MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

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7. Critical Transport and Magnetization of La 0.67Ca 0.33MnO 3 In homogeneous La 0.67 Ca 0.33 MnO 3 , it is clear that the magnetoresistance maximizes near the ferromagnetic Curie temperature T C and rapidly decreases at lower or higher temperatures. The magnetoresistance also slowly saturates as the magnetic field is increased past several Tesla. Thus, the conductivity behaves much like the magnetization: above T C the conductivity and magnetization are low, while below T C the conductivity and magnetization rapidly increase. Furthermore, near T C both the conductivity and magnetic moment can be increased by an applied magnetic field. The theory of double exchange, which has been developed to explain these properties of the manganites [7, 112, 155], predicts this correlation between the conductivity and the magnetization. The relationship between the conductivity (or resistivity) and the magnetization has been examined both experimentally and theoretically. Several theoretical models [31, 112, 121, 155, 156, 161-164] predict an M 2 dependence of the resistivity (or conductivity). The first term of the Taylor series expansion of the resistivity (or conductivity) in terms of M should be M 2 for all models due to symmetry considerations [150]. Experimentally, a correlation between the resistivity and magnetization can be found by plotting one as a function of the other [24, 114, 115, 121, 158, 165]. These plots show that the resistivity is roughly proportional to the square of the magnetization M 2 for small M. For larger M however, the resistance decreases more slowly in relationship to M 2 as if it were saturating before the magnetization does. Thus the relationship between the resistivity and the magnetization is more complicated than ρ ∝ M 2 . This relationship may instead be well described by an M 2 dependence of the conductivity in a slightly more complicated circuit [150]. In the previous chapter, only the 128
Critical Transport and Magnetization of La 0.67 Ca 0.33 MnO 3 magnetic field H dependence of the resistivity is shown to be more fully described in terms of a magnetoconductive circuit, ρ = ρ ∞ + 1/(σ 0 + σ H 2H 2 ) for T > T C and ρ = ρ ∞ + 1/(σ 0 + σ H |H|) for T < T C , where ρ ∞ , σ 0 , σ H 2 and σ H are parameters. In order to determine if the magnetoconductivity, σ H 2H 2 and σ H |H| can replaced by a common term proportional to M 2 as suggested above, the temperature dependencies and magnitudes of σ H 2, σ H and M need to be examined. Alternatively, it has been found in several cases that the correlation ρ ∝ exp[-M(H,T)/M E ] is a good fit to the data [24, 114, 115]. This formulation does not yet have a good theoretical understanding. In this chapter, which will be published separately, the temperature and field dependence of the magnetization and magnetoresistance, above and below T C are reported. A well annealed La 0.67 Ca 0.33 MnO 3 thin film on a LaAlO 3 substrate grown by MOCVD was used for transport measurements as described in chapter 4. DC conductivity measurements were performed using the method of Van der Pauw [52, 53]. Only the longitudinal magnetoresistance data are shown. The transverse magnetoresistance is nearly identical to the longitudinal as was discussed in chapter 6. After stabilizing the temperature, repeated resistance R vs. H curves were measured and fit with three parameters (ρ ∞ , σ 0 , and σ H 2 or σ H ) to ρ = ρ ∞ + 1/(σ 0 + σ H 2H 2 ) for T > T C and ρ = ρ ∞ + 1/(σ 0 + σ H |H|) for T < T C . The data fit well to these forms except the few degrees near T C (where a combination of the two forms is better) and at low temperatures. For T < 50 K the magnetoresistance shows 2 no sign of saturating (ρ = [ρ∞ + 1/σ0 ] - σH |H|/σ0 ), so only two parameters 2 ([ρ∞ + 1/σ0 ] and σH /σ0 ) can be extracted. 129
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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,
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
Page 120 and 121: 102 Chapter 5 5.1 Ferrimagnetism Th
Page 122 and 123: 104 Chapter 5 calculation predicts
Page 124 and 125: 106 Chapter 5 χ mol (µ B /mol/T)
Page 126 and 127: 108 Chapter 5 of the nonlinear M 2
Page 128 and 129: 110 Chapter 5 rather than a simple
Page 130 and 131: 112 Chapter 5 ln(ρ /Ω cm) 24 22
Page 132 and 133: 114 Chapter 5 A high, temperature i
Page 134 and 135: 116 Chapter 5 5. 3. 1 Relationship
Page 136 and 137: 6. Magnetoconductivity in La 0.67Ca
Page 138 and 139: 120 Chapter 6 resistivity ρ ∝ M
Page 140 and 141: 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)
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 192 and 193: 174 Appendix B c P,H /T (mJ/mol·K
Page 194 and 195: 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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