ (Ref. 41)) results in decrease of the tolerance factor t ¼ pffiffi2rðrA þrþrO Þ (rA, rB, and rO are the ionic radii of A, B, B

O

and O ions) to yield a typical scheme of the tilt transitions occurring in perovskites upon progressive deviation of t from 1 (i.e., no tilting ! antiphase tilting ! antiphase and in-phase tilting).43 Recent investigation of interplay of the octahedral tilts and polar order in BiFeO3 has shown that the preference of the compound to adopt a FE or AFE state is intimately linked to the geometric rotation pattern of the FeO6 octahedra: the antipolar distortions become energetically favorable when in-phase rotations of the FeO6 octahedra appear in the structure.44 Accordingly, the ferroelectric-antiferroelectric transformation in the Bi1xLnxFeO3 series could be basically considered as arising via the cation spacing-driven change of the octahedra tilt pattern [aaa! (aacþ)/(aac)]. This scenario, however, cannot be directly applied to the Mn-modified systems. Indeed, previous investigations of the (Bi, Ln)Fe1xMnxO3 series possessing a fixed A-sublattice composition22–28 have found that, despite the opposite influence of the Mn doping on tolerance factor (in these systems, primitive cell volume decreases with increasing Mn content), the B-site substituents give rise to the picture of structural changes that would be observed for the representative compounds upon increasing the lanthanide concentration. When compared with the Bi1xNdxFeO3 series, the tolerance factor approach should predict a broadening of the concentration range of polar phase in the Bi1xNdxFe1xMnxO3 system. In reality, suppression of the rhombohedral phase in the Bi1xNdxFeO3 perovskites occurs at the higher concentration of doping

034102-4


J. Appl. Phys. 115, 034102 (2014)

element (x 0.125).21 It is reasonable to suppose that decrease of the total polarizability induced by the change in an electronic configuration of the B-site ions27 can influence on stability of the initial octahedra tilt pattern in the BiFeO3-based compounds. Indeed, first-principles density functional calculations show that with decreasing amplitude of the polar distortions in BiFeO3, the aaa rotation pattern can become energetically less favorable than the aacþ alternative.44 B. Local ferroelectric behavior

Previous investigations of effect of the lanthanide and manganese substitution on the macroscopic polarization of BiFeO3 have shown that the chemically modified ceramic materials retain the leaky dielectric behavior inconsistent with a possibility to achieve the saturated ferroelectric hysteresis loops.45–47 Taking into account that in case of the macroscopic polarization vs. electric field measurements intrinsic ferroelectric behavior can be masked by the large leakage currents characteristic of bismuth ferromanganites,22,48 ferroelectric testing of Bi1xNdxFe1xMnxO3 samples was performed with a piezoresponse force microscopy, which was proven to be an appropriate technique for investigation of semi-insulating materials.49,50 PFM measurements of the mechanically polished Bi1xNdxFe1xMnxO3 (x 0.1) ceramics found periodic variations in the local out-of-plane piezoelectric response forming a clear stripe-like pattern of the ferroelectric/ferroelastic domains inside individual grains of the samples (Figs. 4(a)–4(d)). Neither domain sizes scale nor piezoresponse strength (the latter is comparable with that characteristic of pure BiFeO3) change significantly within the concentrational range of the single-phase rhombohedrally distorted compounds. A switchable character of polarization in the rhombohedral phase of the Bi1xNdxFe1xMnxO3 series is confirmed by the local piezoresponse versus dc voltage measurements (Fig. 4(h)); however, a large dispersion of the measured signal typical of ceramic materials does not allow the compositional dependence of the maximum piezoelectric coefficient to be reliably evaluated. PFM measurements performed for the structurally inhomogeneous x ¼ 0.11 compound have revealed a complex picture of the local piezoelectric activity consistent with the coexistence of ferroelectric (regions demonstrating a periodic contrast) and antiferroelectric (areas with an intermediate contrast) grains in the sample (Figs. 4(e) and 4(f)). In agreement with a centrosymmetric character of crystal structure of the x 0.12 compounds, no distinct PFM contrast was found for single-phase orthorhombic samples (Fig. 4(g)). C. Magnetic properties

Although BiFeO3 belongs to the so-called “type-I” multiferroics, in which ferroelectricity and magnetism appear largely independently of one another,51 an inhomogeneous magnetoelectric interaction dramatically affects magnetic subsystem of this material to stabilize cycloidal antiferromagnetic ordering in the B-sublattice.52 The modulated structure can be suppressed by applying a strong magnetic

FIG. 4. The scanning probe microscopy measurements of the Bi1xNdxFe1xMnxO3 ceramics: amplitude (left column) and phase (right column) PFM images and piezoresponse hysteresis loops obtained for two different grains of the x ¼ 0.05 sample.

field to release a weak ferromagnetic moment of 0.25 emu/g.53 Magnetization measurements performed for the Bi1xNdxFe1xMnxO3 compounds have revealed a correlation between the crystal structure/ferroelectric state and magnetic properties of the samples under study (Fig. 5). The single-phase rhombohedral compounds exhibit the magnetization behavior (Fig. 5(a)) consistent with a dominant BiFeO3-like antiferromagnetic state. Indeed, a small remanent magnetization observed in these samples is far below the value expected for doping-stabilized weak ferromagnetic phase27 and varies in a relatively narrow range from 0.023 emu/g for x ¼ 0.05 to 0.033 emu/g for x ¼ 0.1. Moreover, the 0.05 < x 0.1 compounds demonstrate a metamagnetic behavior similar to that characteristic of the Bi1xLnxFeO3 solid solutions upon the field-induced suppression of the magnetic cycloid.18,19,54 Indeed, while x ¼ 0.05 samples exhibit a linear field dependence of the magnetization up to the maximum field available in the experiment (60 kOe), a clear deviation from the linearity appears in the virgin M(H) dependences obtained for the x ¼ 0.07, 0.09, and 0.1 compounds (Fig. 5(a)). The threshold field for the deviation of the M(H) curves from a linear law gradually decreases from Hd 50 kOe for x ¼ 0.07 to Hd 35 kOe for x ¼ 0.1. In pure BiFeO3, such a deviation starts to develop around 85 kOe (at room temperature).19 Accordingly, in the rhombohedral phase of the Bi1xNdxFe1xMnxO3 series, the doping-driven threshold

034102-5


J. Appl. Phys. 115, 034102 (2014)

Bi1xNdxFeO3 series,20 a substantial (approximately 25%) decrease of the room-temperature spontaneous magnetization takes place for the Bi1xNdxFe1xMnxO3 compounds near the rhombohedral-orthorhombic phase boundary. The behavior reflecting the change of the average number of eg electrons on the B site is consistent with a decrease of the Neel point observed in the BiFe1xMnxO3 series with increasing Mn content.22 As a result, a gradual decrease of the room-temperature spontaneous magnetization takes place in the antiferroelectric phase of (Ln, Bi)Fe1xMnxO3 series with increasing Mn concentration.25,26 Near the R3c/Pnam phase boundary, the rhombohedral and orthorhombic samples demonstrate very close magnetization at maximum field, thus confirming stabilization of a pure weak ferromagnetic state upon the metamagnetic transition in the ferroelectric phase. IV. CONCLUSIONS

FIG. 5. The field dependences of the magnetization obtained for the Bi1xNdxFe1xMnxO3 compounds at room temperature. The inset shows compositional dependence of the remanent magnetization.

field decrease should occur with a close to constant rate of 5 kOe per 1% Nd/Mn. Extrapolation of the linear decrease to H ¼ 0 yields critical concentration xc ¼ 0.17 for the substitution-induced removal of the magnetic cycloid in the rhombohedral phase. If the cycloidal modulation would be suppressed, a weak ferromagnetism stabilized by the Dzyaloshinskii-Moriya interaction55,56 could appear in the polar phase.57 In BiFeO3-based materials, the crossover from a cycloidal antiferromagnetic ordering to one which is weakly ferromagnetic can be interpreted in terms of the development of local strain heterogeneities at low doping levels, which would act to suppress coupling between gradients of the magnetic order parameter.58 In Bi1xNdxFe1xMnxO3 system, the critical concentration for the substitution-driven magnetic transformation exceeds the threshold value required to induce the ferroelectric-antiferroelectric structural phase transition (x ¼ 0.11) to make impossible existence of the intermediate ferroelectric and weak ferromagnetic phase. Magnetic state of the co-substituted compounds drastically changes upon the rhombohedral to orthorhombic transition (Fig. 5(b)). The orthorhombic samples demonstrate a weak ferromagnetic behavior similar to the characteristic of the isostructural Bi1xLnxFeO3 solid solutions.17–21 Spontaneous magnetization in BiFeO3-based materials is suggested to have a similar origin (namely, a canting of the antiferromagnetic alignment of the magnetic moments of B-site ions stabilized by the Dzyaloshinskii-Moriya interaction) for polar and nonpolar phases.18 When compared with

Room-temperature X-ray diffraction, piezoresponse force microscopy, and SQUID-magnetometry measurements of the Bi1xNdxFe1xMnxO3 (0.05 x 0.25) compounds were performed to follow the effect of simultaneous A/B-site chemical substitution on the crystal structure and multiferroic properties of the antiferromagnetic and ferroelectric BiFeO3. The substitution suppresses existing polar displacements to give rise to the ferroelectric-antiferroelectric (R3c ! Pnam) structural phase transition (at x ¼ 0.11) followed by stabilization of the orthorhombic structure (S.G. Pnma) characteristic of the end member of the (1 x)BiFeO3-(x)NdMnO3 series. The compositionally induced ferroelectric-antiferroelectric transition is accompanied by change of magnetic state. The polar samples demonstrate a dominant antiferromagnetic behavior. Magnetic field modifies the antiferromagnetic alignment to stabilize a weak ferromagnetic state. A threshold field inducing the AFM-wFM transformation depends on the composition and decreases with increasing dopant content. A critical Nd/Mn concentration that would yield weak ferromagnetism at H ¼ 0 exceeds the upper limit of the compositional range of the polar phase existence, so the purely weak ferromagnetic state is realized for the nonferroelectric compounds only. ACKNOWLEDGMENTS

This work was supported by funds from FEDER (Programa Operacional Factores de Competitividade COMPETE) and from FCT-Fundaç~ao para a Ciência e a Tecnologia under the project PEst-C/FIS/UI0036/2011 and program “Ciência 2008.” 1

W. Eerenstein, N. D. Mathur, and J. F. Scott, Nature 442, 759 (2006). S.-W. Cheong and M. Mostovoy, Nature Mater. 6, 13 (2007). 3 R. Ramesh and N. A. Spaldin, Nature Mater. 6, 21 (2007). 4 K. F. Wang, J.-M. Liu, and Z. F. Ren, Adv. Phys. 58, 321 (2009). 5 N. A. Hill, J. Phys. Chem. B 104, 6694 (2000). 6 G. Catalan and J. F. Scott, Adv. Mater. 21, 2463 (2009). 7 I. Sosnowska, T. Peterlin-Neumaier, and E. Steichele, J. Phys. C 15, 4835 (1982). 8 I. O. Troyanchuk, N. V. Tereshko, D. V. Karpinsky, A. L. Kholkin, M. Kopcewicz, and K. B€arner, J. Appl. Phys. 109, 114102 (2011). 2

034102-6 9


V. A. Khomchenko, I. O. Troyanchuk, V. Sikolenko, and J. A. Paix~ao, J. Mater. Sci. 48, 3852 (2013). 10 V. A. Khomchenko, I. O. Troyanchuk, D. M. T€ obbens, V. Sikolenko, and J. A. Paix~ao, J. Phys.: Condens. Matter 25, 135902 (2013). 11 D. Sando, A. Agbelele, D. Rahmedov, J. Liu, P. Rovillain, C. Toulouse, I. C. Infante, A. P. Pyatakov, S. Fusil, E. Jacquet, C. Carretero, C. Deranlot, S. Lisenkov, D. Wang, J.-M. Le Breton, M. Cazayous, A. Sacuto, J. Juraszek, A. K. Zvezdin, L. Bellaiche, B. Dkhil, A. Barthelemy, and M. Bibes, Nature Mater. 12, 641 (2013). 12 A. M. Mulders, Nat. Phys. 9, 398 (2013). 13 F. Kubel and H. Schmid, Acta Crystallogr., Sect. B: Struct. Sci. 46, 698 (1990). 14 A. Palewicz, I. Sosnowska, R. Przenioslo, and A. W. Hewat, Acta Phys. Pol., A 117, 296 (2010). 15 J. B. Neaton, C. Ederer, U. V. Waghmare, N. A. Spaldin, and K. M. Rabe, Phys. Rev. B 71, 014113 (2005). 16 D. Lebeugle, D. Colson, A. Forget, and M. Viret, Appl. Phys. Lett. 91, 022907 (2007). 17 D. A. Rusakov, A. M. Abakumov, K. Yamaura, A. A. Belik, G. Van Tendeloo, and E. Takayama-Muromachi, Chem. Mater. 23, 285 (2011). 18 I. O. Troyanchuk, D. V. Karpinsky, M. V. Bushinsky, V. A. Khomchenko, G. N. Kakazei, J. P. Araujo, M. Tovar, V. Sikolenko, V. Efimov, and A. L. Kholkin, Phys. Rev. B 83, 054109 (2011). 19 V. A. Khomchenko, I. O. Troyanchuk, D. V. Karpinsky, and J. A. Paix~ao, J. Mater. Sci. 47, 1578 (2012). 20 I. Levin, S. Karimi, V. Provenzano, C. L. Dennis, H. Wu, T. P. Comyn, T. J. Stevenson, R. I. Smith, and I. M. Reaney, Phys. Rev. B 81, 020103 (2010). 21 I. O. Troyanchuk, D. V. Karpinsky, M. V. Bushinsky, O. S. Mantytskaya, N. V. Tereshko, and V. N. Shut, J. Am. Ceram. Soc. 94, 4502 (2011). 22 S. M. Selbach, T. Tybell, M.-A. Einarsrud, and T. Grande, Chem. Mater. 21, 5176 (2009). 23 A. A. Belik, A. M. Abakumov, A. A. Tsirlin, J. Hadermann, J. Kim, G. Van Tendeloo, and E. Takayama-Muromachi, Chem. Mater. 23, 4505 (2011). 24 V. A. Khomchenko, I. O. Troyanchuk, D. V. Karpinsky, S. Das, V. S. Amaral, M. Tovar, V. Sikolenko, and J. A. Paix~ao, J. Appl. Phys. 112, 084102 (2012). 25 V. A. Khomchenko, I. O. Troyanchuk, M. I. Kovetskaya, M. Kopcewicz, and J. A. Paix~ao, J. Phys. D: Appl. Phys. 45, 045302 (2012). 26 V. A. Khomchenko, I. O. Troyanchuk, T. M. R. Maria, D. V. Karpinsky, S. Das, V. S. Amaral, and J. A. Paix~ao, J. Appl. Phys. 112, 064105 (2012). 27 V. A. Khomchenko, D. V. Karpinsky, L. C. J. Pereira, A. L. Kholkin, and J. A. Paix~ao, J. Appl. Phys. 113, 214112 (2013). 28 V. A. Khomchenko, I. O. Troyanchuk, M. I. Kovetskaya, and J. A. Paix~ao, J. Appl. Phys. 111, 014110 (2012). 29 J. Bielecki, P. Svedlindh, D. T. Tibebu, S. Cai, S.-G. Eriksson, L. B€orjesson, and C. S. Knee, Phys. Rev. B 86, 184422 (2012). 30 S. Saxin and C. S. Knee, Dalton Trans. 40, 3462 (2011).

J. Appl. Phys. 115, 034102 (2014) 31

J. Rodrıguez-Carvajal, Physica B 192, 55 (1993). A. M. Glazer, Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 28, 3384 (1972). 33 A. M. Glazer, Acta Crystallogr., Sect. A 31, 756 (1975). 34 R. Aso, D. Kan, Y. Shimakawa, and H. Kurata, Sci. Rep. 3, 2214 (2013). 35 D. C. Arnold, K. S. Knight, F. D. Morrison, and P. Lightfoot, Phys. Rev. Lett. 102, 027602 (2009). 36 M. Avdeev, J. D. Jorgensen, S. Short, G. A. Samara, E. L. Venturini, P. Yang, and B. Morosin, Phys. Rev. B 73, 064105 (2006). 37 A. S. Gibbs, K. S. Knight, and P. Lightfoot, Phys. Rev. B 83, 094111 (2011). 38 S. Karimi, I. M. Reaney, Y. Han, J. Pokorny, and I. Sterianou, J. Mater. Sci. 44, 5102 (2009). 39 A. M. Glazer, K. Roleder, and J. Dec, Acta Crystallogr., Sect. B: Struct. Sci. 49, 846 (1993). 40 E. T. Maguire, A. M. Coats, J. M. S. Skakle, and A. R. West, J. Mater. Chem. 9, 1337 (1999). 41 R. D. Shannon, Acta Crystallogr., Sect. A 32, 751 (1976). 42 C.-J. Cheng, D. Kan, S.-H. Lim, W. R. McKenzie, P. R. Munroe, L. G. Salamanca-Riba, R. L. Withers, I. Takeuchi, and V. Nagarajan, Phys. Rev. B 80, 014109 (2009). 43 I. M. Reaney, E. L. Colla, and N. Setter, Jpn. J. Appl. Phys., Part 1 33, 3984 (1994). 44 Y.-M. Kim, A. Kumar, A. Hatt, A. N. Morozovska, A. Tselev, M. D. Biegalski, I. Ivanov, E. A. Eliseev, S. J. Pennycook, J. M. Rondinelli, S. V. Kalinin, and A. Y. Borisevich, Adv. Mater. 25, 2497 (2013). 45 J. Schiemer, R. L. Withers, M. A. Carpenter, Y. Liu, J. L. Wang, L. Noren, Q. Li, and W. Hutchison, J. Phys.: Condens. Matter 24, 125901 (2012). 46 W. Hu, Y. Chen, H. Yuan, G. Li, Y. Qiao, Y. Qin, and S. Feng, J. Phys. Chem. C 115, 8869 (2011). 47 M. Kumar and K. L. Yadav, Appl. Phys. Lett. 91, 242901 (2007). 48 A. Ianculescu, F. P. Gheorghiu, P. Postolache, O. Oprea, and L. Mitoseriu, J. Alloys Compd. 504, 420 (2010). 49 W. Eerenstein, F. D. Morrison, F. Sher, J. L. Prieto, J. P. Attfield, J. F. Scott, and N. D. Mathur, Philos. Mag. Lett. 87, 249 (2007). 50 V. V. Shvartsman, W. Kleemann, R. Haumont, and J. Kreisel, Appl. Phys. Lett. 90, 172115 (2007). 51 D. Khomskii, Physics 2, 20 (2009). 52 A. K. Zvezdin and A. P. Pyatakov, Phys. Status Solidi B 246, 1956 (2009). 53 A. M. Kadomtseva, Yu. F. Popov, A. P. Pyatakov, G. P. Vorob’ev, A. K. Zvezdin, and D. Viehland, Phase Transit. 79, 1019 (2006). 54 G. Le Bras, D. Colson, A. Forget, N. Genand-Riondet, R. Tourbot, and P. Bonville, Phys. Rev. B 80, 134417 (2009). 55 I. Dzyaloshinsky, J. Phys. Chem. Solids 4, 241 (1958). 56 T. Moriya, Phys. Rev. 120, 91 (1960). 57 C. Ederer and N. A. Spaldin, Phys. Rev. B 71, 060401 (2005). 58 J. A. Schiemer, R. L. Withers, Y. Liu, and M. A. Carpenter, Chem. Mater. 25, 4436 (2013). 32