Structural and Electrical Transport Properties of ...

Structural and Electrical Transport Properties of Doped Nd-123 Superconductors Shaban Reza Ghorbani

Stockholm 2002 Doctoral Dissertation Royal Institute of Technology Solid State Physics Department of Physics & IMIT

Akademisk avhandling som med tillst˚ and av Kungl Tekniska H¨ ogskolan framl¨ agges till offentlig granskning f¨ or avl¨ aggande av teknisk doktorsexamen fredagen den 17 jauuari 2003 kl 10.00 i Kollegiesalen, Administrationsbyggnaden, Kungl Tekniska H¨ ogskolan, Valhallav¨ agen 79, Stockholm. Thesis for the degree of PhD in the subject area of Condensed Matter Physics. ISBN 91-7283-400-5 TRITA-FYS-5284 ISSN 0280-316X ISRN KTH/FYS/FTF/R--03/5284--SE c Shaban Reza Ghorbani, December 15, 2002 Universitetsservice US AB, Stockholm 2002

Structural and Electrical Transport Properties of Doped Nd-123 Superconductors Shaban Reza Ghorbani, Solid State Physics, IMIT, Royal Institute of Technology, KTH-Electrum 229, SE-164 40 Kista-Stockholm, Sweden

Abstract It is generally believed that one of the key parameters controlling the normal state and superconducting properties of high temperature superconductors is the charge carrier concentration p in the CuO2 planes. By changing the non-isovalent doping concentration on the RE site as well as the oxygen content in (RE)Ba2 Cu3 O7−δ , an excellent tool is obtained to vary the hole concentration over a wide range from the underdoped up to the overdoped regime. In the present thesis the focus is on the doping effects on the structural and normal state electrical properties in Nd-123 doped with Ca, La, Pr, Ca-Pr, and Ca-Th. The effects of doping have been investigated by X-ray and neutron powder diffraction, and by measurements of the resistivity, thermoelectric power S, and Hall coefficient RH . The thermoelectric power is a powerful tool for studies of high temperature superconductivity and is highly sensitive to details of the electronic band structure. S as a function of temperature has been analyzed in two different two band models. The parameters of these models are related to charactristic features of the electron bands and a semiempirical physical description of the doping dependence of S is obtained. Some important results are following: (i) The valence of Pr in the RE-123 family. Results from the structural investigations, the critical temperature Tc , and the thermoelectric power indicated a valence +4 at low doping concentration, which is in agreement with results of charge neutral doping in the RE-123 family. (ii) Hole localization. The results of bond valence sum (BVS) calculations from neutron diffraction data showed that hole localization on the Pr+4 site was the main reason for the decrease of the hole concentration p. Different types of localization were inferred by S measurements for Ca-Th and Ca-Pr dopings. (iii) Competition between added charge and disorder. The results of RH measurements indicated that Ca doping introduced disorder in the CuO2 planes in addition to added charge. This could be the main reason for the observed small decrease of the bandwidth of the density of states in the description of a phenomenological narrow band model. (iv) Empirical parabolic relation between γ and p. S data were analyzed and well described by a two-band model with an additional linear T term, γT . An empirical parabolic relation for γ as a function of hole concentration has been found. Key words: high temperature superconductors, critical temperature, resistivity, thermoelectric power, Hall coefficient, X-ray diffraction, Neutron diffraction, NdBa2 Cu3 O7−δ , hole concentration, substitution. ISBN 91-7283-400-5 • TRITA-FYS-5284 • ISSN 0280-316X • ISRN KTH/FYS/FTF/R--03/5284--SE

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Preface The work presented in this thesis was carried out at the Department of Solid State Physics, Royal Institute of Technology (KTH), Stockholm, Sweden. The first part of this thesis gives an introduction to selected aspects of structure and electronic transport properties in sintered high temperature superconductors. The second part consists of the original papers on which this thesis is based. This thesis is based on the following publications: I. Thermoelectric power and resistivity of Nd1−x Cax Ba2 Cu3 Oy and Nd1−x Lax Ba2 Cu3 Oy ¨ Rapp S. R. Ghorbani, P. Lundqvist, M. Andersson, M. Valldor, and O. Physica C 339, 245 (2000). II. Thermoelectric power and resistivity of Nd1−x Prx Ba2 Cu3 O7−δ ¨ Rapp S. R. Ghorbani, M. Andersson, P. Lundqvist, M. Valldor, and O. Physica C 353, 77 (2001). III. Thermoelectric power of charge-neutral Nd1−2x Cax Mx Ba2 Cu3 O7−δ (M=Th and Pr); Evidence for different types of localization ¨ Rapp S. R. Ghorbani, M. Andersson, and O. Phys. Rev. B 66, 104519 (2002). IV. An anomalous dip in thermoelectric power of Nd1−x Prx Ba2 Cu3 O7−δ ¨ Rapp S.R. Ghorbani and O. Physica C (in press). V. Neutron diffraction studies of Nd1−x Prx Ba2 Cu3 O7−δ ; Evidence for hole localization ¨ Rapp S. R. Ghorbani, M. Andersson,and O. Submitted to Phys. Rev. B. VI. Normal state Hall effect in Nd1−x Cax Ba2 Cu3 O7−δ ; Competition between added charge and disorder ¨ Rapp S. R. Ghorbani, M. Andersson, and O. Physica C (in press). v

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Preface

The author has also contributed to the following publications, which are not included in this thesis: VII. High pressure electrical resistivity studies of composition controlled melt processed Nd-123 based bulk material R. Selva Vennila, T. K. Jaya Arun, F. M. Freny Joy, N. Victor Jaya, ¨ Rapp S. R. Ghorbani, and O. In Advances in High Pressure Science and Technology, edited by A. K. Bandyopadhyay, D. Varandani, and Krishan Lal (National Physical Laboratory, New Delhi, 2001), p. 453. VIII. High pressure high-temperature electrical resistivity study on Ca doped Nd-123 based high Tc superconductor R. Selva Vennila, T. K. Jaya Arun, N. Victor Jaya, S. R. Ghorbani, and ¨ Rapp O. In Advances in High Pressure Science and Technology, edited by A. K. Bandyopadhyay, D. Varandani, and Krishan Lal (National Physical Laboratory, New Delhi, 2001), p. 458.

Comments on My Participation I have played an important role in the work of all publications included in the thesis. I have prepared many of the sintered samples of doped NdBa2 Cu3 O7−δ , made the measurements and the analysis, and also written most of the papers. ¨ Rapp, my superContributions from the others can be summarized as follows: O. visor, and M. Andersson have been involved in most aspects of the work and in particular discussions on the manuscripts for the publications. In paper I, the measurements and data analysis were made by me following the ideas by P. Lundqvist, who has also been involved on the discussions of paper II. M. Valldor has made the ¨ Rapp produced the manuscript of paper III. X-ray diffraction in papers I and II. O.

Acknowledgments I would like to thank a lot of people for their support in various ways during this work: ¨ First of all my supervisor Professor Osten Rapp for help with ideas and interpretations and who with great patience has helped me write comprehensible articles and thesis, and always finds time for discussion. Magnus Andersson who helped and taught me how to make measurements at low temperature and for reviewing this thesis, articles, and valuable discussions in the field of HTSC. Pieter Lundqvist for his fruitful discussions and Andreas Rydh and Bj¨ orn Lundqvist for help with the equipment in our laboratory. Ingrid Bryntse, Martin Valldor at Arrhenius Laboratory, Stockholm University with help in the sample preparation and X-ray powder diffraction. H˚ akan Rundl¨ of at Studsvik for help with powder neutron diffraction and Gunnar Svensson at Arrhenius Laboratory, Stockholm University for clarifying discussion on the Rietveld refinement method. Hans Larsson and Christer Torpling for providing liquid helium and Askell Kjerulf and Johan Axn¨ as and Amir Abbas Jalali for computer problem help, Therese Bj¨ orn¨ angen, Yuri Eltsev, Shun-Hui Han, Beatriz Espinosa, S¨ oren Kahl, and all my Iranian friends for general discussions. Therese and Sören are also acknowledged for LATEX help. My wife Mahnaz and my children - Saeid, Sahar, and Sepideh - for patiently waiting nights, their support, and encouragement and for giving me other sides of life than physics. Finally, I would like to thank my and my wife’s families for their support. Financial support from various sources is gratefully acknowledged: The Ministry of Science, Research and Technology (MSRT) of Iran; equipment and laboratory expenses from the Swedish Superconductivity Consortium, the Swedish Agencies Vetenskapsr˚ adet, and the SSF OXIDE program; travel grants from the Knut and Alice Wallenberg foundation and from the Ragnar and Astrid Signeul foundation.

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Contents

1 Introduction 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Characteristic Properties of Superconductors . . . . . 1.2.1 Zero resistivity . . . . . . . . . . . . . . . . . . 1.2.2 Meissner effect . . . . . . . . . . . . . . . . . . 1.2.3 Critical magnetic field and current density . . . 1.2.4 Type I and Type II superconductors . . . . . . 1.2.5 Josephson effect . . . . . . . . . . . . . . . . . 1.3 Low and High Temperature Superconductors . . . . . 1.3.1 Conventional superconductors and BCS model 1.3.2 High Temperature Superconductors (HTSC) .

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2 Doping in the 123 cuprate superconductors 2.1 Oxygen stoichiometry . . . . . . . . . . . . . 2.2 Substitution at the Ba site . . . . . . . . . . . 2.3 Substitution at the Cu site . . . . . . . . . . 2.4 Substitution at the rare earth site . . . . . . . 2.4.1 Structure . . . . . . . . . . . . . . . . 2.4.2 Critical temperature . . . . . . . . . . 2.4.3 Bond Valance Sums (BVS) . . . . . . 2.4.4 Praseodymium valence . . . . . . . . .

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3 Normal state electrical transport properties 3.1 Resistivity . . . . . . . . . . . . . . . . . . . . 3.2 Thermoelectric power (S) . . . . . . . . . . . 3.2.1 Thermoelectric power in HTSC . . . . 3.2.2 Models for S . . . . . . . . . . . . . . 3.3 Hall effect . . . . . . . . . . . . . . . . . . . . 3.3.1 Hall effect in HTSC . . . . . . . . . . ix

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x 4 Experimental Techniques 4.1 Sample Preparation . . . . . . . . . . . . . . . . . . . . 4.2 Sample Characterization . . . . . . . . . . . . . . . . . . 4.2.1 X-ray powder diffraction . . . . . . . . . . . . . . 4.2.2 Neutron powder diffraction . . . . . . . . . . . . 4.2.3 Rietveld method . . . . . . . . . . . . . . . . . . 4.3 Electrical Resistance Measurements . . . . . . . . . . . . 4.3.1 Electrical contacts and measurement technique . 4.4 Thermoelectric Power (S) Measurements . . . . . . . . . 4.4.1 Sample holder . . . . . . . . . . . . . . . . . . . 4.4.2 S measurement procedures and data acquisition 4.5 Hall Coefficient Measurements . . . . . . . . . . . . . .

Contents

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5 Brief summary of results 5.1 Thermoelectric power and resistivity of Nd1−x Cax (or Lax )Ba2 Cu3 O7−δ . (Paper I) . . . . . . . . . . . . . . 5.2 Thermoelectric power and resistivity of Pr-doped Nd-123. (Papers II and IV) . . . . . . . . . . . . . . . . 5.3 Different types of localization in Ca-Pr and Ca-Th doped Nd-123. (Paper III) . . . . . . . . . . . . . . . . . . . 5.4 Evidence for hole localization by Pr in Nd(Pr)-123 from neutron diffraction. (Paper V) . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Competition between added charge and disorder in Ca-doped Nd123. (Paper VI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 1

Introduction 1.1

Overview

The phenomenon of superconductivity has attracted many scientists after its discovery by Kamerlingh Onnes in 1911 [1]. The superconductivity was discovered by resistance measurements, a charge transport property. Complementary to resistivity the other electrical transport properties such as thermoelectric power and Hall effect have given outstanding information in the elucidation of the basic properties of superconductors. These properties are highly sensitive to details of the charge transport. They probe the behaviour of the material’s electronic band structure in general, the nature of carriers, the carrier density, and scattering mechanisms in particular. Among the striking features of high temperature superconductivity (HTSC) are the extraordinary transport properties in the normal state, which are believed to be inconsistent with the conventional electron-phonon scattering mechanism. Systematic studies of these properties appear to be a fruitful way of understanding the nature of the carriers and the mechanism of transport in HTSC and related compounds. Since the beginning of HTSC the unusual normal state transport properties (see, for example, [2]) of the HTSC have been suspected to give clues to the basic mechanisms responsible for superconductivity. The normal state resistivity, ρ, has shown a linear behaviour in temperature over a wide range from Tc to nearly 1000 K [3] for some optimaly doped samples. In the overdoped regime a Fermi-liquid behaviour (i.e., ρ ∝ T α with α = 1 to 2) becomes dominant [2]. The underdoped samples exhibit a nearly linear T dependence with deviations at low temperatures [4]. Moreover, the temperature dependence of the Hall coefficient, RH is too strong to be easily understood in materials with transport thought to be dominated by a single band (e.g. Ref. [5]). For optimally doped materials the inverse Hall coefficient (1/RH ) decreases linearly with temperature. At other doping levels there are significant deviations from this simple behaviour [6]. 1

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Chapter 1. Introduction

Copper-oxide superconductors are prototypes of layered structures, containing CuO2 planes and an oxygen configuration related to the perovskite structure. The parent compounds are often antiferromagnetic Mott insulators with quasi-two dimensionality. These two-dimensional features are essential for achieving HTSC by doping, e.g., oxygen doping or substitutions of non-isovalent elements. A common view of HTSC is that the CuO2 planes act as electrical conductors, and the intermediate parts as charge reservoirs, supplying charge to the conduction in the plane. The outline of this thesis is as follows. Some basic concepts of superconductivity are presented in chapter 1. Chapter 2 gives a brief overview of doping in the 123 cuprates superconductors with the main focus on subjects related to the present work, i.e. substitution at the rare earth site. Chapter 3 summarizes the trends and empirical relations of the normal state electrical properties for the high temperature superconductors especially for RE-123 systems. In chapter 4 the sample preparation and the different experimental techniques that have been used are described, and in chapter 5 our main results are summarized.

1.2

Characteristic Properties of Superconductors

The superconducting state is mainly characterized by two most remarkable properties. They are the zero resistivity (section 1.2.1), which was observed in 1911 by Kamerlingh Onnes [1] and perfect diamagnetism (section 1.2.2), which was discovered by W. Meissner and R. Ochsenfeld in 1933 [7].

1.2.1

Zero resistivity

The absence of the electrical resistivity is a well-known property of the superconducting state. At a characteristic temperature called the critical temperature, Tc , the resistance drops abruptly to an unmeasurable small value. Figure 1.1 shows a result from the discovery. This behaviour is remarkably different from the continuously decreasing resistance of nonsuperconducting metals down to a constant value at low temperature and suggests that superconductivity represents a physically different state. In fact, the material undergoes a phase transition from a normal state to a superconducting state at Tc , as evidenced e.g. from the specific heat. The most efficient way to demonstrate the zero resistance or rather to determine an upper limit of the resistivity is to induce a current in a superconducting loop and to detect the decay of the magnetic fields produced by the supercurrents. Upper limits of 3.6 × 10−23 [9] and 7 × 10−23 Ωcm [10] have been reported for low and high temperature superconductors, respectively. Such a resistivity is more than 10 orders of magnitude smaller than that of high purity copper at low temperatures. From a technological point of view zero resistivity is of great interest for applications. Also for high temperature superconductors some power application have been developed.

1.2. Characteristic Properties of Superconductors

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Figure 1.1. Resistivity vs. temperature for Hg which marked the discovery of superconductivity by K. Onnes in 1911 (from Ref. [8]).

For example, prototype transformers (5/10 MVA) [11], fault current limiters, and transmission cables (50 m long, 3000 A) have been constructed and tested [12].

1.2.2

Meissner effect

The magnetic properties of the superconducting state are as dramatic as the electrical ones. It was found [7] that a magnetic field is expelled from the interior of a field-cooled superconductor as soon as the superconducting state is reached. This behaviour is called the Meissner effect and occurs only if the magnetic field is relatively small. The superconductor therefore acts as a perfect diamagnetic, as illustrated in figure 1.2. The figure also shows a schematic image of magnetic field lines from a magnet levitating above a superconductor.

1.2.3

Critical magnetic field and current density

Kamerlingh Onnes showed that the temperature above which superconductivity is destroyed, depends on applied magnetic field and the current that was passed through the material. Therefore, the superconducting state is defined by three important factors: critical temperature Tc , critical field Bc , and critical current

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Chapter 1. Introduction (a)

(b)

B Magnet

Superconductor T>Tc

T 3 the hole concentration of the different CuO2 planes may be different due to the difficulties to reach the optimum hole concentrations in all CuO2 planes.

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Chapter 2

Doping in the 123 cuprate superconductors A number of theories have been proposed to explain the normal state and superconducting properties of HTSC. Examples of models describing the cuprate normal state are a modified Fermi liquid theory[42–45], spin-polarons [46] or polarons [47, 48], a Luttinger liquid model [49, 50], and charge stripes [51]. However, there is no agreement as to which model is appropriate. The only consensus on the electronic properties of the normal state of HTSC is that they are not conventional. The superconducting properties of the 123 system can be controlled via chemical substitution and/or changing the oxygen stoichiometry. The amount of hole doping has been recognized to be a key parameter that determines the physics in these materials as previously mentioned. Doping of the RE-123 system by non-isovalent impurities strongly affects the charge-carrier system, leading to significant changes in both the electronic and the superconducting properties. Some results from varying oxygen stoichiometry (section 2.1) and doping on Ba site (section 2.2) and the two Cu sites (section 2.3) are first briefly summarized. Substitutions on the rare earth position are described in some detail in section 2.4.

2.1

Oxygen stoichiometry

One of the most interesting properties of the (RE)Ba2 Cu3 O7−δ compound is its ability to support a large oxygen non-stoichiometry. In fact, its oxygen content can be varied from six (δ = 1) to seven (δ = 0) in a continuous way. The oxygen deficiency occurs in the CuO chains (for notation see figure 1.7), which contain copper (Cu1) and oxygen atoms (O1). The chain plane acts as a charge reservoir for the CuO2 double planes. The doping is mainly made by annealing at different temperatures or by quenching in liquid nitrogen after annealing at a constant temperature and different oxygen partial pressure, p(O2 ). Annealing at temperature 13

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Chapter 2. Doping in the 123 cuprate superconductors

Figure 2.1. Oxygen content, x, as a function of p(O2 ) at different temperatures for YBa2 Cu3 O6+x . The figure is taken from [52].

above 300 ◦ C is often a convenient way to control charge density. Figure 2.1 shows the oxygen stoichiometry as a function of temperature and p(O2 ) [52]. It is well known that the oxygen stoichiometry and oxygen defect structure are crucial for determining the occurrence or suppression of superconductivity in the cuprates. Figure 2.2 shows a temperature-oxygen content phase diagram (T vs δ) of YBa2 Cu3 O7−δ , and some relations between structural and physical properties. At full oxygen content the structure is orthorhombic, Ortho I phase, with filled chains and the fractional site occupancy of the two chain sites O1 and O5 close to 1 and 0, respectively. With decreased oxygen concentration a transition within the orthorhombic phase to Ortho II take place. This phase consists of an alternating sequence of one empty and one full chain [53]. At oxygen content of about δ ≈ 0.6 an orthorhombic-tetragonal (O-T) phase transition takes place where the oxygen around the Cu1 atom is randomly distributed between the O1 and O5 positions. It was found that the Cu1-O4 bond length decreases and the Cu2-O4 bond length increases with decreasing oxygen content in agreement with a charge transfer model

2.2. Substitution at the Ba site

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[54]. For further decreasing oxygen content a metal-insulator transition follows, and finally an antiferromagnetic insulator. Tc decreases with increasing δ and displays two pronounced plateaus at 60 K and 90 K for δ ≈ 0.5 and δ ≈ 0, respectively. The plateau at 60 K is attributed to the Ortho II phase.

Figure 2.2. T-δ phase diagram of YBa2 Cu3 O7−δ as a function of the oxygen content in the Cu1 chains. The figure was taken from Ref. [55].

2.2

Substitution at the Ba site

Among the most studied two and three valent substitutions such as Ca, Sr, La, Pr, and Nd, only Sr+2 and La+3 have been found to enter only the barium site in the 123 structure [56]. With substitution of Sr in (RE)Ba2−x Srx Cu3 O7−δ , the oxygen content does not change significantly and Tc decreases linearly at a rate of dTc /dx ≈ -10 K [57–59]. Compared to charge dopings, giving a parabolic doping dependence of Tc , this is a slow change in agreement with a charge neutral doping. With increasing Sr content, the resistivity increases which is due to increasing disorder, with an increase of the O5 site occupancy and a corresponding decrease in the O1 site occupation [60]. Substitution of La on the Ba site adds electrons into the 123-system. For La doping into YBa2−x Lax Cu3 O7−δ , Tc first increases with x by a little more than 2 K at small values of x and then decreases at higher doping levels. This behaviour arises since fully oxygen doped Y-123 is slightly overdoped [61, 62]. The variation

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of the oxygen content is small up to x = 0.4, where an orthorhombic-tetragonal phase transition occurred, and charge compensation is accomplished by a reduction of the formal copper valence. At higher doping levels an increasing oxygen content compensates for most of the additional La doping [63].

2.3

Substitution at the Cu site

Studies of doping at the two different copper sites (see figure 1.7) include substitutions of Co, Al, Fe, Ga, Ni, and Zn. Rietveld refinements from neutron diffraction data have shown that Co, Al, Ga, and Fe occupy the Cu1 position, while at high Fe doping level also the Cu2 position is occupied [59]. Zn and Ni enter the Cu2 plane site as indicated by NMR [64–66]. Tc is invariably suppressed by substitution of copper by other metals. The rate of the Tc suppression is different for magnetic and non-magnetic substitution. With substitutions of magnetic Ni and non-magnetic Zn (M) ions on the copper sites in the YBa2 Cu1−x Mx O7−δ compound, Tc decreases linearly with dTc /dx ≈ -110 K [67] and -410 K [67–71], respectively. Tc varies with a parabolic dependence for the three valent Co [59], Al [59], Ga [68], and Fe [72] dopings as expected for electron doping of the 123 compounds.

2.4

Substitution at the rare earth site

Doping substitutions on the rare earth site in Y-123 compounds have been widely studied. In principle, non-isovalent substitutions offer a powerful tool to vary the charge in the CuO2 plane, and therefore, to study the behaviour of structural and superconducting properties with varying carrier concentration. A useful approach to obtain further information about the role of doping in HTSC and the variation of the critical temperature in doped systems is to use the bond valance sum (BVS) method, based on a relation between valence and atomic distance (2.4.3). In this section, the replacement of Y by other rare earth metals is first discussed. Most of these substitutions do not change the superconducting properties significantly. Then partial substitutions of other elements and co-dopings are described in some detail. Tarascon et al. [73] studied systematically the series RE-123. They determined that the same orthorhombic structure could be formed with all rare earth elements, except for RE = Pm, Ce, and Tb. This is due, at least in the two latter cases, to the strong tendency for a valence larger than +3. Systematic neutron powder diffraction studies have been published for all RE123 alloy systems for δ = 0, and 1 [28, 74–76]. In general, there are common trends for changing properties with the rare earth ionic radius, rRE . With decreasing rRE : • Most interatomic distances decrease linearly. The Cu2-O4 distance increases.

2.4. Substitution at the rare earth site

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• The variations of the lattice parameters are small. Cell volume decreases linearly. • There is trend of a decreasing Tc . This may be due in part to the fact that compounds with small rRE could be slightly overdoped when fully oxygenated, whereas large rRE compounds are optimally doped [62, 77]. • The orthorhombicity parameter, defined as [(b − a)/(b + a)], increases. The most interesting doping substitutions are the partial substitutions. Each substitution generates new series of compounds and is often connected with a new set of characteristics. In general, these compounds are described in a two dimensional phase diagram (oxygen content, δ, and concentration of the substituent, x). There are interesting empirical relations between the physical properties and doping dependencies. This is a vast field. We will restrict ourselves to some of the most important themes especially in connection to our studies. In the rest of this section some relations for the partial substitutions on the RE site of 123 superconductors will be described with Ca, La, Pr, and charge neutral dopings of Ca-Pr, and Ca-Th.

2.4.1

Structure

The crystal structure determines largely physical properties of materials. HTSC are sensitive to structural and compositional modifications [78]. Therefore, understanding the effect of doping on the evolution of the structural and superconducting properties is one of the keys towards the understanding of superconductivity in copper oxides. The crystal structure of the pure and doped RE-123 has been studied through X-ray, neutron diffraction, and transmission electron microscopy (e.g. [79–84]). Lattice strain can be introduced when doping with a cation (ion with a positive charge) [85, 86]. One usually considers two different effects due to cation doping: 1. Carrier redistribution is caused by the differences of the valence between the doping and host elements. 2. A size effect on various properties results from the difference of the radii of the doping and host elements. The substitution of RE by doping elements with different sizes results in changes of unit cell parameters and interatomic distances. In this thesis the structural parameters have been studied with substitution of Ca, Pr, and co-doping Ca with Pr and Th on the RE sites in the RE-123 system. I.

Calcium

Two valent Ca enters at low doping levels primarily in the trivalent rare earth position in 123 superconductors. In Y-123, the solubility limit for Ca is just below 20%.

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Above this level the BaCuO2−υ impurity phase is formed [33, 87, 88]. With increasing Ca concentration the oxygen content is constant at low doping concentration as observed from neutron diffraction studies on Y1−x Cax Ba2 Cu3 O7−δ [88, 89] and near-edge X-ray absorption spectroscopy on single crystal Y(Ca)-123 [90]. However, some measurement have indicated that the oxygen content decreased with increasing Ca concentration [91–93], which may suggest that the reduction in oxygen content is due to the sample preparation technique [94]. Neutron diffraction studies have shown that with increasing substitution of Ca on RE site in Y-123, the a- and c-axis lattice parameters and the cell volume increased, while the b-axis decreased [88, 89]. On the other hand substitution of Ca on the Nd site in Nd-123 resulted in a decrease in both the a- and b-axes lattice parameters and a small increase in the c-axis parameter [paper I]. This is not surprising since the radius of Ca is only one percent larger than that of Nd, while Y is about 10% smaller than Ca. Substitution of Ca on Nd sites [paper I], resulted in a decrease in the orthorhombicity, which may suggest an increase in the O5 occupancy [95], and/or an increase in oxygen vacancy concentration. These effects are accompanied by a disordering of the chain oxygen [88]. The Cu2-Cu2 bond-length and similarly the buckling of the CuO2 plane decrease with increasing Ca doping and the Cu2-O4 distance increases, which have been taken as signs of electron doping [54, 59]. II.

Praseodymium

Pr-123 constitutes a remarkable exception in the RE-123 systems. It is the only one of the RE-123 family in the orthorhombic structure which is not superconducting in sintered samples while some authors have found superconductivity in single crystals [96, 97]. Structural analysis can give an insight into this issue by the study of the evaluation of the structural properties as a function of rRE in (RE)1−x Prx Ba2 Cu3 O7−δ . The a, b, and c lattice parameters all increased with increasing Pr concentration in Y-123 [98] and Gd-123 [99]. The variation of the c-axis lattice parameter depends on the rRE size. Okada et al. [100] made a structural study of Gd1−x (RE)x Ba2 Cu3 O7−δ with RE=Pr and Nd. They found that the c-axis parameter decreased with increasing Pr doping up to a doping level of approximately 15% and above this the c-axis parameter was approximately constant, while with increasing Nd concentration it increased continuously. This result is in agreement with a Pr valence close to +4 at low doping level as was suggested for (RE)1−x Prx Ba2 Cu3 O7−δ with RE=Y [101, 102], Eu [103], Gd [102] and Nd [papers II, III]. A particular useful parameter is the Cu2-Cu2 separation, which is proportional to rRE [98]. Neutron diffraction studies were made by Neumeier et al. [98] for Y1−x Prx Ba2 Cu3 O7−δ . They found that the Cu2-Cu2 distance was rather constant up to x=0.20, with an apparent large relative expansion in the 0.2< x 0) but for x > 0.4 the resistivity curves display a maximum just above Tc . For further increasing Pr concentration superconductivity disappears, and a metal-insulator transition takes place. Similar results were also found for Pr-doped RE-123 with RE=Eu [103], Yb [152], Tm and Sm [153], and Nd (paper V). The strong influence of Pr doping on the resistivity of Y-123 and a metal-insulator like transition at about ≈ 60% Pr is also illustrated by the results of Peng et al. (figure 3.2) [150]. Sun et al. [148] found a simple relation between ρ0 and Tc , which was

Figure 3.1. Resistivity vs. temperature for Y1−x Prx Ba2 Cu3 O7−δ . The figure is taken from Ref. [148]

3.1. Resistivity

31

similar to the results for ion irradiated YBa2 Cu3 O7−δ [154]. In this relation, Tc decreased linearly with increasing ρ0 and it can be seen in the different RE-123 compounds even though the rate of Tc depression, dTc /dx, is different [103, 152, 153].

Figure 3.2. ρ(100K) vs. Pr doping concentration, x, for Pr-doped Y-123. The figure is taken from Ref. [150].

The resistivity of charge neutral dopings of Ca-M (M=Pr, Th) in (RE)1−2x Cax Mx Ba2 Cu3 O7−δ superconductors with RE=Y, Nd, and Sm has been frequently studied as mentioned. The results showed that the resistivity of these samples increased smoothly with increasing charge neutral doping level but the rates of these changes were different. B. Lundqvist et al. [130] made a comparison of the electrical resistivity at room temperature as a function of Ca-Pr and Ca-Th doping concentration in RE-123 systems with RE=Y, Sm, and Nd. They found that the room temperature resistivity, ρ290K , increased weakly with doping for Ca-Pr, while for Ca-Th doping there was a strong increase of ρ290K (figure 3.3). P. Lundqvist et al. [81] found that the rate of changing resistivity for increasing Ca-Pr concentration was smaller than for samples doped with Ca or Pr only. With p0 for the hole concentration of an undoped Sm-123 sample, they simply assumed that at doping level x, the hole concentration of a Ca-doped sample was p0 + x, while for a Pr-doped sample it was p0 − x corresponding to creation and destruction of a hole per atom for Ca and Pr doping, respectively. For these alloys ρ at 275 K roughly followed ≈ 1/(x + p0 ) while for Ca-Pr co-doping ρ(x) was a weakly increasing linear function of doping concentration. These results further support that Ca-Pr is a charge neutral doping at low doping concentrations.

32

Chapter 3. Normal state electrical transport properties

Figure 3.3. Normalized room temperature resistivity vs. charge neutral doping concentration, x in (RE)1−2x Cax Mx Ba2 Cu3 O7−δ (M=Th,Pr). For Ca-Pr doped Nd-123; • [130], and [107], for Ca-Pr doped Sm-123; [81], for Ca-Th doped Y-123; [130] and ♦ [128], for Ca-Th doped Nd-123; ◦ [130], and [95], and for Ca-Th doped Sm-123; [81]. The figure is taken from Ref. [130].

3.2

Thermoelectric power (S)

Electrical carriers transport energy as well as charge. A conductor which is open circuited and has no electric current flowing through it but which has a temperature gradient along its length can develop an electric field E along the gradient direction E = S∇T.

(3.1)

∇T = dT /dx is the temperature gradient. This electric field gives rise to a potential difference ∆V = V2 − V1 between two points of the conductor with a temperature difference ∆T ; ∆V = S∆T.

(3.2)

S is the thermoelectric power or Seebeck coefficient. The thermoelectric power can be expressed as [155] S=−

2 π 2 kB T 3|e|

1 ∂σ(,) σ(,) ∂,

, "="F

(3.3)

3.2. Thermoelectric power (S)

33

where σ(,) is the electrical conductivity as a function of the energy ,. ,F is the Fermi energy, kB Boltzmann’s constant, and e the electron charge. The expression for the electrical conductivity using the Boltzmann method in the relaxation-time approximation is e2 2 v (,)τ (,)D(,), (3.4) 3 where v is the velocity, τ the relaxation time, and D the electron density of states. σ(,) =

3.2.1

Thermoelectric power in HTSC

The thermoelectric power is important for understanding the HTSC. Studies of S are complementary to resistivity and Hall effect measurements. S is highly sensitive to details of the charge transport mechanisms, and information can be obtained concerning the nature of carriers, the charge concentration, and the band structure. Studies of S as a function of carrier concentration and temperature have been made on La2−x Srx CuO4 [156, 157], Y-123 [34, 39, 158–161], Bi-based [162–166], Tl-based [164, 167], and Hg-based [168, 169] systems. It has been found that S of HTSC shows the following general features: (I) In semiconducting and insulating strongly underdoped cuprates with low hole concentration S is large and positive and its value decreases with increasing hole concentration. (II) For metallic cuprates, close to optimal doping, S is small and has a characteristic behaviour for both underdoped and optimally doped samples. At temperatures above Tc , S first rises with increasing temperature towards a broad maximum at Tmax and then decreases almost linearly with temperature at least up to room temperature. Absolute values of both S(T ) and Tmax , however, exhibit a strong and systematic decrease with increasing p. (III) For overdoped cuprates with larger hole concentration, S is negative. (IV) Changes in the temperature dependence of S could be a simple way for distinguishing plane and chain contributions to transport properties, since the chain contribution to S has a positive dS/dT while the plane contribution typically has a negative slope. It is interesting to note that for electron-doped oxide superconductors [170] the absolute value of S is large and negative for samples with negative dρ/dT . The magnitude of S also decreases with increasing electron carrier concentration and S changes from negative to positive values at larger carrier concentration. Studies on HTSC show that key parameters have been recognized to be the hole concentration (per Cu atom) in the CuO2 planes and the distribution of holes between the CuO2 planes and the CuO chains. Through systematic studies in several HTSC, Obertelli et al. [167] found a universal relation between the room

34


temperature S, the critical temperature, and the hole concentration in both the underdoped and overdoped regimes. In this universal relation they have assumed that CuO chains play no significant role, which may not be valid for all cuprates [171], [paper III]. The result by Obertelli et al. is shown in figure 3.4. It can be used as a tool to empirically estimate the hole concentration.

Figure 3.4. Room temperature S, S290K , vs. hole concentration and Tc /Tcmax for various HTSC in both the underdoped (logarithmic scale for S) and overdoped (linear scale) regions. The figure is taken from Ref. [167].

Another characteristic feature of S(T ) is the variation of the temperature Tmax at the maximum of S(T ), in HTSC cuprate systems such as La2−x Srx CuO4 [172], Bi-2212 [163, 173], and Tl-2212 [174]. Tmax and p change in the opposite way when doping concentration increases. Measurements of S are shown in figure 3.5 for charge neutral dopings with equal amounts of Ca and Pr in Nd1−2x Cax PrxBa2 Cu3 O7−δ . It was shown that with increasing doping, Tmax decreased for Ca doping [paper I], increased for Pr doping [paper IV], and was approximately constant for charge neutral dopings with an equal amount of Ca and M with M=Pr and Th [paper III]. The hole concentration in the CuO2 planes was estimated for hole (Ca) and electron (Pr) doping in Nd-123 from the universal relation by Obertelli et al. [167].


35

Figure 3.5. S vs. temperature for charge neutral doping by an equal amount of Ca and Pr in Nd1−2x Cax Prx Ba2 Cu3 O7−δ [paper III]. The solid curves are undistinguishable fits to either Eq. 3.6 or 3.8. These two equations will be discussed in section 3.2.2.

The results are shown in figure 3.6. The approximately equal slopes of the relation between hole concentration and doping concentration for Ca-doped Nd-123 [paper I], Y-123 [161], and Pr-doped Nd-123 [paper II] suggests a Pr valence close to +4 at low doping concentration. This is supported by the nearly constant Tmax for charge neutral dopings (figure 3.5).

3.2.2

Models for S

Although some common features of S have been found in HTSC such as the relation of Obertelli et al. [167] between S290K and hole concentration, there is still no satisfactory explanation for the behaviour of S and a wealth of theoretical models and experiments remain controversial. Some models proposed or taken up to describe S data of HTSC are the Hubbard model [175, 176], the carrier diffusion and phonon-drag model [177, 178], a two band model with an additional T-linear term [163], the two-band model of Xin et al. [179], the Nagasoa and Lee model [180], and a phenomenological narrow-band model [181]. We will describe two of these models which have been used in our work. These models are the two-band model with additional T-linear term [163] and a

36


Figure 3.6. Hole concentration, p, as estimated from S290K vs. doping concentration, x, for Nd1−x Mx Ba2 Cu3 O7−δ with M=Ca (, paper I), Pr (•, paper II), and for Y1−x Cax Ba2 Cu3 O6.96 (◦, [161]). The curves are a linear fit to data.

phenomenological narrow-band model [181]. The points near Tc were not considered when data were analyzed in these models due to the sharp peak near Tc and the effect of superconducting fluctuations [182]. I.

Two-band model with additional T-linear term

Gottwick et al. [183] proposed a two-band model, which is a superposition of a broad and a narrow band, for analyzing the thermoelectric power data of CeNix samples. The narrow band has width Γ and is centered at ,0 , close to the Fermi energy ,F . Using a Lorentzian form of the density of state as proposed by Hirst [184] and within Boltzmann theory and the relaxation time approach, the following relations were obtained: AT B2 + T 2 2|,0 − ,F | , |e| [(,0 − ,F )2 + Γ2 ] 3 . 2 π 2 kB

S

=

A = B2

=

(3.5)

Forro et al. [163] modified the two-band model by Gottwick et al. with addition of a normal-band contribution as a linear temperature term. S of Bi-2212 single


37

crystal with varying oxygen content was analyzed in the temperature region above Tc using the following expression: AT S= + γT. (3.6) B2 + T 2 We have analyzed the thermoelectric power of Ca-, Pr-, CaPr- and CaTh-doped Nd-123 samples [papers I, II, III]. It was found that Eq. 3.6 could well describe the observations (e.g. curves in figure 3.5). The parameter γ was found to vary with hole concentration p in a parabolic way for Nd-123 doped with either Ca, Pr, or Ca-Pr (figure 3.7). The hole concentration was determined from the universal relation between p and S290K [167]. The maximum of this parabola was close to the charge concentration corresponding to the maximum superconducting transition temperature Tc . This relation is interesting since it gives a further example of a parabolic relation between p and other high-Tc superconducting properties e.g. Tc [62] and n/m∗ [185, 186]. However, this result for γ(p) is empirical and not understood in detail. As can be seen in figure 3.7, the relation breaks down for Ca-Th doping. This is apparently due to a break down of the relation between S290K and p, where p was found to increase with Ca-Th doping concentration [107], while the universal relation between S290K and p indicates that p decreases with doping concentration because S290K increases with x [paper III].

Figure 3.7. The parameter γ as a function of hole concentration, p for Nd1−x Mx Ba2 Cu3 O7−δ with M=Ca [paper I], Pr [paper II], and for Nd1−2x Cax Mx Ba2 Cu3 O7−δ with M=Pr and Th [paper III].

38


II.

Phenomenological narrow-band model

A phenomenological narrow-band model was developed by Gasumyants et al. [181] to explain the behaviour of several electrical transport properties ρ(T ), S(T ), and RH (T ), in the normal state of Y-123 alloys. This model supposes the existence of a narrow peak in the electron density of states, DOS, close to the Fermi level as inferred from positron-annihilation [187] and transmission spectroscopy studies [188]. A Van Hove singularity near the Fermi level may be the most probable reason for the peak [189]. When the Fermi level, ,F , is located in the DOS peak, the narrow band width of the peak determines the transport properties particularly when the DOS of the peak is significantly larger than the background DOS. This model contains three main parameters for ρ(T ) and S(T ) and an additional one for RH : 1. The band filling by electrons F = n/N , where n is the electron concentration and N is the number of states in the band. 2. The total effective band width wD in the density of state D(,). 3. The conductivity effective band width wσ in the longitudinal conductivity σ(,). 4. For RH the transverse effective band width wσH in the transverse conductivity σH (,). Approximate analytical expressions were derived for the temperature dependence of the transport properties, using rectangular approximations for D(,), σ(,), and σH (,). According to this model, the expressions for ρ(T ), S(T ), and RH (T ) are given by

ρ

=

S

=

RH

=

µ∗

=

1 1 + z −2 + 2z −1 cosh wσ∗ , z −1 sinh wσ∗ kB wσ∗ 1 − ( [z −1 + cosh wσ∗ − ∗ (cosh µ∗ e sinh wσ∗ wσ z+u + cosh wσ∗ )ln( )] − µ∗ ), z + u−1 < σH > (z − 1)(v − 1)2 (1 + zu)2 (z + u)2 , < σ >2 z(1 + z)(z + v)(1 + zv)(u2 − 1)2 ∗ sinh(F wD ) µ = ln ∗ ]. kB T sinh[(1 − F )wD

(3.7)

(3.8) (3.9) (3.10)

∗ Here wD = wD /(2kB T ), wσ∗ = wσ /(2kB T ), wσ∗H = wσH /(2kB T ), z = exp(µ∗ ), v = exp(wσ∗H ), and u = exp(wσ∗ ). µ is the electron chemical potential and kB the Boltzmann constant. < σ > and < σH > are the averages of the longitudinal and


39

transverse (Hall electrical) conductivity in the intervals wσ and wσH , respectively. In the high temperature limit (wD < kB T ), S becomes [181]

S=

F kB ln . e 1−F

(3.11)

According to this equation S is independent of temperature. In this range of temperature the sign and magnitude of S depend on the band filling parameter F , where S > 0 for F > 1/2, S = 0 at F = 1/2, and S < 0 for F < 1/2. Experimental results for S(T ) have been well described by Eq. 3.8 in YBa2 Cu3 Oy samples with varying oxygen content [181] and substitutions, non-isovalent dopings in Y-123 [190, 191], charge neutral dopings in Nd-123 [paper III], and in Bi2212 [192, 193]. The curves in figure 3.5 give one example for Nd-123 compounds. Elizarova et al. [194] found a universal correlation between the effective band width wD and the critical temperature from analysis of S in Y-123 and related alloys (figure 3.8).

Figure 3.8. Critical temperature, Tc as a function of the effective conduction band width, wD for oxygen reduced Y-123 (, [181]), YBa2−x Lax Cu3 O7−δ (◦, [190]), SmBa2−x Prx Cu3 O7−δ (, [195]), Y1−x Prx Ba2 Cu3 O7−δ (, [195]), Y1−x Cax Ba2 Cu3−x Cox O7−δ (•, [194]), and Nd1−x Cax Ba2 Cu3 O7−δ (× and , [papers I, VI]).

40

3.3


Hall effect

Hall effect measurements is another important tool for clarifying charge transport mechanisms of the cuprates. The importance of the Hall effect is emphasized by the need to determine the sign and mobility of the dominating charge carriers. When an electrical charge q moves with velocity 8v along a direction perpendic8 ular to an applied magnetic field, it experiences a force (the Lorentz force q8v × B), which acts to deflect the charge perpendicular to both current and magnetic field. In figure 3.9, a constant current I flows along the y-axis from left to right in the presence of a magnetic field B in the z-direction. Charges subject to the Lorentz force initially drift away from the current line towards the x-axis direction. This causes a charge separation to build up on the sides of the sample, which produces an electric field Ex perpendicular to the directions of the current and magnetic fields in the negative x direction for positive q, and in the positive x direction for negative q. This charge creates a potential drop across the sample in the x-direction, the Hall voltage VH , of magnitude VH =

IB . qnd

(3.12)

d is the sample thickness, and q the elementary charge. In this simple one band picture the Hall coefficient RH is obtained for holes (q = e) and electrons (q = −e) and is

RH RH

1 n|e| 1 = − n|e| =

(holes),

(3.13)

(electrons).

(3.14)

z B +

I -

w

+ -

+ -

+

V=V H +

-

+

Ex

I y

d

x

V=0

Figure 3.9. Experimental arrangement for Hall effect measurements showing an electrical current I in the y direction passing through a bar-shaped sample of width w and thickness d in a uniform magnetic field B in the z direction.

3.3. Hall effect

41

With electric fields Ey and Ex in the longitudinal and transverse directions respectively, the Hall angle ΘH is defined by cotΘH =

Ey ρ = . Ex BRH

(3.15)

ρ is the longitudinal resistivity. The mobility µ is the charge carrier drift velocity 8v per unit longitudinal electric field Ey , µH =

|8v | j RH 1 = = , = Ey nqEy ρ BcotΘH

(3.16)

j is the longitudinal current density (I/wd). The Hall mobility µH is the mobility determined by Hall effect measurements.

3.3.1

Hall effect in HTSC

Studies of the normal state Hall effect have been conducted since the discovery of the HTSC [196]. The Hall coefficient RH deviates from the conventional Fermi Liquid behaviour [197] as does also the resistivity with a complicated dependence on temperature [198], carrier doping [4, 199], and disorder [200]. RH measurement indicated that the majority carriers are holes in RE-123 systems. Hall effect measurements as a function of carrier concentration and temperature have been made in several hole-doped compounds, e.g., Y-123 [201–203], La-214 [204, 205], Tl-2201 and Tl-1212 [199, 206], Bi-2212 [207, 208], and Hg-1212 [206, 209] and in the electron-doped compounds, such as Nd2−x Cex O4 [210–212]. Figure 3.10 shows typical RH results in hole-doped and electron-doped compounds as a function of temperature and doping concentration. RH shows a drastic temperature dependence at low temperature, while at high temperatures (∼1000 K) it is nearly constant. It has been found that RH of HTSC in general shows the following features in the normal state: (I) RH has a temperature dependence of approximately 1/T in a quite wide range of temperatures. dRH /dT < 0 is observed in the hole-doped compounds while dRH /dT > 0 is realized in the electron-doped compounds. (II) Fermi surface is similar in the hole-doped and the electron-doped compounds [213], while RH has different signs. (III) |RH | |1/ne| at low temperatures in the underdoped compounds. Models proposed to describe the Hall effect,include a model based on a temperature-dependent charge carrier density [214], magnetic skew scattering [215], Anderson’s Luttinger-liquid model [200, 216], and a phenomenological narrow band model [181]. The interpretation of the observed experimental results is still under discussion.

42


Figure 3.10. The Hall coefficient RH vs. temperature T for La2−x Srx CuO4 (hole doping) and Nd2−x Cex CuO4 (electron doping). The figure is taken from Ref. [213].

The phenomenological narrow band model was discussed in section 3.2.2. In this model, Eq. 3.9 was used to empirically describe the temperature dependence of RH . The Andersson model will be discussed below. I.

Anderson model

In 1991, Anderson [216] proposed that the conductivity is different in the longitudinal and transverse directions, and governed by two different mechanisms and thus two relaxation times due to spin-charge separation in the CuO2 planes. In this model; i) longitudinal (transport) scattering is governed by holon-spinon interactions, with a relaxation time following a T −1 dependence (τtr ∝ T −1 ); ii) transverse (Hall) scattering is governed by spinon-spinon interactions, with a relaxation time following a ≈ T −2 dependence (τH ∝ T −2 ). τtr gives the wellknown linear-T resistivity, while τH gives the temperature dependence of the Hall angle cotΘH ; cotΘH =

ρ = αT 2 + β. RH B

(3.17)

3.3. Hall effect

43

α and the impurity-induced contribution β are temperature independent constants. Equation 3.17 was initially found to hold for YBa2 Cu3−x Znx O7−δ by Chien et al. [200]. It has subsequently been confirmed for a large number of HTSC systems (e.g. [199, 201–203, 205–207, 209]). However, in some cases a deviation is observed from a T 2 dependence in HTSC systems [202]. It has been shown that α is independent of Ca doping concentration in Y1−x Cax Ba2 Cu3 Oy samples [203] and in Nd1−x Cax Ba2 Cu3 O7−δ [paper VI] while β increases linearly with x. From studies of the Hall mobility µH in several HTSC, Yakabe et al. [203] found that the T-dependence part of µ−1 H is roughly constant regardless of carrier concentration, and disorder (figure 3.11).

2 Figure 3.11. µ−1 H as a function of T for different HTSC. The solid and broken curves are for Y0.5 Ca0.5 Ba2 Cu3 O6.38 and YBa2 Cu3 O6.488 [203], the open triangles and closed circles are for La2−x Srx CuO4 with x = 0.1 and 0.15, respectively [204]. The open squares, closed triangles, and open circles are for Bi2 Sr2 CaCu2 O8 [207], TlBa2 CuO6+δ [199], and HgBa2 Ca2 Cu3 O8+δ [217], respectively. The figure was taken from Ref. [203]

44

Chapter 4

Experimental Techniques This chapter will describe how samples were prepared and the techniques used for study of the structural properties, and how the electrical transport properties were determined as a function of temperature and doping concentration. First, the preparation of samples is outlined (section 4.1), followed by sample characterization (section 4.2). Finally, the measurement techniques used for studies of the transport properties are described (sections 4.3, 4.5, 4.4).

4.1

Sample Preparation

In order to study physical properties of materials it is important to obtain homogeneous single-phase samples. Therefore, it is necessary to choose starting materials with high purity to avoid introducing defects and impurity phases into the structure. The synthesis is well described in Ref. [126], and therefore the process will be given briefly here. Sintered samples of Nd1−x Mx Ba2 Cu3 O7−δ (with M=Ca, La, and Pr) and Nd1−2x Cax Mx Ba2 Cu3 O7−δ (with M=Pr or Th) were synthesized by a solid state reaction to form a bulk polycrystalline material. Starting materials were high purity RE2 O3 (RE = Nd, and La), BaCO3 , CuO, CaCO3 , Pr6 O11 , and ThO2 . Powders of the appropriate amounts of the starting materials were carefully mixed and ground in a mortar. To improve the homogeneity of the mixture, a small amount of acetone was added and grinding proceeded until most of the acetone had evaporated. After careful mixing and milling, the powder was pressed to cylindrical pellets with a diameter of 12 mm and a height of 2-3 mm. The pellets were sintered in air at 900, 920, and 920 o C for about 14 hours with intermediate grindings. The three sinterings were necessary to ensure a full homogeneity of the sample. The pellets were then cut into bars with typical dimensions 0.5 × 2.5 × 10 mm3 and annealed in flowing oxygen at 460 o C for 3 days. Then the temperature was decreased to room temperature at a rate of 12 o C/hr. Such slow cooling has been found to give a good sample quality for Nd-based 1:2:3 samples [107]. 45

46

4.2

Chapter 4. Experimental Techniques

Sample Characterization

The present samples have been characterized by different diffraction techniques, which have different advantages and disadvantages and thus complement each other. Information of the detailed atomic structure is of great importance when interpreting results from different measurements. In this work the samples were analyzed by a sensitive X-ray powder diffraction technique to check sample purity and to determine cell parameters (section 4.2.1). For one sample series neutron powder diffraction was used in addition for detailed investigation of atomic structure (section 4.2.2).

4.2.1

X-ray powder diffraction

Usually X-ray diffraction experiments are preferred among other characterization techniques since they are fast, inexpensive and easy to perform. The present materials have been characterized by X-ray powder diffraction. A Guinier-H¨ agg camera was used. This technique offers a number of advantages, such as high resolution of the patterns obtained, a small amount of sample needed (< 50 mg), and shorter exposure time due to focused beam intensity. For our studies, Cu Kα1 radiation with a wavelength λ = 1.54053 ˚ A has been used. Powder of the sample was mixed with silicon powder, which acts as an internal standard. The sample was placed in front of the opening in the camera and the diffraction pattern was taken up on a film. For increased sensitivity and for more accurate data handling, the film was read by a computerized film microdensitometer system [218].

4.2.2

Neutron powder diffraction

Neutron diffraction has been widely applied to high-Tc superconductors and is a powerful tool for studies of static and dynamic atomic and magnetic structures due to the physical characteristics of the neutron, i.e. charge, mass, magnetic moment. The rather weak interaction with matter results in a large penetration depth and can therefore be used to study bulk properties of matter. This is also important for the investigation of materials under extreme conditions such as very high pressure, low and high temperature, and high magnetic field. The neutron scattering amplitude depends on the energy levels in the atomic nuclei and therefore the scattering from light atoms like oxygen is much stronger than for X-rays. This makes it possible to determine oxygen sites and Cu-O bond lengths in HTSC. Furthermore, neutrons can easily distinguish between isotopes. The neutron powder diffraction data were collected at the Swedish research reactor R2 in Studsvik. Monochromatic neutrons with a wavelength of 1.470 ˚ A were obtained from a double-monochromator system. The neutron flux at the sample position was approximately 2 × 106 cm−2 s−1 . Powdered sintered samples of mass of about 5 g were placed in a 6 mm diameter vanadium tube, and data were collected with 35 3 He detectors which scanned a 2θ range of 4.00o − 132.92o

4.2. Sample Characterization

47

Counts

in steps of 0.08o . In figure 4.1 the diffraction pattern for NdBa2 Cu3 O7−δ is shown as an example. 11000 9000 7000 5000 3000 1000 -1000 -3000 0

20

40

60

80

100

120

140

2 θ (º) Figure 4.1. Neutron powder diffraction for NdBa2 Cu3 O7−δ [paper V]. The short vertical bars below the data indicate the positions of Bragg reflections. The difference between calculated and observed intensities is shown in the lower part

4.2.3

Rietveld method

The conventional diffraction technique using integrated intensities from Bragg peaks in the powder pattern is favoured for high symmetry structures. However, this method is impractical for structures with low degree of symmetry or with large unit cells, since the problem with overlapping Bragg peaks becomes severe in such cases. H. Rietveld [219, 220] considered the possibility of handling all the observed intensities yio at each step i instead of integrated intensities Ij at each peak j. The Rietveld method is a powerful tool for extraction of structural information from powder diffraction pattern such as atomic coordinates, temperature factors, quantitative phase analysis. In the Rietveld method, the intensity measured at each step i is the sum of the contributions from several Bragg reflections. The measured intensities are then compared to calculated intensities from a model for all Bragg reflections that can contribute to the observed intensities. A reasonable good starting model is required when using this method since no integrated intensities are calculated. The residual

48


Sy (Eq. 4.1) is minimized in a least-squares refinement using reasonable parameters for the peak shapes, structure, and unit cell parameters, in an initial assumption. wi (yio − yic )2 , (4.1) Sy = i

where wi is a weight function. yio and yic are the observed and calculated intensities in step i, respectively. The refinable parameters may be divided into instrumental and sample parameters. The instrumental contributions are the instrumental profile function, the zero position, the background, and the wavelength. The parameters reflecting the contributions from the sample are scale factors, lattice parameters, occupancies, temperature factors, coordinates, absorption coefficients etc. The peak shapes depend both on the experimental instrument and sample features, such as crystallite size and absorption. The peak functions were fitted to the Pseudo-Voigt (PV) function which turned out to be a satisfactory approximation. The PV function (Eq. 4.2) is a linear combination of a Lorentzian (L, Eq. 4.3) and a Gaussian (G, Eq. 4.4) of the same Full Width at Half Maximum (FWHM). Hj (Eq. 4.5) models the FWHM of the j th Bragg reflection [221]. P V (x)

=

L(x) =

G(x)

=

Hj2 (2θ) =

ηL(x) + (1 − η)G(x) 0 ≤ η ≤ 1, 1 2 , πHj 1 + 4 x22 Hj 1/2 (4ln2) −(4ln2)x2 exp , Hj2 Hj π 1/2

(4.2)

U tan2 θj + V tanθj + W.

(4.5)

(4.3)

(4.4)

x is (2θi − 2θj ). The mixing parameter η can be refined as a linear function of 2θ with the refinable variables η0 and X, e.g η = η0 + X × 2θ. U , V , and W are refinable parameters. The quality of the refinement was checked by several agreement factors: RBragg

=

Rp

=

j

|Ijo − Ijc | j Ijo

|yio i

− yic | i yio

Rwp

=

Rexp

=

χ2

=

wi (yio − yic )2 2 i wi yio 1/2 (N − P + C) 2 i wi yio 2 Rwp Rexp i

(the Bragg f actor),

(4.6)

(the prof ile f actor),

(4.7)

1/2 (the weighted prof ile f actor), (4.8) (the expectation f actor), (the goodness of f it).

(4.9) (4.10)

4.3. Electrical Resistance Measurements

49

Ijo and Ijc are the observed and calculated integrated intensities for the different Bragg peaks j. (N-P+C) is the number of degrees of freedom. N is the number of observations (e.g. the number of yi ’s used), P is the number of refined parameters, and C is the number of constraints applied. In order to estimate the quality of the refined results we must consider a global view of the difference between the calculated profiles and the measured data combined with the agreement factors. From mathematical point of view Rwp is the most meaningful of these R’s because the numerator is the residual being minimized in the refinement. The integrated intensity factor RBragg is based on a comparison of observed and calculated integrated intensities. χ2 is usually taken as the quality measure of the fit and convergence. The refinement of the neutron diffractograms was made with the FullProf program [222] using the orthorhombic space group Pmmm. The parameters were refined by adding a few at a time in order to avoid any false minima. At first the scale factor, zero point for 2θ, cell parameters, background parameters, and the peak shape parameters were refined successively from reasonable estimates. After the preliminary refinements, atomic parameters, i.e. the z coordinates, temperature factors, and the occupation numbers were refined to convergence. Refinement of anisotropic temperature factors was only employed for oxygen at the Cu-O chain site, which was found to lead to better refinements. A detailed description of the Rietveld method can be found in the book by Young [221].

4.3

Electrical Resistance Measurements

An electrical resistance measurement is generally one of the easiest and most straightforward ways to provide useful information about the sample quality, normal state properties, and superconducting critical temperature. Typically, a linear dependence of resistivity on temperature is observed in the normal state, and has often been used as an indication of sample quality. The extrapolation of this linear relation to T = 0 K should be close to zero for a good sample. HTSC are chemically complex materials. Several superconducting phases may exist in one sample. For example, a two step transition from the normal to the superconducting state reflects the presence of at least two superconducting phases. The temperature coefficient of resistance α is a convenient material parameter of the normal state because it does not depend on sample geometry. This parameter was calculated from the slope of the resistance-temperature relation around 275 K normalized to the resistance at 275 K. α is thus defined as 1 dR . (4.11) α= R275 dT T =275K Disorder gives a contribution to the resistance that is almost independent of temperature in the normal state. This will increase the resistivity and by Eq. 4.11 hence decrease α.

50


In HTSC, the transition from the normal to the superconducting state is less sharp than in conventional superconductors especially in magnetic field, and therefore we need a consistent definition of Tc for these superconductors. A convenient approach to define Tc is the temperature corresponding 50 % of the resistance drop. The Tc corresponding to 10 and 90 % of the normal state resistance can be used to define a transition width ∆Tc = Tc (90%) − Tc (10%).

Figure 4.2. Resistance vs. temperature for Nd-123. The Tc resulting from different definitions of the critical temperature are indicated.

The electrical contacts and the resistance measurement techniques (section 4.3.1) used in this work are described in the rest of this section.

4.3.1

Electrical contacts and measurement technique

Resistance measurements were made with a standard four point contact configuration. For the electrical contacts, silver paint was applied in narrow strips on the sample. In order to improve the contact resistance, the sample was heat treated in flowing oxygen at 300 o C for 30 min and quenched to room temperature. Finally thin copper wires were connected with silver paint as shown in figure 4.3. Two different cryostats have been used for resistance measurements in zero magnetic field and in fields. The first one was a 4 He cryostat (see figure 4.4a). It consists of an inner part with radiation shields, a sample holder, and an outer part, which is filled with liquid nitrogen. To minimize the heat conduction, the cryogenic baths are isolated from the outside by vacuum. The sample holder is placed in a sample space. The sample holder used in our experiments takes up to four samples at the same time. The area where the samples are mounted was covered with a

4.3. Electrical Resistance Measurements I+

51

V+

V-

I-

Figure 4.3. Typical sample contact layout with contact wires for resistance measurements.

thin layer of varnish to prevent electrical short-circuits. In order to improve thermal connection to the copper block, Apiezon grease was used. The temperature was measured with a calibrated Pt resistor. The second cryostat was a 4 He gas flow cryostat, which is equipped with a 12 T NbTi/Nb3 Sn superconducting magnet. The superconducting coil is located in a bath of liquid helium. A description and handling of this cryostat was given by Andersson [223]. Figure 4.4b shows the sample cell and the standard sample holder inside this cryostat. An extra shield around the sample holder is inserted into the sample cell in order to provide additional isolation of the sample from the flowing He gas. In the temperature range 4.2-300 K cooling is obtained by flowing 4 He gas in the sample cell, where the sample holder is placed (inside the extra shield). Two needle valves are used to control gas flow and thereby the cooling power. One is placed at the 4 He inlet tube at the bottom of the sample cell and the second one is

Filling tubes

Pt thermometer

Radiation shields

Carbon thermomete r Vacuum spaces

Pt thermometer on the shield

Plug-in Sam pleposition

Liquid Nitrogen

Sample holder

Carbon-glass thermometer Inner vacuum shield

Sample space Liquid Helium

Heater winding

Sample cell

He gas inlet (a)

(b)

Figure 4.4. (a) Schematic view of the 4 He cryostat. (b) Sample cell with sample holder and shield in the 4 He gas flow cryostat.

52


at the pumping station. In addition, the incoming gas can be preheated. Different thermometers have been used for measurement of the sample temperature and for temperature control and regulation. The platinum thermometers have a high sensitivity above 30 K. Below this temperature the sensitivity decreases with the temperature. Carbon resistors have a strong temperature dependence below 20 K and are therefore useful thermometers in this range. These thermometers have a high magnetoresistance and therefore they need an accurate calibration in magnetic field. Carbon-glass thermometers have a great advantage compared to platinum and carbon thermometers. They are less sensitive to magnetic fields in the whole temperature range 1-300 K. The Carbon-glass thermometers have been calibrated and have an accuracy of about 0.1% in temperature in the temperature range between 5-100 K. The resistance measurements were made with a Solartron 7081 digital multimeter with sensitivity 10 nV and a Keithley 220 current source with an internal current of less than or equal to 1mA. The temperature was measured with a platinum or carbon-glass thermometer in the sample holder. The data were collected with a computer connected to the instruments.

4.4

Thermoelectric Power (S) Measurements

Figure 4.5 shows a simple thermoelectric power circuit. It consists of sample and wires with junctions at different temperatures T1 and T2 = T1 + ∆T . The thermoelectric power S can be evaluated from a measurement of the potential difference ∆V across the sample and wires. picovoltmeter

Sample

T1

T2

Heater

Figure 4.5. Experimental set up for measuring thermoelectric power. The temperature difference is ∆T = T2 − T1 across the sample.

The measured voltage is

T2

∆V = T1

Ss dT −

T2

Sw dT,

(4.12)

T1

where T1 is the temperature of the cold part of the sample and T2 is the temperature of the warm part. Ss and Sw are the Seebeck coefficients of the sample and the connecting wires, respectively. If the temperature gradient is small, one obtains

4.4. Thermoelectric Power (S) Measurements

53

for a sequence of different ∆T :s from Eq. 4.12 that the slope of the straight line relating ∆V to ∆T , can be expressed as: d(∆V ) = Ss − Sw = S ∗ , d(∆T )

(4.13)

Ss = Sw + S ∗ ,

(4.14)

resulting in

where S ∗ is the measured thermoelectric power. The sign adopted for S ∗ is such that the thermoelectric power of the sample is positive relative to wires if the current tends to flow from sample to wire at the cold side.

4.4.1

Sample holder

The thermoelectric power measurements were made with a sample holder shown in figure 4.6. This sample holder has the possibility to measure two samples at the

(silicon diode) (silicon diode)

Figure 4.6. Schematic view of the sample holder for measuring thermoelectric power. The figure was taken from [224].

54


same time. The samples are attached directly to the two cooper blocks, named warm and cold in the figure, with silver paint. There are two heaters on the sample holder. The large heater (25 Ω) is wound around the main part of the sample holder. It is used to increase the main temperature of sample holder. The cold copper block is attached to the main part and should have about the same temperature. The warm copper block is attached to the main part with a thin bar of stainless steel in order to reduce heat transfer from the warm copper block to the main part. It has a small heater, which creates the temperature gradient. Silicon diode thermometers, which are suitable due to their small size, were calibrated to measure the temperature in the whole temperature range 4.2 - 300 K. They are positioned as close to the sample as possible. This sample holder has been described in detail elsewhere [224].

4.4.2

S measurement procedures and data acquisition

The sample is cooled in the 4 He cryostat (figure 4.4a) to a cold temperature Tcold and then heated slowly with the large heater during the measurements. A temperature gradient ∆T is created by heating one side of the sample relatively fast with a small heater periodically. This period is called small sweep. Figure 4.7 shows the temperature as a function of time. In order to obtain S ∗ , during the small sweep the voltage ∆V is measured for different temperature gradients and a straight line is fitted to data according to Eq. 4.13 (figure 4.8). The data were corrected for the contribution of the copper connecting leads. The temperature for the whole small sweep T at which S ∗ is obtained, is taken as the average of all temperatures during the whole small sweep. S measurements were made on sintered bars, using a small, reversible temperature difference of ≤ 2K.

T Twarm

Tcold

∆Tmax

t Small sweep Figure 4.7. The temperature for the warm and the cold side of the sample as a function of the time.

4.5. Hall Coefficient Measurements

55

Figure 4.8. The potential difference ∆V as a function of the temperature gradient ∆T , and the least square fitted straight line from which S ∗ was obtained.

To read the temperature a Lake Shore LS340 temperature controller were used. Two of the silicon diodes thermometers were measured by the temperature regulator and the third one (for a second sample), by a voltmeter and a Keithley 2400 current source. The voltage along the sample is measured with an E.M. Electronics picovoltmeter (Model P13) together with a Keithley multiplexer model. Data were collected by a computer and analyzed with a program written for HP-VEE (Hewlett Packard Visual Engineering Environment), which controls the temperature regulator and gives the possibility to stabilize a given temperature. A more through description of the program is given elsewhere [225].

4.5

Hall Coefficient Measurements

Hall voltage VH was measured with a standard five point contact configuration as shown in figure 4.9 using a field sweep technique. The electrical contacts were performed as mentioned in section 4.3.1. A variable resistance was used to compensate the offset voltage at each temperature in zero magnetic field. Hall voltage measurements were made on sintered bars with typical dimensions 0.5 × 2.5 × 6 mm3 . VH as a function of the magnetic field B was linear for all samples for temperature above Tc and magnetic field up to 8 T (figure 4.10). The Hall coefficient RH was inferred from the slope of the VH vs B relation at each temperature. The temperature was stabilized and controlled by a Lake Shore 340 temperature regulator. The Hall voltage measurements were made with a constant current source (Keithley 220) and a DC picovoltmeter (EM Electronics, Model P13) with

56


I+

VH

B

I-

Figure 4.9. Contact layout with contact wires for Hall voltage measurements.

Figure 4.10. Hall voltage measurements VH as a function of magnetic field B and temperature for NdBa2 Cu3 O7−δ .

a resolution of 100-300 pV. It was limited by the source resistance and variation of the thermoelectric power during the experiment . The picovoltmeter acted as a preamplifier to a standard voltmeter (Schlumberger 7081). The effect of thermoelectric powers in the measurement circuit were reduced by averaging over voltages measured with positive and negative currents (+, -, +).

Chapter 5

Brief summary of results This chapter contains a brief summary of the most important results of the original papers. Paper numbers refer to the list in the preface.

5.1

Thermoelectric power and resistivity of Nd1−x Cax (or Lax )Ba2 Cu3 O7−δ . (Paper I)

X-ray powder diffraction showed that the a- and b-axis lattice parameters decreased with increasing doping and the c-axis lattice parameter increased in both the Nd1−x Cax Ba2 Cu3 O7−δ and the Nd1−x Lax Ba2 Cu3 O7−δ series. In the case of La doping, the XRD results indicated an impurity phase of BaCuO2+ν , which increased with La doping. The critical temperature Tc decreased with increasing Ca and La doping. For all samples, the thermoelectric power S was positive and followed roughly a linear temperature dependence with negative slop above Tc . Both the room temperature resistivity and the thermoelectric power indicated that hole concentration changes with increasing doping in different directions for the two dopings. The hole concentration was estimated from the room temperature thermoelectric power [167]. From these results, it was inferred that 26 % of the La atoms are substituted on the Ba sites. The results for S were analyzed in a two-band model with an additional linear T term which was found to well describe the data.

5.2

Thermoelectric power and resistivity of Pr-doped Nd-123. (Papers II and IV)

Analyzes of the c-axis lattice parameter, cell volume, critical temperature, resistivity, and thermoelectric power all suggested that the Pr ions have a valence close to +4 at low doping concentration. The superconducting critical temperature was 57

58

Chapter 5. Brief summary of results

described by a parabolic term and a linear term. An anomaly has been observed in S(T ) for x ≥ 0.20 in the form of a dip at 78 K of order 15 % of S (paper IV). We analyzed the thermoelectric power as a function of temperature with a two-band model with an additional linear T term, γT . The thermoelectric power of the samples was well accounted for in this model and a qualitative physical interpretation of the parameters was obtained. A schematic picture was suggested for a possible development of the density of states around the Fermi energy as the doping concentration was increased. An empirical parabolic relation between the change in γ as a function of carrier concentration and the hole concentration was found.

5.3

Different types of localization in Ca-Pr and Ca-Th doped Nd-123. (Paper III)

In order to understand similarities and differences between Ca-Pr and Ca-Th charge neutral dopings, the thermoelectric power was measured as a function of temperature and doping concentration x for Nd1−2x Cax Mx Ba2 Cu3 O7−δ (with M=Pr, Th) samples. Similar to room temperature resistivity ρ290K [130], the room temperature S290K increased strongly with Ca-Th doping, while it increased slowly with Ca-Pr doping, in spite of the similarly depressed Tc . S(x, T ) was found to be well described by two different semiempirical two band models: a two-band model with an additional linear T term [163], and the phenomenological narrow band model [181]. Localization increases for both dopings as evidenced in the former model by the displacement of the Fermi energy towards the localized part of the band, and in the latter one by the decrease of the ratio of the conductivity band width to the total band width. These changes were in general more prominent for Ca-Th doping, which together with a stronger increase of the electrical resistivity indicated that the localization tendency is driven by electronic disorder for this doping. For Ca-Pr doping the results suggested that in addition to a weaker disorder effect, mobile charge carriers localize with increasing doping concentration.

5.4

Evidence for hole localization by Pr in Nd(Pr)123 from neutron diffraction. (Paper V)

Structural analysis from neutron powder diffraction data showed that there were small structural distortions within the unit cell in Nd1−x Prx Ba2 Cu3 O7−δ . The oxygen occupation in the chains and the total oxygen content were roughly independent of Pr doping concentration. Bond valence sums (BVS) were calculated from the neutron diffraction data assuming either a constant valence or a mixed valence for Cu and Pr ions. Figure 5.1 shows the Cu2 valence, which is calculated with the BVS calculation, as a function of critical temperature Tc in Nd1−x PrxBa2 Cu3 O7−δ . The planar Cu2 valence was independent of Pr doping in Nd(Pr)-123 as well as for charge

5.5. Competition between added charge and disorder from Hall effects ...

59

neutral dopings. The chain Cu1 valence was also roughly constant. On the other hand, the hole concentration in the planes and chains decreased with increasing Pr doping as inferred from BVS calculation. This indicated that hole localization on the Pr+4 site was a main reason for the decrease of the hole concentration in the planes.

Figure 5.1. Normalized Cu2 valence vs. Tc for Nd1−x Prx Ba2 Cu3 O7−δ (, paper V), for Nd1−2x Cax Prx Ba2 Cu3 O7−δ (◦, [107]), and for Nd1−2x Cax Thx Ba2 Cu3 O7−δ (, [95]).

5.5

Competition between added charge and disorder in Ca-doped Nd-123. (Paper VI)

The Hall effect and resistivity of sintered samples of Nd1−x Cax Ba2 Cu3 O7−δ were studied in the normal state in order to further understand the role of Ca. The Hall coefficient RH could be well described by two different models. The first one was the phenomenological narrow band model [181] and the second one was Anderson, s model [216]. The results in both models indicated that disorder in the CuO2 plane increased with increasing Ca doping concentration. Disorder gave an increasing contribution to the effective band width in the density of states wD , while added charge decreased wD . This competition between added charge and disorder introduced into the CuO2 planes by Ca doping could be the main reason for the observed small decrease of wD .

60

Bibliography [1] H. Kamerlingh Onnes, Comm. Phys. Lab. Leiden 122, 81 (1911). [2] B. Batlogg, in Physics of High-Temperature Superconductors, edited by S. Maekawa and M. Sato (Springer-Verlag, Berlin, 1992). [3] M. Gurvitch and A. T. Fiory, Phys. Rev. Lett. 59, 1337 (1987). [4] T. Ito, K. Takenaka, and S. Uchida, Phys. Rev. Lett. 70, 3995 (1991). [5] N. P. Ong, in Physical Properties of High-Temperature Superconductors, edited by D. M. Ginsberg (World Scientofic, Singapore, 1990). [6] A. Carrington, A. P. Mackenzie, C. T. Lin, and J. R. Cooper, Phys. Rev. Lett. 69, 2855 (1992). [7] W. Meissner and R. Ochsenfeld, Naturwissenschaften 21, 787 (1933). [8] C. Kittel, Introduction to Solid State Physics, 6th ed. (J. Wiley & Sons, New York, 1986). [9] D. J. Quinn and W. B. Ittner, Journal of Applied Physics 33, 748 (1962). [10] F. J. Kedves, S. Mészáros, K. Vad, G. Hal´ asz, B. Keszei, and L. Mihály, Solid State Commun. 63, 991 (1987). [11] S. W. Schwenterly, S. P. Mehta, M. S. Walker, and R. H. Jones, Physica C 382, 1 (2002). [12] B. Batlogg, Solid State Commun. 107, 639 (1998). [13] B. D. Josephson, Phys. Lett. 1, 251 (1962). [14] P. W. Anderson and J. M. Rowell, Phys. Rev. Lett. 10, 230 (1963). [15] J. Bardeen, L. N. Cooper, and J. R. Schriffer, Phys. Rev. 106, 162 (1957). [16] J. Bardeen, L. N. Cooper, and J. R. Schriffer, Phys. Rev. 108, 1175 (1957). 61

62

BIBLIOGRAPHY

[17] E. Maxwell, Phys Rev. 78, 477 (1950). [18] J. W. Garland, Phys. Rev. Lett. 11, 114 (1963). [19] J. G. Bednorz and K. A. M¨ uller, Z. Phys. B 64, 189 (1986). [20] M. K. Wu, J. R. Ashburn, C. J. Torng, P. H. Hor, R. L. Meng, L. Gao, Z. J. Huang, Y. Q. Wang, and C. W. Chu, Phys. Rev. Lett. 58, 908 (1987). [21] H. Maeda, Y. Tanaka, M. Fukutomi, and T. Asano, Jpn. J. Appl. Phys. 27, L209 (1988). [22] M. Nagoshi, T. Suzuki, Y. Fukuda, K. Terashima, Y. Nakanishi, M. Ogita, A. Tokiwa, Y. Syono, and M. Tachiki, Phys. Rev. B 43, 10445 (1991). [23] U. Endo, S. Koyama, and T. Kawai, Jpn. J. Appl. Phys. 27, L1476 (1988). [24] S. S. P. Parkin, V. Y. Lee, E. M. Engler, A. I. Nazzal, Y. C. Huang, G. Gorman, R. Savoy, and R. Beyers, Phys. Rev. Lett. 60, 2539 (1988). [25] A. Schilling, M. Cantoni, J. D. Gou, and H. R. Ott, Nature 363, 56 (1993). [26] J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, and J. Akimitsu, Nature 410, 63 (2001). [27] J. D. Jorgensen, Physics Today June, 34 (1991). [28] M. Guillaume, P. Allenspach, W. Henggeler, J. Mesot, B. Roessli, U. Staub, P. Fischer, A. Furrer, and V. Trounov, J. Phys.: Cond. Matter 6, 7963 (1994). [29] T. Timusk and B. Statt, Rep. Prog. Phys. 62, 61 (1999). [30] B. Batlogg, R. Buhrman, J. R. Clem, D. Gubser, D. Larbalestier, D. Liebenberg, J. Rowell, R. Schwall, D. T. Shaw, and A. W. Sleight, J. Supercond. 10, 583 (1997). [31] L. D. Rotter, Z. Schlesinger, R. T. Collins, F. Holtzberg, C. Field, U. W. Welp, G. W. Crabtree, J. Z. Liu, Y. Fang, K. G. Vandervoort, and S. Fleshler, Phys. Rev. Lett. 67, 2741 (1991). [32] R. G. Buckley, M. P. Staines, E. M. Haines, M. Ziaei, and B. P. Clayman, Physica C 235-240, 1237 (1994). [33] G. V. M. Williams, J. L. Tallon, R. Michalak, and R. Dupree, Phys. Rev. B 54, R6909 (1996). [34] J. L. Tallon, J. R. Cooper, P. S. I. P. N. de Silva, G. V. M. Williams, and J. W. Loram, Phys. Rev. Lett. 75, 4114 (1995).

BIBLIOGRAPHY

63

[35] I. Tomeno, T. Machi, K. Tai, and N. Koshizuka, Phys. Rev. B 49, 15327 (1994). [36] H. Ding, M. R. Norman, J. C. Campuzano, M. Randeria, A. F. Bellman, T. Yokoya, T. Takahashi, T. Mochiku, and K. Kadowaki, Phys. Rev. B 54, R9678 (1996). [37] J. L. Tallon, G. V. M. Williams, M. P. Staines, and C. Bernhard, Physica C 235-240, 1821 (1994). [38] Q. M. Zhang, X. S. Xu, X. N. Ying, A. Li, Q. Qiu, Y. N. Wang, G. J. Xu, and Y. H. Zhang, Physica C 337, 277 (2000). [39] G. V. M. Williams and J. L. Tallon, J. Supercond. 258, 41 (1996). [40] J. J. Capponi, E. M. Kopnin, S. M. Loureiro, E. V. Antipov, E. Gautier, C. Chailliout, B. Souletie, M. Brunner, J. L. Tholence, and M. Marezio, Physica C 256, 1 (1996). [41] R. S. Liu, J. L. Tallon, and P. P. Edwards, Physica C 182, 119 (1991). [42] C. M. Varma, P. B. Littlewood, S. Schmitt-Rink, E. Abrahams, and A. E. Ruckenstein, Phys. Rev. Lett. 63, 1996 (1989). [43] J. C. Phillips, Phys. Rev. B 43, 3656 (1991). [44] P. Monthoux and D. Pines, Phys. Rev. B 47, 6069 (1993). [45] E. G. Maksimov, Phys. Usp. 43, 965 (2000). [46] N. F. Mott, Adv. Phys. 39, 55 (1990). [47] S. Y. Tian and Z. X. Zhao, Physica C 170, 279 (1990). [48] M. J. Rice and Y. R. Wang, Phys. Rev. B 36, 8794 (1987). [49] M. Ogata and P. W. Anderson, Phys. Rev. Lett. 70, 3087 (1993). [50] P. W. Anderson, The Theory of superconductivity in the High-Tc cuprate superconductors (Princeton University Press, Princeton, 1997). [51] N. L. Wang, A. W. MacConnell, and B. P. Clayman, Phys. Rev. B 60, 14883 (1999). [52] K. Kishio, J. Shimoyama, T. Hasegawa, K. Kitazawa, and K. Fueki, Jpn. J. Appl. Phys. 26, L1228 (1987). [53] P. Burlet, V. P. Plakthy, C. Marin, and J. Y. Henry, Phys. Lett. A 167, 401 (1992).

64

BIBLIOGRAPHY

[54] J. D. Jorgensen, B. W. Veal, A. P. Paulikas, L. J. Nowicki, G. W. Crabtree, H. Claus, and W. K. Kwok, Phys. Rev. B 41, 1863 (1990). [55] A. Furrer, Neutron Scattering in Layered Copper-Oxide superconductors (Kluwer Academic Publishers, Netherlands, 1998), p. 89. [56] H. Fjellv˚ ag, P. Karen, A. Kjekshus, and A. F. Andresen, Physica C 162-164, 49 (1989). [57] A. Ono, T. Tanaka, H. Nozaki, and Y. Ishizawa, Jpn. J. Appl. Phys. 26, L1687 (1987). [58] P. Karen, H. Fjellv˚ ag, A. Kjekshus, and A. F. Andresen, J. Solid State Chem. 92, 57 (1991). [59] M. Kakihana, S. G. Eriksson, L. B¨ orjesson, L. G. Johansson, C. Str¨ om, and M. K¨ all, Phys. Rev. B 47, 5359 (1993). [60] B. W. Veal, W. K. Kwok, A. Umezawa, G. W. Crabtree, J. D. Jorgensen, J. W. Downey, L. J. Nowicki, A. W. Mitchell, A. P. Paulikas, and C. H. Sowers, Appl. Phys. Lett. 51, 279 (1987). [61] J. J. Neumeier, Appl. Phys. Lett. 61, 1852 (1992). [62] J. L. Tallon and N. E. Flower, Physica C 204, 237 (1993). [63] R. J. Cava, B. Botalogg, R. M. Fleming, S. A. Sunshine, A. Ramirez, E. A. Rietman, S. M. Zahurak, and R. B. Van Dover, Phys. Rev. B 37, 5912 (1988). [64] K. Ishida, Y. Kitaoka, T. Yoshitomi, N. Ogata, T. Kamino, and K. Asayama, Physica C 179, 29 (1991). [65] A. V. Mahajan, H. Alloul, G. Collin, and J. F. Marucco, Phys. Rev. Lett. 72, 3100 (1994). [66] T. M. Riseman, H. Alloul, A. V. Mahajan, P. Mendels, N. Blanchard, G. Collin, and J. F. Marucco, Physics C 235-240, 1593 (1994). [67] P. Mendels, H. Alloul, G. Collin, N. Blanchard, J. F. Marucco, and J. Bobroff, Physics C 235-240, 1595 (1994). [68] G. Xiao, M. Z. Cieplak, A. Gavrin, F. H. Streitz, A. Bakhshai, and C. L. Chien, Phys. Rev. Lett. 60, 1446 (1988). [69] I. Felner, I. Nowik, E. R. Bauminger, D. Hechel, and U. Yaron, Phys. Rev. Lett. 65, 1945 (1990). [70] H. Alloul, P. Mendels, H. Casalta, J. F. Marucco, and J. Arabski, Phys. Rev. Lett. 67, 3140 (1991).

BIBLIOGRAPHY

65

[71] G. Ilonca, M. Mehbod, A. Lanckbeen, and R. Deltour, Phys. Rev. B 47, 15265 (1993). [72] J. M. Tarascon, P. Barboux, P. F. Miceli, L. H. Greene, and G. W. Hull, Phys. Rev. B 37, 7458 (1988). [73] J. M. Tarascon, W. R. McKinnon, L. H. Greene, G. W. Hull, and E. M. Vogel, Phys. Rev. B 36, 226 (1987). [74] M. Guillaume, P. Allenspach, J. Mesot, B. Roessli, U. Staub, P. Fischer, and A. Furrer, Z. Phys. B 90, 13 (1993). [75] D. B. Currie and M. T. Weller, Physics C 214, 204 (1993). [76] S. Ramesh and A. J. Freemen, Physics C 230, 135 (1994). [77] H. Luetgemeier, I. Heinmaa, D. Wagener, and S. M. Hosseini, 2nd Workshop on Phase Separation in Cuprate Superconductors and Cottbus and Germany (Springer-Verlag, Heidelberg, 1993), p. 225. [78] T. J. Kistenmacher, Phys. Rev. B 38, 8862 (1988). [79] G. Van Tendeloo, H. W. Zandbergen, and S. Amelinckx, Solid State Commun. 63, 603 (1987). [80] M. Hervieu, B. Domenges, C. Michel, J. Provost, and B. Raveau, J. Solid State Chem. 71, 263 (1987). ¨ Rapp, and I. Bryntse, Physics C 289, 137 (1997). [81] P. Lundqvist, P. Grahn, O. [82] X. Obradors, R. Yu, F. Sandiumenge, B. Martinez, N. Vilalta, V. Gomis, T. Puig, and S. Pinol, Supercond. Sci. Technol. 10, 884 (1997). [83] K. Saito, H. U. Nissen, C. Beeli, L. Wolf, and W. Schauer, Phys. Stat. Sol. (a) 166, 861 (1998). [84] J. G. Wen, T. Satoh, M. Hidaka, S. Tahara, N. Koshizuka, and S. Tanaka, Physics C 337, 249 (2000). [85] X. S. Wu, W. M. Chen, X. Jin, and S. S. Jiang, Physics C 273, 99 (1996). [86] X. S. Wu, S. S. Jiang, W. M. Chen, Z. S. Lin, X. Jin, Z. Q. Mao, G. J. Xu, and Y. H. Zhang, Physics C 294, 122 (1998). [87] J. L. Tallon, C. Bernhard, H. Shaked, R. L. Hitterman, and J. D. Jorgensen, Phys. Rev. B 51, 12911 (1995). [88] G. B¨ ottger, I. Mangelschots, E. Kaldis, P. Fischer, Ch. Kr¨ uger, and F. Fauth, J. Phys. Cond. Matter 8, 8889 (1996).

66

BIBLIOGRAPHY

[89] V. P. S. Awana, S. K. Malik, and W. B. Yelon, Physica C 262, 272 (1996). [90] M. Merz, N. N¨ ucker, P. Schwesis, S. Schuppler, C. T. Chen, V. Chakarian, J. Freeland, Y. U. Idzerda, G. Muller-Vogt M. Kläser, and Th. Wolf, Phys. Rev. Lett. 80, 5192 (1998). [91] C. Greaves and P. R. Slater, Supercond. Sci. Technol. 2, 5 (1989). [92] J. T. Kucera and J. C. Bravman, Phys. Rev. B 51, 8582 (1995). [93] A. Sedky, A. Gupta, V. P. S. Awana, and A. V. Narlikar, Phys. Rev. B 58, 12495 (1998). [94] J. L. Tallon and G. V. M. Williams, Phys. Rev. B 61, 9820 (2000). ¨ Rapp, R. Tellgren, and I. Bryntse, Phys. Rev. B 56, 2824 [95] P. Lundqvist, O. (1997). [96] H. B. Blackstead and J. D. Dow, Phys. Rev. B 51, 11830 (1996). [97] Z. Zou, J. Ye, K. Oka, and Y. Nishihara, Phys. Rev. Lett. 80, 1074 (1998). [98] J. J. Neumeier, T. Bjørnholm, M. B. Maple, J. J. Rhyne, and J. A. Gotaas, Physica C 160, 191 (1990). [99] G. Cao, Y. Qian, X. Li, H. Wu, Z. Chen, and Y. Zhang, Physica C 248, 92 (1995). [100] A. Okada, J. Arai, and K. Umezawa, Physica C 235-240, 817 (1994). [101] J. J. Neumeier, T. Bjørnholm, M. B. Maple, and I. K. Schuller, Phys. Rev. Lett. 63, 2516 (1989). [102] T. C. Poon and J. Gao, Physica C 256, 161 (1996). [103] G. Nieva, S. Ghamaty, B. W. Lee, M. B. Maple, and I. K. Schuller, Phys. Rev. B 44, 6999 (1991). ¨ Rapp, Physica C 160, 65 [104] M. Andersson, Z. Heged¨ us, M. Nygren, and O. (1989). ¨ Rapp, and R. Tellgren, Physica C 205, 105 (1993). [105] M. Andersson, O. ¨ Rapp, and R. Tellgren, Solid State commun. 81, 425 (1992). [106] M. Andersson, O. ¨ Rapp, R. Tellgren, and Z. Heged¨ [107] P. Lundqvist, C. Tengroth, O. us, Physica C 269, 231 (1996). [108] H. Shakeripour and M. Akhavan, Supercond. Sci. Technol. 14, 213 (2001).

BIBLIOGRAPHY

67

[109] R. G. Kulkarni, R. L. Raibgkar, G. K. Bichile, I.A. Shaikht, J. A. Bhalodia, G. J. Baldha, and D. G. Kuberkar, Supercond. Sci. Technol. 6, 678 (1993). [110] J. B. Torrance, A. Bezinge, A. I. A. I. Nazzal, T. C. Huang, S. S. Parkin, D. T. Keane, S. J. Laplaca, P. M. Horn, and G. A. Held, Phys. Rev. B 40, 8872 (1989). [111] J. L. Tallon, Physics C 176, 547 (1991). [112] Y. Tokura, J. B. Torrance, T. C. Huang, and A. I. Nazzal, Phys. Rev. B 38, 7156 (1988). [113] J. L. Tallon, Physica C 168, 85 (1990). [114] R. J. Cava, A. W. Hewat, E. A. Hewat, B. Batlogg, M. Marezio, K. M. Rabe, J. J. Krajeweski, W. F. Peck, and L. W. Rupp, Physica C 165, 419 (1990). [115] A. G. Joshi, D. G. Kuberkar, and R. G. Kulkarni, Physics C 320, 87 (1999). [116] K. M. Pansuria, D. G. Kuberkar, G. J. Baldha, and R. G. Kulkarni, Supercond. Sci. Technol. 12, 579 (1999). [117] Y. Xu and W. Guan, Phys. Rev. B 45, 3176 (1992). [118] Y. Dalichaouch, M. S. Torikachvili, E. A Early, B. W. Lee, C. L. Seaman, N. Yang, H. Zhou, and M. B. Maple, Solid State Commun. 65, 1001 (1988). [119] A. Kebede, C. S. Jee, J. Schwegler, J. E. Crow, T. Mihalisin, G. H. Myer, R. E. Salomon, P. Schlottmann, M. V. Kuric, S. H. Bloom, and R. P. Guertin, Phys. Rev. B 40, 4453 (1989). [120] Z. Tomkowicz, Physica C 320, 173 (1999). [121] G. Y. Guo and W. M. Temmerman, Phys. Rev. B 41, 6372 (1990). [122] R. Fehrenbacher and T. M. Rice, Phys. Rev. Lett. 70, 3471 (1993). [123] A. I. Liechtenstein and I. I. Mazin, Phys. Rev. Lett. 74, 1000 (1995). [124] W. H. Tang and J. Gao, Physica C 315, 59 (1999). [125] J. J. Neumeier and H. A. Zimmerman, Phys. Rev. B 47, 8385 (1993). [126] P. Lundqvist, Structure and physical properties of doped 123Superconductors and search for new Superconducting hydrides, PhD thesis, TRITA-FYS 5241, Royal Institute of Technology, Sweden, 1998. ¨ Rapp, T. L. Wen, Z. Heged¨ [127] M. Andersson, O. us, and M. Nygren, Phys. Rev. B 48, 7590 (1993).

68

BIBLIOGRAPHY

[128] O. Hartmann, E. Karlsson, E. Lidstr¨ om, R. W¨ appling, P. Lundqvist, Z. ¨ Rapp, Physica C 235-240, 1695 (1994). Heged¨ us, and O. [129] R. D. Shannon, Acta Crystallogr. A 32, 751 (1976). ¨ Rapp, Phys. Rev. B 57, 14428 (1998). [130] B. Lundqvist, P. Lundqvist, and O. [131] I. D. Brown and R. D. Shannon, Acta Crystallogr. A 29, 266 (1973). [132] I. D. Brown and D. Altermatt, Acta Crystallogr. B 41, 244 (1985). [133] P. Lundqvist, Czechoslovak Journal of Physics 46-S, 947 (1996). [134] I. D. Brown, J. Solid State Chem. 82, 122 (1989). [135] I. D. Brown, J. Solid State Chem. 90, 155 (1991). [136] F. W. Lytle, G. van der Laan, R. B. Greegor, E. M. Larson, C. E. Violet, and J. Wong, Phys. Rev. B 41, 8955 (1990). [137] H. B. Rodousky, J. Mater. Res. 7, 1917 (1992). [138] H. Iwasaki, J. Sugawara, and N. Kobayashi, Physics C 185-189, 1249 (1991). [139] A. Matsuda, K. Kinoshita, T. Ishii, H. Shibata, T. Watanable, and T. Yamada, Phys. Rev. B 38, 2910 (1988). [140] M. Merz, N. N¨ ucker, E. Pellegrin, P. Schwesis, S. Schuppler, M. Kielwein, M. Kunpfer, M. S. Golden, J. Fink, C. T. Chen, V. Chakarian, Y. U. Idzerda, and A. Erb, Phys. Rev. B 55, 9160 (1997). ¨ Rapp, Z. Heged¨ [141] M. Andersson, O. us, T.L. Wen, and M. Nygren, Physica C 190, 255 (1992). [142] Y. Ren, H. B. Tang, Q. W. Yan, P. L. Zhang, Y. L. Liu, C. G. Qui, T. S. Ning, and Z. Zhang, Phys. Rev. B 38, 11861 (1988). [143] E. P¨ orschke, P. Meuffels, and B. Rupp, Mater. Res. Soc. Symp. Proc. 166, 181 (1990). [144] B. Roessli, P. Allenspach, P. Fischer, J. Mesot, U. Staub, H. Maletta, P. Br¨ uesch, C. Ritter, and A. W. Hewat, Physica B 180-191, 396 (1992). [145] S. S. Tsuei, A. Gupta, and G. Koren, Physica C 161, 415 (1989). [146] A. Carrington, D. J. C. Walker, A. P.Mackenzie, and J. R. Cooper, Phys. Rev. B 48, 13051 (1993). [147] K. Takenaka, K. Mizuhashi, H. Takagi, and S. Uchida, Phys. Rev. B 50, 6534 (1994).

BIBLIOGRAPHY

69

[148] A. G. Sun, L. M. Paulius, D. A. Gajewski, M. B. Maple, and R. C. Dynes, Phys. Rev. B 50, 3266 (1994). [149] J. J. Neumeier and M. B. Maple, Physca C 191, 158 (1992). [150] J. L. Peng, P. Klavins, R. N. Shelton, H. B. Radousky, P. A. Hahn, and L. Bernardez, Phys. Rev. B 40, 4517 (1989). [151] P. Karen, H. Fjellv˚ ag, O. Braaten, A. Kjekshus, and H. Bratsberg, Acta Chem. Scan. 44, 994 (1990). [152] V. Badri and U. V. Varadaraju, Phys. Rev. B 52, 10504 (1995). [153] S. K. Malik, C. V. Tomy, and P. Bhargava, Phys. Rev. B 44, 7042 (1991). [154] J. M. Valles, Jr., A. E. White, K. T. Short, R. C. Dynes, J. P. Garno, A. F. Levi, M. Anzlower, and K. Baldwin, Phys. Rev. B 39, 11599 (1989). [155] N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, Florida, 1976). [156] J. R. Cooper, B. Alavi, L. W. Zhou, W. P. Beyermann, and G. Gr¨ uner, Phys. Rev. B 35, 8794 (1987). [157] M. Sera and M. Sato, Physca C 185-189, 1339 (1991). [158] K. R. Krylov, A. I. Ponomarev, I. M. Tsidilkovski, V. I. Tsidilnitski, G. V. Bazuev, V. L. Kozhevneikov, and S. M. Cheshnitski, Phys. Lett. A 131, 203 (1988). [159] H. T. Trodahl and A. Mawdsley, Phys. Rev. B 36, 8881 (1987). [160] J. S. Zhou, J. P. Zhou, J. B. Goodenough, and J. T. MacDevitt, Phys. Rev. B 51, 3250 (1995). [161] C. Bernhard and J. L. Tallon, Phys. Rev. B 54, 10201 (1995). [162] D. Mandrus, L. Forro, C. Kendeziora, and L. Mihaaly, Phys. Rev. B 44, 2418 (1991). [163] L. Forro, J. Lukatela, and B. Keszei, Solid State Commun. 73, 501 (1990). [164] C. N. R. Rao, T. V. Ramakrishnan, and N. Kumar, Physica C 165, 183 (1990). [165] X. H. Chen, T. F. Li, M. Yu, K. Q. Ruan, C. Y. Wang, and L. Z. Cao, Physica C 290, 317 (1997). [166] M. Y. Choi and J. S. Kim, Phys. Rev. B 59, 192 (1999).

70

BIBLIOGRAPHY

[167] S. D. Obertelli, J. R. Cooper, and J. L. Tallon, Phys. Rev. B 46, 14928 (1992). [168] K. Isawa, A. T. Okiwa-Yamamoto, M. Itoh, S. Adachi, and H. Yamauchi, Physica C 217, 11 (1993). [169] C. K. Subramaniam, M. Paranthaman, and A. B. Kaiser, Phys. Rev. B 51, 1330 (1995). [170] X. Q. Xu, S. J. Hagen, W. Jiang, J. L. Peng, Z. Y. Li, and R. L. Greene, Phys. Rev. B 45, 7356 (1992). [171] Y. Ando, Y. Hanaki, S. Ono, T. Murayama, K. Segawa, N. Miyamoto, and S. Komiya, Phys. Rev. B 61, R14956 (2000). [172] J. S. Zhou and J. B. Goodenough, Phys. Rev. B 51, 3104 (1995). [173] J. B. Mandal, S. Keshri, P. Mandal, A. Poddar, A. N. Das, and B. Ghosh, Phys. Rev. B 46, 11840 (1992). [174] S. Keshri, J. B. Mandal, P. Mandal, A. Poddar, A. N. Das, and B. Ghosh, Phys. Rev. B 47, 9048 (1993). [175] J. F. Ewak and G. Beni, Phys. Rev. B 13, 652 (1976). [176] P. M. Chaikin and G. Beni, Phys. Rev. B 13, 647 (1976). [177] J. L. Cohn, S. A. Wolf, V. Selvamanickam, and K. Salama, Phys. Rev. Lett. 66, 1098 (1991). [178] H. J. Trodahl, Phys. Rev. B 51, 6175 (1995). [179] Y. Xin, K. W. Wang, C. X. Fan, Z. Z. Sheng, and F. T. Chan, Phys. Rev. B 48, 557 (1993). [180] N. Nagaosa and P. A. Lee, Phys. Rev. Lett. 64, 2450 (1990). [181] V. E. Gasumyants, V. I. Kaidanov, and E. V. Valdimirskaya, Physica C 248, 255 (1995). [182] K. Maki, J. Low Temp. Phys. 14, 419 (1974). [183] U. Gottwick, K. Gloos, S. Horn, F. Steglich, and N. Grewe, J. Magn. Magn. Mater. 47-48, 536 (1985). [184] L. L. Hirst, Phys. Rev. B 15, 1 (1977). [185] Y. J. Uemura, G. M. Luke, B. J. Sternlib, J. H. Brewer, J. F. Coralan, W. N. Hardy, R. Kadono, J. R. Kempton, R. F. Kiefl, P. Mulhern S. R. Kreitzman, T. M. Riesman, D. L1. Williams, B. X. Yang, S. Uchida, H. Takagi, J. Gopalakrishnan, A. W. Sleight, M. A. Subramanian C. L. Chien, M. Z. Cieplak, G. Xiao, V. Y. Lee, B. W. Statt, C. E. Stronach, W. J. Kossler, and X. H. Yu, Phys. Rev. Lett. 62, 2317 (1989).

BIBLIOGRAPHY

71

[186] Y. J. Uemura, A. Keren, L. P. Le, G. M. Luke, W. D. Wu, Y. Kubo, T. Manako, Y. Shimakawa, M. Subramanian, J. L. Cobb, and J. T. Markert, Nature 364, 605 (1993). [187] T. Takahashi, H. Matsuyama, H. Katayama-Yoshida, K. Seki, K. Kamiya, and H. Inokuchi, Physica C 170, 416 (1990). [188] M. Sato, R. Horiba, and K. Nagasaka, Phys. Rev. Lett. 70, 1175 (1993). [189] D. M. Newns, C. C. Tsuei, R. P. Huebener, P. J. M. van Bentum, P. C. Pattnaik, and C. C. Chi, Phys. Rev. Lett. 73, 1695 (1994). [190] V. E. Gasumyants, V. I. Kaidanov, and E. V. Valdimirskaya, Phys. Solid State 40, 14 (1998). [191] V. E. Gasumyants, M. V. Elizarova, and I. B. Patrina, Phys. Rev. B 59, 6550 (1999). [192] V. E. Gasumyants, M. V. Elizarova, and I. B. Patrina, Supercond. Sci. Technol. 13, 1600 (2000). [193] D. Rama Sita and R. Singhj, Physica C 296, 21 (1998). [194] M. V. Elizarova and V. E. Gasumyants, Phys. Solid State 41, 1248 (1999). [195] V. E. Gasumyants, M. V. Elizarova, and R. Suryanarayanan, Phys. Rev. B 61, 12404 (2000). [196] N. P. Ong, Z. Z. Wang, J. Clayhold, J. M. Tarascon, L. H. Greene, and W. R. McKinnon, Phys. Rev. B 35, 8807 (1987). [197] P. W. Anderson, Science 256, 1526 (1992). [198] T. R. Chien, D. A. Brawner, Z. Z. Wang, and N. P. Ong, Phys. Rev. B 43, 6242 (1991). [199] T. Manako, Y. Kubo, and Y. Shimakawa, Phys. Rev. B 46, 11019 (1992). [200] T. R. Chien, Z. Z. Wang, and N. P. Ong, Phys. Rev. Lett. 67, 2088 (1991). [201] N. Y. Chen, V. C. Matijasevic, J. E. Mooij, and D. Van der Marel, Phys. Rev. B 50, 16125 (1994). [202] B. Wuyts, V. V. Moshchalkov, and Y. Bruynseraede, Phys. Rev. B 53, 9418 (1996). [203] H. Yakabe, I. Terasaki, M. Kosuge, Y. Shiohara, and N. Koshizuka, Phys. Rev. B 54, 14986 (1996). [204] M. Suzuki, Phys. Rev. B 39, 2312 (1989).

72

BIBLIOGRAPHY

[205] H. Y. Hawang, B. Batlogg, H. Takagi, H. L. Kao, J. Kwo, R. J. Cava, J. J. Krajewski, and W. F. Peck, Phys. Rev. Lett. 72, 2636 (1994). [206] A. A. Gapud, J. Z. Wu, and B. W. Kang, Phys. Rev. B 64, 052505 (2001). [207] C. Kendziora, D. Mandrus, L. Mihaly, and L. Forro, Phys. Rev. B 46, 14297 (1992). [208] A. V. Samoilov, Phys. Rev. Lett. 71, 617 (1993). [209] J. M. Harris, H. Wu, N. P. Ong, R. L. Meng, and C. W. Chu, Phys. Rev. B 50, 3246 (1994). [210] J. Takeda, T. Nishikawa, and M. Sato, Physica C 231, 293 (1994). [211] P. Fournier, X. Jiang, W. Jiang, S. N. Mao, T. Venkatesan, C. J. Lobb, and R. L. Greene, Phys. Rev. B 56, 14149 (1997). [212] S. Uchida, H. Takagi, and Y. Tokura, Physica C 162-164, 1676 (1989). [213] H. Kontani, K. Kanki, and K. Ueda, Phys. Rev. B 59, 14723 (1999). [214] Y. Kubo, T. Kondo, Y. Shimakawa, T. Manako, and H. Igarashi, Phys. Rev. B 45, 5553 (1992). [215] A. T. Fiory and G. S. Grader, Phys. Rev. B 38, 9198 (1988). [216] P. W. Anderson, Phys. Rev. Lett. 67, 2092 (1991). [217] A. Carrington, D. Colson, Y. Dumont, C. Ayache, A. Bertinotti, and J. F. Marucco, Physica C 234, 1 (1994). [218] K. E. Johansson, T. Palm, and P. E. Werner, J. Phys. E 13, 1289 (1980). [219] H. M. Rietveld, Acta Cryst. 22, 151 (1967). [220] H. M. Rietveld, J. Appl. Cryst. 2, 65 (1969). [221] R. A. Young, The Rietveld Method (Oxford University Press Inc, New York, 1993). [222] J. Rodriguez-Carvajal, FullProf program, e-mail: [email protected]. [223] M. Andersson, The Oxford Cryostat, Manual, TRITA-FYS 5150, Royal Institute of Technology, Sweden, 1991. [224] M. Rodmar, Studies of Electronic Transport in Quasicrystals, PhD thesis, TRITA-FYS 5246, Royal Institute of Technology, Sweden, 1999. [225] P. Lundstr¨ om, Thermopower Measurements of Quasicrystals, Master’s thesis, TRITA-FYS 5248, Royal Institute of Technology, Sweden, 1999.