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title page
Abstract
Contents
CHAPTER 1. Introduction 11
CHAPTER 2. The Monte-Carlo study of the temperature-driven spin reorientation transition in an antiferromagnetic system 14
2.1. Introduction 14
2.2. Microscopic model 15
2.3. Numerical method 17
2.4. Results 19
2.5. Discussion 27
2.6. Summary 27
CHAPTER 3. Thermoelectric Power in the Double Exchange Model 29
3.1. Introduction 29
3.2. Theoretical formalism 30
3.3. Truncation polynomial expansion method 33
3.4. High temperature result 36
3.5. Low temperature behavior 39
3.6. Summary 42
CHAPTER 4. Superexchange Interaction in Orthorhombic Perovskite Oxides : RMnO₃ and Se1-xTexCuO3 systems(이미지참조) 43
4.1. Introduction 43
4.2. GdFeO₃-type distortion 45
4.3. Cooperative Jahn-Teller distortion and orbital ordering 48
4.4. Microscopic model 51
4.5. Superexchange interaction in RMnO₃ systems 54
4.5.1. Introduction 54
4.5.2. Nearest neighbor interaction 57
4.5.3. Next nearest neighbor interaction 63
4.5.4. Magnetic ground state 68
4.5.5. Summary 71
4.6. Superexchange interaction in Se1-xTexCuO3 systems(이미지참조) 72
4.6.1. Introduction 72
4.6.2. Orbital ordering 74
4.6.3. Magnetic interaction 75
4.6.4. Summary 79
CHAPTER 5. Summary 80
Bibliography 82
요약문 91
감사의 글 92
Table 3.1. Chebyshev polynomials 34
Table 3.2. The Heikes formula results of the thermoelectric powers in different electron densities (S∞=- κB/|e| ln 2-n/n).(이미지참조) 38
Table 4.1. Theoretical values of the tolerance factors (f), a-a-b+ tilting angle(ω), and angles of inter-plane (Φ₁) and intra-plane (Φ₂) M-O-M chains in some perovskite oxides....(이미지참조) 47
Table 4.2. Experimental data of the octahedral deformation under the Jahn-Teller distortion in the perovskite oxides. M-O bond lengths, two Jahn-Teller distortion modes, the distortion angles, and the distortion... 51
Table 4.3. Expressions of the direct Coulomb integral Udμν and exchange integral Jdμν for different d orbital pairs with Racah parameters A, B, and C....(이미지참조) 53
Table 4.4. Fixed parameters for the orthorhombic perovskite RMnO₃. 58
Table 4.5. The theoretical values of superexchange parameters solving our model Hamiltonian with the structural data from table 4.1 and 4.2. 63
Table 4.6. Fixed parameters for calculating the superexchange interaction in the perovskite cuprite. 75
Fig. 2.1. The probability distribution of the angle θ between the M and z-axis for K₂/J=-0.047 and KD/J=-0.007. In this case, the fourth-order term of the single-ion anisotropy is neglected....(이미지참조) 19
Fig. 2.2. The thermal average of total anisotropic energy (HA) of Eq. (2.1c) as a function of temperature for K₂/J=-0.047 and KD/J=-0.007....(이미지참조) 20
Fig. 2.3. The temperature-dependent easy axis behavior. (a) For fixed KD/J=-0.007 with varying K₂/J : K₂/J=-0.045 (open square), K₂/J=-0.047, (solid square), K₂/J=-0.049 (open circle), and...(이미지참조) 22
Fig. 2.4. The probability distributions of θ for two different cases : (a) K₂/J=-0.045, K₄/J=-0.004, and KD/J=-0.007 and (b) K₂/J=-0.052, K₄/J=0.004, and KD/J=-0.007....(이미지참조) 24
Fig. 2.5. Thermal behaviors of easy axes. (a) For fixed K₄/J=-0.004 with varying K₂/J. (b) For fixed K₄/J=0.004 with varying K₂/J. (c) For fixed K₂/J=-0.045 with varying K₄/J....(이미지참조) 26
Fig. 3.1. The high temperature behaviors of the thermoelectric powers (S(T)) for different electron densities n and Hund's coupling parameter JH in the double exchange model....(이미지참조) 37
Fig. 3.2. The real (S(T)) and approximated (Sa(T)) thermoelectric powers for the case of JH=10 in the double exchange model. Inset shows data of S(T) and Sa(T) for the case of JH=0 Here, unit of JH is t.(이미지참조) 38
Fig. 3.3. The low temperature behavior of the thermoelectric power S(T) for n=1/32 and JH=10. Lattice size is N=16x16. In inset, the S(T) behaviors for different lattice sizes (16x16, 24x24, and 32x32)...(이미지참조) 40
Fig. 3.4. (a) The thermal behavior of the thermoelectric power near TC in the bias system (H=0.025). The peak and dip feature appears. (b) The field dependence of the thermoelectric power near TC....(이미지참조) 41
Fig. 4.1. Crystal Structure of the distorted perovskite oxides (AMO₃) whose space group is Pbnm. The octahedra consist of one transition metal(M) in center and six oxygens in corners.... 46
Fig. 4.2. Two main Jahn(Janh)-Teller (JT) distortion modes in the Oh symmetry : (a) The orthorhombic (q2) and (b) tetragonal (q3) distortion modes. The distortion strength and angle are defined by ρ=√q22+q32...(이미지참조) 49
Fig. 4.3. The schematic diagram of neighboring MO6 octahedra in the distorted perovskite oxides. Due to the strong octahedral crystal field, it is easy for orbital states of d electrons in two octahedra to be illustrated...(이미지참조) 52
Fig. 4.4. The magnetic phase diagram of RMnO₃ system with respect to rare-earth ions. Data are from Ref.[98] (close triangle), Ref.[109] (open circle), and Ref.[110] (open square). 55
Fig. 4.5. Schematic diagram of the orbital ordering patterns for two different Mn-O-Mn chains. This discrepancy causes the anisotropic magnetic interaction. 57
Fig. 4.6. (a) The superexchange parameters for the ab plane interaction (Jab) and c axis interaction (Jc) as a function of the titling angle ω with t2g hopping or without t2g hopping....(이미지참조) 60
Fig. 4.7. The eg hoping contribution of the nearest neighbor interaction (a) with and (b) without the hopping change due to the Jahn-Tellet distortion. To examin the eg hoping contribution, we set tpdπ=0.0.(이미지참조) 62
Fig. 4.8. Schematic diagram of next nearest neighbor interaction channels. Let the lattice be rotated by 90° on the pivot of one Mn site. Position of manganese and oxygens is invariant but orbital shape is exactly... 64
Fig. 4.9. (a) The superexchange parameters for the next nearest neighbor interaction along the a axis (Ja) and b axis (Jb) as a function of the titling angle ω with t2g hopping or without t2g hopping....(이미지참조) 66
Fig. 4.10. Phase diagram of the magnetic ground states of the classical Heigenberg spin described by Eq 4.13. In this calculation, Jb and Jc are positive and Jc/Jb are fixed by 2.5....(이미지참조) 69
Fig. 4.11. Experimental data of the saturated magnetization and Cu-O1-Cu (c axis) and Cu-O2-Cu (ab plane) angles in Se1-xTexCuO3 (Ref. [89]).(이미지참조) 73
Fig. 4.12. Spin density contour plots in the ab and ac planes of SeCuO₃ in its ferromagnetic phase. 74
Fig. 4.13. The superexchange parameters (a) in the ab plane (Jab) and (b) along the c axis (Jc) for the d9 perovskite oxides. Parameters to calculate Jab and Jc are presented in table 4.6.(이미지참조) 76
Fig. 4.14. (a) Schematic diagram of an A-site ion and Cu-O-Cu chain along the c axis. (b) Tilting angle dependence of the A-O distance (dA) and spσ bond strength between the A-site ion and oxygen (tspσ) for the...(이미지참조) 78
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