Title Page
ABSTRACT
Contents
Abbreviations 17
Chapter 1. Introduction 18
1.1. Origin of Magnetism 19
1.2. Types of Magnetism 21
1.3. Stoner Model of Ferromagnetism 24
1.4. Magnetic Instability 27
1.5. Quantum Well Effect 28
1.6. Spin-Orbit Coupling Interaction 29
1.7. Magnetocrystalline Anisotropy 32
1.8. Current-Induced Magnetization Switching 37
1.9. Spin and Orbital Hall Effects 39
Chapter 2. Methodology and Computational Details 40
2.1. Density Functional Theory 40
2.1.1. Born-Oppenheimer Approximation 40
2.1.2. Hohenberg-Kohn Theorems 41
2.1.3. Kohn-Sham Equations 43
2.1.4. Local Density Approximation 45
2.1.5. Generalized Gradient Approximation 46
2.2. Solving Kohn-Sham Equations 47
2.2.1. Plane Waves 49
2.2.2. Localized Atomic Orbitals 50
2.2.3. Atomic Sphere 50
2.3. Computing MCA Energy 51
2.3.1. Force Theorem 53
2.3.2. Second-order Perturbation Theory 54
2.4. Computing Spin and Orbital Hall Conductivities 56
2.4.1. Kubo Formula for SHC and OHC 57
2.4.2. Wannier Interpolation 58
Chapter 3. Magnetocrystalline Anisotropy of Co Thin Films 60
3.1. Introduction 60
3.2. Numerical Methods 63
3.3. Results and Discussions 66
3.3.1. Bulk hcp and fcc Co 66
3.3.2. hcp and fcc Co Films 70
3.4. Summary 79
Chapter 4. Quantum Well Effect on Magnetism of Pd(111) Films 80
4.1. Introduction 80
4.2. Numerical Methods 83
4.3. Results and Discussions 84
4.4. Summary 95
Chapter 5. Spin and Orbital Hall Conductivities of 3d/5d Metals 96
5.1. Introduction 96
5.2. Numerical Methods 98
5.3. Results and Discussions 101
5.4. Summary 108
Chapter 6. Conclusions 109
References 111
초록 118
Table 1.1. Anisotropy constants K obtained from experiments, and experimental and theoretical EMCA of bulk Fe, Co, and Ni in μeV/atom.[이미지참조] 35
Table 2.1. Nonvanishing angular momentum matrix elements between d states for Lz and Lₓ angular momentum operators.[이미지참조] 55
Table 3.1. Calculated EMCA for hcp and fcc bulk Co, respectively. Experimental and previous theoretical results are also given for comparison.[이미지참조] 67
Table 5.1. Calculated and experimental lattice constants. Values in the parentheses are c/a ratio of the hcp structure. 99
Figure 1.1. (a) An electron orbiting a proton in a hydrogen atom is analogous to (b) a current flowing in a circular loop. 20
Figure 1.2. Schematic illustration of five types of magnetism 21
Figure 1.3. A schematic band structure of the Stoner model of ferromagnetism. Energy states of different spins are split by the exchange interaction, and states near the Fermi level are spin-polarized. 25
Figure 1.4. Calculated values of the Stoner product and the Stoner exchange constant I for 32 elemental metals. Reproduced from Ref. [25]. 26
Figure 1.5. Intrinsic spin-orbit coupling interaction. The frame of nucleus and electron are schematically shown, respectively. 31
Figure 1.6. (a) Schematic crystals of bcc Fe, fcc Ni, and hcp Co. (b) Magnetization in Fe, Co, Ni in different crystal axis when applied magnetic fields showing anisotropy. Fig. 1.6(b) is... 33
Figure 1.7. Working principles of (a) spin-transfer torque (STT) and (b) spin-orbit torque-based devices 38
Figure 2.1. Schematic representation of the self-consistent loop for the density functional calculation. 48
Figure 2.2. An overview of the theoretical and computational options for solving the density function of the one-particle equation. Reproduced from Ref. [80]. 49
Figure 2.3. EMCA as a function of the number of k points used for numerical integration over the full Brillouin zone for hcp Co in bulk.[이미지참조] 52
Figure 3.1. Schematical hexagonal unit cell of Co in hcp and fcc stacking sequences. The side and top views are shown in the upper and lower sections. Red, blue, and green spheres represent... 64
Figure 3.2. (a) Orbital- and spin-decomposed EMCA of bulk hcp and fcc Co. Solid and open symbols stand for hcp and fcc Co, respectively. Different symbols represent different spin...[이미지참조] 69
Figure 3.3. Partial density of states (PDOS) of d-orbitals with magnetic quantum number m for (a) hcp and (b) fcc Co in bulk. Upper and lower parts show the majority (↑) and minority (↓)... 70
Figure 3.4. (a) EMCA of hcp (red-solid) and fcc (blue-empty) films as a function of Co thickness. Red dashed and blue dash-dotted lines are calculated EMCA of bulk for comparison (b) EMCA of...[이미지참조] 72
Figure 3.5. Density of states at Fermi level N(EF) of (a) hcp and (b) fcc surface layers as a function of Co thickness. Black, blue, and red lines denote the d states with magnetic quantum...[이미지참조] 73
Figure 3.6. (a) Orbital- and spin-decomposed EMCA of surface layers in hcp and fcc Co of 27 ML. Solid and open symbols stand for hcp and fcc Co, respectively. Different symbols...[이미지참조] 75
Figure 3.7. (a)-(b) Partial density of states (PDOS) for d orbitals of hcp and fcc surface layers of 27 ML Co film with magnetic quantum number m. Upper and lower parts show the majority... 76
Figure 3.8. (a)-(b) Two-dimensional k-resolved EMCA for hcp and fcc surface layer of 27 ML Co film. (c)-(d) Band structures for majority (↑) and minority (↓) spin states along high...[이미지참조] 78
Figure 4.1. (a) Total energy difference between the paramagnetic (PM) and ferromagnetic (FM) states and (b) total spin and orbital magnetic moments as functions of the film thickness at... 85
Figure 4.2. Total energy difference between the paramagnetic (PM) and ferromagnetic (FM) states (red circle) and total spin magnetic moments (blue square) as a function of lattice... 87
Figure 4.3. Band structure of bulk Pd along the high symmetry points. The Fermi level is indicated by a horizontal dash–dotted line. 88
Figure 4.4. (a) Three-dimensional Fermi surface in the first Brillouin zone. (b) Slice of Fermi surface with Fermi surface nesting along the [111] direction. Red, green, and yellow colors... 89
Figure 4.5. Density of state at the Fermi level N(EF) with respect to the Pd(111) film thickness. The filled symbol denotes stable FM cases. The dashed line indicates N(EF) that is required for...[이미지참조] 90
Figure 4.6. (a) Band structure of the 30-ML Pd(111) film in a PM state along the high symmetry lines and (b) the zoom-in band structure near the Fermi level. The Fermi level is set to zero. 91
Figure 4.7. Variation of the surface energy Eₛ(N) with the Pd(111) film thickness. The solid circles are calculated values, and the red line is the fitting curves. 93
Figure 4.8. Variation of the second-order derivative of surface energy △²Eₛ(N) with the Pd(111) film thickness. The solid circles are calculated values, and the red line is the fitting curves. 94
Figure 5.1. Spin Hall conductivity of light (Al, V, Cr), magnetic (Fe, Co, Ni), and heavy (Ta, W, Pt) metals from FLEUR and VASP calculations with PBE and LDA. 101
Figure 5.2. Orbital Hall conductivity of light (Al, V, Cr), magnetic (Fe, Co, Ni), and heavy (Ta, W, Pt) metals from FLEUR and VASP calculations with PBE and LDA. 102
Figure 5.3. Orbital Hall k-resolved Berry curvature for fcc structures: (a) Al, (b) Ni, and (c) Pt. Upper panel: k-resolved Berry curvature; Lower panel: Total Berry curvature along k-path. The... 104
Figure 5.4. Orbital Hall k-resolved Berry curvature for bcc structures: (a) V, (b) Ta, (c) Cr, (d) W, and (e) Fe. Upper panel: k-resolved Berry curvature; Lower panel: Total Berry curvature... 106
Figure 5.5. Orbital Hall k-resolved Berry curvature for hcp Co. Upper panel: k-resolved Berry curvature; Lower panel: Total Berry curvature along k-path. The color scheme is in logarithmic... 107