MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

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174 Appendix B c P,H /T (mJ/mol·K 2 ) 110 100 90 80 70 60 50 40 SrRuO 3 Specific Heat 0 T zfc 0 T rem 8 T -5 0 50 100 150 200 250 300 350 Temperature 2 (K 2 ) 30 0 50 100 150 200 250 300 350 Temperature 2 (K 2 ) Above 13 K and below 3 K the data in Figure B- 1 deviate from a straight line. The deviation above 13K can be fit by an expression for the specific heat of a thermally activated Einstein (optical) phonon mode, with an Einstein temperature of Θ Ε = 140 K. Both β and Θ Ε are field independent within experimental error. The temperature range below 3 K is not large enough to draw conclusion about the functional form of the low-temperature upturn. A field independent term proportional to T 3 ln(T) is expected from the non- spinwave spin fluctuations [91, 194, 199]. A Shottky anomaly due to free ∆c P,H /T (mJ/mol·K 2 ) 1 0 -1 -2 -3 -4 c P,H /T (rem) - c P,H /T (zfc) c P,H /T (8T) - c P,H /T (zfc) Figure B- 1 Heat capacity of SrRuO 3 cooled in zero field (zfc), in an 8 T magnetic field, and in zero field after being magnetized (rem). Inset, difference between the heat capacity measured after cooling in zero field with that in 8 T and the remnant magnetized state.
c P,H /T (mJ/mol·K) 65 60 55 50 45 40 Specific Heat of SrRuO 3 SrRuO 3 Specific Heat in Zero Field c P,H (T) = γT + βT 3 + 2mJ/(mol·K 5/2 ) T 3/2 c P,H (T) = γT + βT 3 H=0 Remnant H=0 Zero Field Cooled 35 0 25 50 75 100 125 150 Temperature 2 (K 2 ) Figure B- 2. Zero field heat capacity data fit with two free parameters, γ and β. Solid line, including the T 3/2 contribution expected theoretically for spin waves (see text). Dashed line, without any T 3/2 contribution. paramagnetic spins will give a low temperature upturn but should also be noticeable as Curie paramagnetism in magnetization measurements. Adding a positive T 3/2 term to the model for the specific heat, as expected for pure spin wave excitations (3.2.2.2.8) [95], does not improve the fit (Figure B- 2). Assuming 6 nearest neighbors, spin 1, and T C = 163 to determine J, this value is A = 2mJ mol -1 K -5/2 . Previous magnetization measurements on thin films suggest that this term is correct within a factor of 2 [186]. Using a functional form of γT + AT 3/2 + βT 3 , the coefficient A is less than 1.2 (0 T zfc), 2.5 (8 T), and 0.6 (0 T rem) mJ mol -1 K -5/2 for each of the three data sets i n 175
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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
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2 Chapter 1 in themselves, but the
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4 Chapter 1 ferromagnetic metals up
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6 Chapter 1 e g t 2g e g t 2g CaMnO
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8 Chapter 1 near T C (magnetic susc
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10 Chapter 2 reactions, the rate li
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12 Chapter 2 Otherwise one has to s
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14 Chapter 2 atmosphere or vacuum.
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16 Chapter 2 a particular diffracti
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18 Chapter 2 Thus XAFS probes the l
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20 Chapter 3 relationships resistiv
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22 Chapter 3 inadequate. l ≈ a is
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24 Chapter 3 Hall effect measuremen
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26 Chapter 3 3.1.2.3 Contacts Bad c
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28 Chapter 3 3.1.2.5 Apparatus Tran
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30 Chapter 3 materials as metals or
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32 Chapter 3 overcome the barrier a
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34 Chapter 3 The dichotomy between
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36 Chapter 3 position; however, thi
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38 Chapter 3 Complex materials ofte
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40 Chapter 3 3.2.1.1 Apparatus The
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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
Page 142 and 143: 124 Chapter 6 ∆R/R (%) 1 0 -1 -2
Page 144 and 145: 126 Chapter 6 R(H)-R(-H) (µΩ cm)
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Page 148 and 149: 130 Chapter 7 2 ) M 2 (µ B The foc
Page 150 and 151: 132 Chapter 7 for T > T C . The reg
Page 152 and 153: 134 Chapter 7 spin-relaxation measu
Page 154 and 155: 136 Chapter 7 1/χ (10kOe/µ B ) 5
Page 156 and 157: 138 Chapter 7 γ < 1. Also, at a co
Page 158 and 159: 140 Chapter 7 ∆R/R (%) 10 0 -10 -
Page 160 and 161: 142 Chapter 7 (Figure 7-6), in so f
Page 162 and 163: 144 Chapter 7 The related form ρ
Page 164 and 165: 146 Chapter 7 σ H (10 -5 mΩcm -1
Page 166 and 167: 148 Chapter 7 σ E exp[M 0 (T)/M E
Page 168 and 169: 150 Chapter 7 σ = σ E exp[M(H,T)/
Page 170 and 171: Appendix A. Critical Behavior and A
Page 172 and 173: 154 Appendix A samples. Magnetizati
Page 174 and 175: 156 Appendix A while the pellet dis
Page 176 and 177: 158 Appendix A M 0 (µ B ) 1.0 0.8
Page 178 and 179: 160 Appendix A (T/T C - 1) γ . Fro
Page 180 and 181: 162 Appendix A provides highly reve
Page 182 and 183: 164 Appendix A 1/χ 0 (emu -1 mol G
Page 184 and 185: 166 Appendix A T 3/2 Coefficient (1
Page 186 and 187: 168 Appendix A magnetization with t
Page 188 and 189: 170 Appendix A excitations for T <
Page 190 and 191: 172 Appendix A β changes from Heis
Page 194 and 195: 176 Appendix B Figure 3 at the 90%
Page 196 and 197: 178 Appendix B are vectors. Thus fo
Page 198 and 199: 180 Appendix B corrections are incl
Page 200 and 201: References [1] G. H. Jonker and H.
Page 202 and 203: 184 References [40] G. J. Snyder an
Page 204 and 205: 186 References [80] E. C. Stoner, P
Page 206 and 207: 188 References [115] M. F. Hundley,
Page 208 and 209: 190 References [151] S. J. L. Billi
Page 210: 192 References [187] L. Klein, (unp
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MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

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