MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

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xii 6.2 Magnetoresistance models 119 6.2.1 General Model 120 6.2.1.1 Magnetoconductivity model 121 6.2.1.1.1 T > T C regime 123 6.2.1.1.2 T < T C regime 124 6.2.1.1.3 Anisotropic magnetoresistance 125 6.2.1.1.4 Hall Effect 126 6.3 Conclusion 127 7. CRITICAL <strong>TRANSPORT</strong> AND MAGNETIZATION OF LA 0.67 CA 0.33 MNO 3 128 7.1 Magnetism near TC 130 7.1.1 Spontaneous magnetization exponent 132 7.1.2 Susceptibility exponent 134 7.1.3 Positive nonlinear susceptibility 135 7.1.4 Additional magnetic interaction 137 7.2 Magnetoresistance 139 7.2.1 Magnetoresistance scaling above TC 142 7.2.2 Magnetoresistance scaling below TC 144 7.2.3 Magnetoresistance scaling at TC 148 7.2.4 Relation to low temperature magnetoresistance 149 7.3 Conclusion 150 Appendix A. Critical Behavior and Anisotropy in Single Crystal SrRuO 3 Appendix B. Magnetic Excitations and Specific Heat in SrRuO 3 References 182 152 173
List of Figures xiii Figure 1-1 The Perovskite structure AMnO 3 where A is a mixture of rare earth and alkaline earth elements e.g. La 0.67Ca 0.33. 3 Figure 1-2 Double exchange and the electronic structure of AMnO 3. 6 Figure 3-1 Effect of changing the scan length for magnetization measurements. A YIG crystal is used. The three data reduction schemes are also compared. The results for the full scan algorithm with scan length less than 5 cm are off scale.41 Figure 3-2 Magnetization of YIG sample as it is rotated along the field axis. 4 3 Figure 3-3 Diamagnetic magnetic susceptibility of typical substrates. The increase in the susceptibility at low temperatures is due to paramagnetic impurities. 4 5 Figure 3-4 Paramagnetic susceptibility and hysteresis loop of a paramagnetic Fe containing organometallic compound [78]. 4 8 Figure 3-5 Effective paramagnetic moment of Fe in the organometallic compound [SC(CH 3) 2C(CH 3)NCH 2CH 2CH 2] 2N - FePF - 6 showing a spin transition [78]. 4 9 Figure 3-6 Calculated inverse magnetic susceptibility of SrRuO 3 using the molecular field model. 50 Figure 3-7 Mean field magnetization calculated in various fields for SrRuO 3 with T C = 165K. Inset show the very small field dependence of the magnetization (forced magnetization) in this model. 5 2 Figure 3-8 Energy spectrum of magnetic excitations. Spin wave excitations have a one-to-one dispersion relation while excitations in the Stoner continuum (shaded region) do not. The intensity of excitations in the Stoner continuum is strongest where the spin waves meet the continuum. 5 6 Figure 3-9 The inflection T C measured for a SrRuO 3 pellet. For H < 1 Tesla the inflection T C is within 1 K of the Arrott T C = 163 K. At higher H the inflection T C increases by only a few degrees. 6 3 Figure 3-10 Correction factor to the T 3/2 contribution of the magnetization in the spin wave theory due to a magnetic field H . 64 Figure 3-11 Correction factor to the T 3/2 contribution of the heat capacity in the spin wave theory due to a magnetic field H . 65 Figure 3-12 SrRuO 3 showing spin-glass like irreversibility of zero-field-cooled and field-cooled measurements in a small field. The field cooled curve may look saturated, but is actually less than 1/10 saturated at low temperatures. A small peak is observed in the zero-field-cooled measurement when the reversibility point is reached. 6 6 Figure 3-13 Initial magnetization of SrRuO 3 pellet at 5 K, after cooling in zero field. The magnetization follows a “S” shaped curve providing an inflection point. 6 7 Figure 3-14 Magnetic irreversibility line for polycrystalline SrRuO 3. Above the line the magnetization is reversible, below it is irreversible. The irreversibility exponent is about 1.5. 6 8 Figure 3-15 Time dependent magnetization of SrRuO 3 pellet at 5 K. The field was increased from 0 to 100 Gauss. The magnetization follows a Log(time) dependence. 70 Figure 3-16 Magnetic susceptibility of a Pt containing “CaRuO 3” crystal. The crystal was aligned with its 2-fold symmetric axis parallel to the applied field has a susceptibility characteristic of antiferromagnetic moments aligning parallel to the field, while the 3-fold axis appears to have moments perpendicular to the field. 71 Figure 3-17 Temperature - tolerance factor phase diagram from reference [100], with the position of Gd 0.67Ca 0.33MnO 3 indicated. 7 3 Figure 3-18 Calculated Arrott Plot for Gd 0.67Ca 0.33MnO 3 using the mean field model with T C = 83.3 K. 7 5
Page 1 and 2: MAGNETISM AND ELECTRON TRANSPORT IN
Page 3: 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: 4.2 Electronic Transport 8 5 4.2.1
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 56 and 57: 38 Chapter 3 Complex materials ofte
Page 58 and 59: 40 Chapter 3 3.2.1.1 Apparatus The
Page 60 and 61: 42 Chapter 3 The second-derivative
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44 Chapter 3 substances. Otherwise,
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46 Chapter 3 3.2.2.1.2 Conduction e
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48 Chapter 3 Susceptibility (emu/G
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50 Chapter 3 H/M (T/μ B ) 80 70 60
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52 Chapter 3 Magnetization (μ B )
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54 Chapter 3 is called the Stoner c
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56 Chapter 3 Energy Magnetic Excita
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58 Chapter 3 moments [84]. Thus, a
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60 Chapter 3 Arrott plot), will the
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62 Chapter 3 Curie temperature, the
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64 Chapter 3 The energy ω of a spi
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66 Chapter 3 3.2.2.2.9 Irreversibil
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68 Chapter 3 ferromagnet will also
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70 Chapter 3 Magnetization (µ B )
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72 Chapter 3 with temperature and f
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74 Chapter 3 by Mn +4 2 (S = 3/2).
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76 Chapter 3 ferromagnet. Instead,
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78 Chapter 3 3.3.1.1 Apparatus The
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4. Intrinsic Electrical Transport a
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82 Chapter 4 M/M 0 1.0 0.8 0.6 0.4
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84 Chapter 4 M/M 0 1.00 0.96 0.92 0
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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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