Title Page
Abstract
Contents
Chapter 1. Introduction 15
1.1. Kitaev model and Jackeli-Khaliullin mechanism 15
1.1.1. Kitaev model 15
1.1.2. Jackeli-Khaliullin mechanism 18
1.2. Review of the present Kitaev candidates and their limitations 20
1.3. Spin-orbital entangled Jeff=1/2 state in cobalt compounds[이미지참조] 22
1.4. Outline of thesis 24
References 25
Chapter 2. Theoretical background 27
2.1. General solution for the linear spin-wave theory 27
2.1.1. Rotating frame method 27
2.1.2. Holstein-Primakoff transformation 28
2.1.3. Linear spin-wave theory 29
2.1.4. Bond-dependent anisotropy with a non-collinear magnetic order 31
2.2. Magnon decay due to multi-magnon Continuum 34
2.2.1. Three-boson interaction and its origin 34
2.2.2. Continuum of the two-magnon density of states 38
References 39
Chapter 3. Experimental techniques 41
3.1. Sample synthesis 41
3.1.1. Solid-state reaction method 41
3.1.2. Bridgman method 44
3.2. Inelastic neutron scattering 44
3.2.1. Basic principle 45
3.2.2. Time-of-flight (ToF) technique 47
3.2.3. INS experiment at the HRC, J-PARC 49
3.2.4. INS experiment at AMATERAS, J-PARC 49
3.2.5. Multi-Ei measurements at J-PARC beamlines[이미지참조] 52
References 54
Chapter 4. Magnetic excitation of van der Waals XXZ-type cobalt honeycomb antiferromagnet CoPS₃ 56
4.1. Introduction 56
4.2. Magnetic excitations of CoPS₃ 58
4.2.1. Absence of spin-orbit exciton 58
4.2.2. Spin-wave spectrum 59
4.3. Discussion 62
4.4. Summary 65
References 66
Chapter 5. Spin dynamics of cobalt Kitaev honeycomb candidates Na₃Co₂SbO₆ and Na₂Co₂TeO₆ 67
5.1. Introduction 67
5.2. Magnetic excitations of NCSO and NCTO 68
5.2.1. Spin-orbit exciton 68
5.2.2. Spin-wave spectrum 71
5.2.3. Magnon damping effect 75
5.3. Discussion 77
5.3.1. Magnetic phase diagram with GKH model 77
5.3.2. Comparison with single-crystal data 79
5.4. Summary 80
References 81
Chapter 6. Magnon breakdown in the cobalt Kitaev triangular antiferromagnet CoI₂ 83
6.1. Introduction 83
6.2. Minimal Hamiltonian for CoI₂ 86
6.3. Magnetic excitations of CoI₂ 88
6.3.1. Paramagnetic excitation 88
6.3.2. Spin-wave spectrum 90
6.4. Magnon damping in CoI₂ 92
6.5. Summary 95
References 95
Chapter 7. Summary and Outlook 97
7.1. Summary 97
7.2. Outlook 98
References 100
Publication lists 102
국문초록 105
Table 4.1. Summary of the magnetic exchange parameters of the magnetic vdW TMPS₃ (TM=Mn, Fe, Co, Ni) family. The angle between the c* axis and the vector that joins the... 64
Table 5.1. Best parameter set with the GKH model 74
Figure 1.1. Schematic showing comparison between (a) geometric frustration and (b) Kitaev model. 16
Figure 1.2. Schematic of the Kitaev model. (a) Illustration of bond-dependent anisotropic interactions in the Kitaev model and Z₂ flux W. (b) Examples of classical spin configuration... 17
Figure 1.3. Real-space spin configuration of a spin-orbital entangled jeff=1/2 state with different quantisation axes. (a) z axis parallel to the [1, 1, 1] direction, which is useful for...[이미지참조] 19
Figure 1.4. (a) Edge-sharing metal-ligand octahedra i and j; the blue and purple spheres depict the transition metal and ligands, respectively. (b) Schematic of destructive... 19
Figure 1.5. Schematic showing the exchange process in the d-electron case. (a) Indirect d- p-d hopping, which is considered in the JK mechanism. (b) Direct d-d hopping, which... 21
Figure 1.6. Phase diagrams in a unifrom magnetic field with (a) AFM Kitaev model and (b) FM Kitaev model. GSL incidates a gapless spin liquid, KSL is a gapped Kitaev spin... 22
Figure 1.7. Spin-orbital entangled Jeff=1/2 state in cobalt ions and exchange interactions. (a) Schematic of a spin-orbital entangled Jeff=1/2 state in cobalt based on the multiplet...[이미지참조] 23
Figure 2.1. (a) General schematic of magnon decay due to a multi-particle continuum. (b) Calculated quasiparticle decay with interaction between a bare state and the continuum... 35
Figure 2.2. (a) Feynman diagrams of two vertices in H₃, magnon 'decay' (left upper) and 'source'; the lower part shows the magnon self-energy from a pair of decay vertex. (b)... 37
Figure 2.3. (a) Intensity of the dynamical structure factors of S=1/2 (upper) and S=3/2 (lower) TLAFs with a magnetic order of 120°, calculated using the 1/S correction. (b)... 38
Figure 2.4. Schematic of the two-magnon scattering process and three-boson terms. (a) the two-magnon decay of a single magnon with kinematic constraints. The magnon dispersion... 39
Figure 3.1. Picture of prepared polycrystalline samples. Left side is CoPS₃ ; right side is Na₃Co₂SbO₆ 42
Figure 3.2. Illustration of the Bridgman technique. (a) Schematic of the Bridgman method. (b) Customised Bridgman furnace for CoI₂ synthesis. (c) Single crystal of CoI₂ prepared... 43
Figure 3.3. Basic of the neutron scattering process. (a) A general geometry of a neutron scattering measurement set-up, including illustration of how neutrons interact with... 45
Figure 3.4. Schematic of the ToF INS measurement set-up 48
Figure 3.5. Details of the HRC spectrometer. (a) Schematic of the HRC spectrometer. (b) Picture of a typical Fermi chopper used in ISIS, UK. (c) Curved Fermi chopper... 50
Figure 3.6. Details of the AMATERAS spectrometer. (a) Schematic view of AMATERAS. (b) Installed disc (left) and inside view (right) of the third fast disc chopper (used for... 51
Figure 3.7. Schematic of the RRM set-up in the HRC and AMATERAS. (a) RRM set-up in the HRC using a Fermi chopper. (b) RRM set-up in the AMATERAS using a multiple... 53
Figure 4.1. (a) Magnetic structure of CoPS₃. Red arrows indicate the spin of Co²⁺ ion. (b) Exchange interaction path of Co²⁺ ions in CoPS₃. 57
Figure 4.2. (a-f) Temperature dependence of the magnetic excitation in CoPS₃. (g) Integrated intensity of magnetic excitations over the momentum range of Q=[0.3, 4] ů¹... 58
Figure 4.3. (a) Best-fit powder-averaged spin-wave spectrum with the XXZ model. (b) Experimental INS data of CoPS₃ (c) Best-fit magnon spectra with the isotropic Heisenberg model. 60
Figure 4.4. (a,b) Constant momentum cut in the range of Q=[1.7 1.8] and Q=[2.2 2.3] ů¹ for the measured data with the best fit simulations. (c,d) Constant energy cut in the... 61
Figure 4.5. The spin-wave dispersion of the isotropic Heisenberg model and the XXZ model, indicating the high-symmetric points of the Brillouin zone. The spin-wave... 63
Figure 5.1. (a-b) Crystal structure of Na₃Co₂SbO₆ and its magnetic structure. (c-d) Crystal structure of Na₂Co₂TeO₆ and its magnetic structure 68
Figure 5.2. The spin-orbit exciton of (a-c) Na₃Co₂SbO₆ and (d-f) Na₂Co₂TeO₆ with respect to the temperature. Constant-Q cuts in (c,f) is integrated intensity of grey boxes in (a,b,d,e).... 69
Figure 5.3. Peak profiles of the spin-orbit excitons. The parameter set from fitting was used for the crystal field analysis 70
Figure 5.4. (a-b) Spin-wave spectrum of NCSO and NCTO at T=3.2 K. (c-d) Simulated powder-averaged spectrum with the generalized Kitaev-Heisenberg model. (e-f)... 72
Figure 5.5. Comparison of the measured spin-wave (left) and simulated powder-averaged spectrum with the AFM and FM Kitaev models (right). 74
Figure 5.6. Two-magnon DOS calculation based on our best-fitting parameters. The one-magnon dispersion εk,m (black line) is displayed with the two-magnon DOS. The lower...[이미지참조] 76
Figure 5.7. Optimized magnetic structures of zig-zag order with GKH model. (a) Eigenstate of E±, wherein spins are aligned orthogonal to the bond direction. (b) Eigenstate of Ep,...[이미지참조] 78
Figure 5.8. Phase diagram of the angle of out-of-plane magnetic moment in the K-Γ-Γ' space. For NCSO, (a) is the best parameter set with AFM Kitaev, (c) FM Kitaev and (e)... 78
Figure 5.9. Calculated spin-wave dispersion along the high-symmetric points at the Brillouin Zone. The different color of dispersion indicates possible domains with 120° rotation. 80
Figure 6.1. (a) Single-ion picture of Co²⁺ ions in CoI₂. (b) Schematic of Kitaev interactions in a triangular lattice. (c) Magnetic structure of CoI₂ (d) Crystal structure of CoI₂ and the... 84
Figure 6.2. (a) Spin-orbit exciton at room temperature. The power-averaged data were measured using the incident energy Ei=52 meV. (b) Constant-momentum cut of power-...[이미지참조] 85
Figure 6.3. (a-c) Magnetic phase diagram of the J₁-J₂-J₃ model with a finite second nearest neighbour intra-layer coupling Jc₂. (d-f) Magnetic phase diagram of the J₁-J±±-J₃ model...[이미지참조] 87
Figure 6.4. (a) Paramagnetic inelastic neutron signal measured at T=13 K by integrating the energy transfer E=[1, 7] meV and that measured along the L-direction with L=[-0.7,... 88
Figure 6.5. (a) Theoretical paramagnetic scattering intensity of the J₁-J±±-J₃ model compared with that of the J₁-J₂-J₃ model. (b-d) Calculated paramagnetic intensity of the...[이미지참조] 90
Figure 6.6. Comparison of inelastic scattering cross-section between the data (left) and theoretical calculation (right) at T=4 K. The upper (lower) row data were measured with... 91
Figure 6.7. (a) Calculated two-magnon DOS based on LSWT result. The upper (lower) column shows the different energy cut-offs with E=12 (6) meV. The white dashed lines... 92
Figure 6.8. (a) Fitted FWHM of the magnon modes along the Γ-K line in Fig. 6. 7(b). The instrumental resolution of each incident energy is indicated by black dashed lines. (b)... 93