MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

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52 Chapter 3 Magnetization (μ B ) Calculated Mean Field Magnetization for SrRuO 3 2.0 1.5 1.0 0.5 Magnetization (μ B ) 2.005 2.000 1.995 1.990 0.0 0 50 100 Temperature (K) 150 200 The molecular field model assumes very little about the microscopic origin of ferromagnetism, only that it makes sense to define a local molecular field. Microscopic models for the interaction of atomic magnetic moments can be formulated into a similar mean field model. In this case, the interatomic exchange energy J can be related to the molecular field constant λ. A microscopic model also leads to a more accurate prediction of the magnetization. At low temperatures, the quantized moments can be collectively excited as discussed in section 3.2.2.2.8 to give the faster decrease in the magnetization than the molecular field model. The microscopic model also gives a more realistic description of the observed properties near the critical point (section 3.2.2.2.4). Mean Field Forced Magnetization 5K 50K 1.985 0 20 40 60 80 100 Magnetic Field (kOe) 5T 5kOe 5 Oe 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.
Electronic and Magnetic Measurements 53 3.2.2.2.2 Itinerant electron Model The ground state properties of a metallic ferromagnet are believed to be fairly well described by the band theory which has advanced in the recent decades [79]. The thermal excitations and finite temperature properties, however, are more difficult because of the effects of strong electron-electron correlations in narrow energy bands. This limits the utility of traditional Hartree-Fock or mean field theory described briefly in this section and requires a treatment of generalized spin density fluctuations described i n section 3.2.2.2.3 to describe fully the magnetic excitations in itinerant electron ferromagnets. The quantum mechanical exchange interaction can lead to ferromagnetism in an electron gas within the band model, commonly known as Stoner ferromagnetism [80, 81] or itinerant electron ferromagnetism. Using the molecular field approximation, a ferromagnetic state is realized for Jn(E F ) > 1 where J is the average intra-atomic exchange energy per atom and n(E F ) is the density of states at the Fermi level. This is also known as the Stoner condition for ferromagnetism. For Jn(E F ) < 1 the material is not ferromagnetic but has a Pauli susceptibility enhanced by 1/(1-Jn(E F )) [82]. This factor is called the Stoner enhancement factor. The effect of the magnetization at finite temperatures can be calculated using the mean field approximation. Specifically, the energy of the up (down) spin band is uniformly lowered (raised) by an amount proportional to the magnetic polarization ζ and a molecular field constant. Since this model assumes electrons are either in up or down spin bands, the excitations are known as single particle, spin flip, or Stoner excitations. There is no energy gap required for Stoner excitations. However, zero or low energy excitations require a non-zero momentum transfer, while excitations with zero momentum transfer require an excitation energy equal to the exchange splitting as can be seen in Figure 3-8. The region of allowed Stoner excitations
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MAGNETISM AND ELECTRON TRANSPORT IN
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I certify that I have read this dis
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Preface Looking back at the many ye
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Table of Contents Abstract v Prefac
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4.2 Electronic Transport 8 5 4.2.1
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List of Figures xiii Figure 1-1 The
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Figure 5-7 Low temperature resistiv
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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
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 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
Page 106 and 107: 88 Chapter 4 dependence of R 2 is s
Page 108 and 109: 90 Chapter 4 magnetoresistance obse
Page 110 and 111: 92 Chapter 4 4. 2. 2 High Temperatu
Page 112 and 113: 94 Chapter 4 measurements (Figure 4
Page 114 and 115: 96 Chapter 4 somewhat too large com
Page 116 and 117: 98 Chapter 4 Magnetization 8 6 4 2
Page 118 and 119: 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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