MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

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38 Chapter 3 Complex materials often have resistivities that are inadequately described by the simple models given above. For example the cuprate superconductors and SrRuO 3 show a linear resistivity well above the Ioffe Regel limit [73]. A more extreme example is Ba 6 Co 25 S 27 which not only has a resistivity minimum but a less than linear resistivity above the minimum [42]. As more materials with complex electronic structures are examined, such non- standard behavior will certainly become more common. 3. 1. 3. 4 Phase transitions Any precise measurement as a function of temperature can usually detect or be influenced by a phase transition. Conductivity data in particular can be quite precise but can also be greatly influenced by subtle electronic, magnetic or structural changes. Thus one should be cautious when fitting data to very similar functional forms. Electronic transitions such as metal-insulator transitions and charge ordering (charge density wave formation) obviously change the conductivity at the ordering temperature. Magnetic transitions are also easily observed in the conductivity since local moments act as scattering centers, or may even help localize/delocalize carriers. Ferromagnetic metals for instance always show a decrease in resistivity as the temperature goes below the Curie temperature [73]. Structural phase transitions usually change the symmetry and volume, which affects the conduction paths and density of the charge carriers. This will subtlety change the conductivity at the transition temperature even if the conduction mechanism remains the same, as shown in section 4.2.5. Careful measurements can help determine the nature of such phase transitions. If the phase transition is reversible and not hysteretic, i.e. the data are the same upon warming and cooling, then the phase transition is probably a single second order process. If the data is hysteretic then a first order process is involved. For example, the ferromagnetic and accompanying metal insulator transition in the manganites appears to be of second order.
Electronic and Magnetic Measurements 39 The charge ordering transition in the nonmagnetic manganites is also not hysteretic and probably second order. However, in samples where both ferromagnetism and charge ordering occur, the conductivity and magnetic susceptibility are hysteretic, indicating a more complex transition. In this case, there is no subgroup-supergroup relationship between the two ordered phases; so to go from the magnetically ordered phase to the charge ordered phase requires a first order (hysteretic) phase transition [74, 75]. In the region near a second order phase transition (critical regime) physical quantities such as electronic transport are often best described by a power law about the critical point, e.g. (T - T C ) n where T C is the critical temperature and n is the critical exponent. For example, the resistivity of a ferromagnet near the Curie temperature should be described by a critical exponent (α) equal to that of the heat capacity [73]. Magnetic critical exponents are described in more detail in section 3.2.2.2.4 3.2 Magnetism The magnetism of a material is usually dominated by the electrons near the Fermi level. Unpaired, localized electrons in insulators have very different magnetism than paired or itinerant ones. Thus, magnetic measurements can detect the subtle electronic structure of a material. Since these measurement do not require contacts, they can be quite easy to perform Ð and have made them quite standard in characterizing new materials. 3. 2. 1 Measurement There are various ways to measure a magnetic field and thus magnetization. The most common instruments to measure D.C. magnetization are the vibrating sample magnetometer, Faraday balance and SQUID magnetometer. Surface magnetization can be accurately measured by the Magneto-optical Kerr effect (MOKE). The apparatus used in this study is a Quantum Design MPMSR 2 SQUID magnetometer.
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MAGNETISM AND ELECTRON TRANSPORT IN
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I certify that I have read this dis
Page 7 and 8: Preface Looking back at the many ye
Page 9 and 10: Table of Contents Abstract v Prefac
Page 11 and 12: 4.2 Electronic Transport 8 5 4.2.1
Page 13 and 14: List of Figures xiii Figure 1-1 The
Page 15 and 16: Figure 5-7 Low temperature resistiv
Page 17: xvii = γT + βT 3 . The triangles
Page 20 and 21: 2 Chapter 1 in themselves, but the
Page 22 and 23: 4 Chapter 1 ferromagnetic metals up
Page 24 and 25: 6 Chapter 1 e g t 2g e g t 2g CaMnO
Page 26 and 27: 8 Chapter 1 near T C (magnetic susc
Page 28 and 29: 10 Chapter 2 reactions, the rate li
Page 30 and 31: 12 Chapter 2 Otherwise one has to s
Page 32 and 33: 14 Chapter 2 atmosphere or vacuum.
Page 34 and 35: 16 Chapter 2 a particular diffracti
Page 36 and 37: 18 Chapter 2 Thus XAFS probes the l
Page 38 and 39: 20 Chapter 3 relationships resistiv
Page 40 and 41: 22 Chapter 3 inadequate. l ≈ a is
Page 42 and 43: 24 Chapter 3 Hall effect measuremen
Page 44 and 45: 26 Chapter 3 3.1.2.3 Contacts Bad c
Page 46 and 47: 28 Chapter 3 3.1.2.5 Apparatus Tran
Page 48 and 49: 30 Chapter 3 materials as metals or
Page 50 and 51: 32 Chapter 3 overcome the barrier a
Page 52 and 53: 34 Chapter 3 The dichotomy between
Page 54 and 55: 36 Chapter 3 position; however, thi
Page 58 and 59: 40 Chapter 3 3.2.1.1 Apparatus The
Page 60 and 61: 42 Chapter 3 The second-derivative
Page 62 and 63: 44 Chapter 3 substances. Otherwise,
Page 64 and 65: 46 Chapter 3 3.2.2.1.2 Conduction e
Page 66 and 67: 48 Chapter 3 Susceptibility (emu/G
Page 68 and 69: 50 Chapter 3 H/M (T/μ B ) 80 70 60
Page 70 and 71: 52 Chapter 3 Magnetization (μ B )
Page 72 and 73: 54 Chapter 3 is called the Stoner c
Page 74 and 75: 56 Chapter 3 Energy Magnetic Excita
Page 76 and 77: 58 Chapter 3 moments [84]. Thus, a
Page 78 and 79: 60 Chapter 3 Arrott plot), will the
Page 80 and 81: 62 Chapter 3 Curie temperature, the
Page 82 and 83: 64 Chapter 3 The energy ω of a spi
Page 84 and 85: 66 Chapter 3 3.2.2.2.9 Irreversibil
Page 86 and 87: 68 Chapter 3 ferromagnet will also
Page 88 and 89: 70 Chapter 3 Magnetization (µ B )
Page 90 and 91: 72 Chapter 3 with temperature and f
Page 92 and 93: 74 Chapter 3 by Mn +4 2 (S = 3/2).
Page 94 and 95: 76 Chapter 3 ferromagnet. Instead,
Page 96 and 97: 78 Chapter 3 3.3.1.1 Apparatus The
Page 98 and 99: 4. Intrinsic Electrical Transport a
Page 100 and 101: 82 Chapter 4 M/M 0 1.0 0.8 0.6 0.4
Page 102 and 103: 84 Chapter 4 M/M 0 1.00 0.96 0.92 0
Page 104 and 105: 86 Chapter 4 Resistivity (10 -3 Ω
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88 Chapter 4 dependence of R 2 is s
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90 Chapter 4 magnetoresistance obse
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92 Chapter 4 4. 2. 2 High Temperatu
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94 Chapter 4 measurements (Figure 4
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96 Chapter 4 somewhat too large com
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98 Chapter 4 Magnetization 8 6 4 2
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100 Chapter 4 above room temperatur
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102 Chapter 5 5.1 Ferrimagnetism Th
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104 Chapter 5 calculation predicts
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106 Chapter 5 χ mol (µ B /mol/T)
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108 Chapter 5 of the nonlinear M 2
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110 Chapter 5 rather than a simple
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112 Chapter 5 ln(ρ /Ω cm) 24 22
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114 Chapter 5 A high, temperature i
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116 Chapter 5 5. 3. 1 Relationship
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6. Magnetoconductivity in La 0.67Ca
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120 Chapter 6 resistivity ρ ∝ M
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122 Chapter 6 The Hall effects are
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124 Chapter 6 ∆R/R (%) 1 0 -1 -2
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126 Chapter 6 R(H)-R(-H) (µΩ cm)
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7. Critical Transport and Magnetiza
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130 Chapter 7 2 ) M 2 (µ B The foc
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132 Chapter 7 for T > T C . The reg
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134 Chapter 7 spin-relaxation measu
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136 Chapter 7 1/χ (10kOe/µ B ) 5
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138 Chapter 7 γ < 1. Also, at a co
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140 Chapter 7 ∆R/R (%) 10 0 -10 -
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142 Chapter 7 (Figure 7-6), in so f
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144 Chapter 7 The related form ρ
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146 Chapter 7 σ H (10 -5 mΩcm -1
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148 Chapter 7 σ E exp[M 0 (T)/M E
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150 Chapter 7 σ = σ E exp[M(H,T)/
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Appendix A. Critical Behavior and A
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154 Appendix A samples. Magnetizati
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156 Appendix A while the pellet dis
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158 Appendix A M 0 (µ B ) 1.0 0.8
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160 Appendix A (T/T C - 1) γ . Fro
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162 Appendix A provides highly reve
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164 Appendix A 1/χ 0 (emu -1 mol G
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166 Appendix A T 3/2 Coefficient (1
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168 Appendix A magnetization with t
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170 Appendix A excitations for T <
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172 Appendix A β changes from Heis
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174 Appendix B c P,H /T (mJ/mol·K
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176 Appendix B Figure 3 at the 90%
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178 Appendix B are vectors. Thus fo
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180 Appendix B corrections are incl
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References [1] G. H. Jonker and H.
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184 References [40] G. J. Snyder an
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186 References [80] E. C. Stoner, P
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188 References [115] M. F. Hundley,
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190 References [151] S. J. L. Billi
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192 References [187] L. Klein, (unp
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MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

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