請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/65396完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 胡崇德 | |
| dc.contributor.author | Mei-Hua Chen | en |
| dc.contributor.author | 陳玫樺 | zh_TW |
| dc.date.accessioned | 2021-06-16T23:40:31Z | - |
| dc.date.available | 2012-08-01 | |
| dc.date.copyright | 2012-08-01 | |
| dc.date.issued | 2012 | |
| dc.date.submitted | 2012-07-25 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/65396 | - |
| dc.description.abstract | Multiferroic LiCu2O2 is an interesting material. When we apply magnetic field, its polarization changes. In type II multiferroic material, it has a spiral spin state as the ground state. These spiral states can be found in many complex transition metal compounds, where competing exchange interactions of the neighboring spins can cause such periodically modulated spin state. The system with competing exchange interactions can be modeled by zigzag spin chain. Therefore, here we consider the zigzag spin chain system with competing nearest and next nearest superexchange interactions. Most importantly, we also considered anisotropic exchange interaction and Dzyaloshinskii-Moriya(DM) interaction. In this thesis, we divide our work into two part; the first part is to model the system and the second part is to analyze the ESR data.
In the first part, we had planed two work. The first one is to find the quantum critical surface of the XXZ zigzag spin chain, and the second one is to find the spiral spin state as the ground state in a zigzag spin chain system. In the first work, we analyze the ground state of a zigzag spin chain with applied magnetic field. Starting from a local Hamiltonian Hi,i+1,i+2 for the i−th, i+1−th, i+2−th spins, a parameter x is introduced to give the applied magnetic field on respective spins as B/(2 + x), xB/(2 + x) and B/(2 + x). We are able to identify the ground state as the fully polarized state and one-magnon states in the region b = (4 + f)^2/8 where b = B/J2, f = J1/J2; J1 and J2 are the nearest neighbor and next nearest neighbor exchange interaction, respectively. With the theorem of positive semi-definite matrix, we showed that b = (4 + f)^2/8 is a quantum critical line for f ≥ 0. For f < 0, we are able to show with the Bethe ansatz that the fully polarized state and one-magnon states have energy lower than those states with |S| ≥ N/6 for b ≥ (4 + f)^2/8. Hence, the line b = (4 + f)^2/8 is likely a quantum critical line for both positive and negative J1. We can generalize our result to xxz zigzag spin chains. In the second work, we intend to identify the conditions for spiral spin state as the ground state in this spin chain system. We start from building the connection between the spiral state and the fully polarized (FP) state with a unitary transform. Under this transformation, anisotropic exchange interaction and the Dzyaloshinskii-Moriya (DM) interaction can be transformed to each other. Then we use positive semi-definite theorem to identify the region of FP state being the GS for the transformed Hamiltonian, and it is the region of spiral spin state as GS of the original Hamiltonian. We showed that, to have the spiral GS, the effect of DM interaction is important, and its strength is related to the pitch angle of spiral spins. Our system indicates the connection between spiral spins and magnetic frustration, which is a feature of the multiferroics. This method not only can be applied to spin-1/2 system, but also to any other spin systems. In the second part of our work, we intend to explain the electron spin resonance (ESR) of LiCu2O2. Based on the icture of classical spins and the spin wave theory, we calculate the low lying excitations. Our result shows that the resonance ν1 ∼ 30GHz corresponds to the spin wave state of wave vector q = Q (where Q = (0.5, 0.174, 0) is the wave vector of spiral spins). The mechanism for the spin gap and hence, the resonance can be either the DM interaction or an anisotropic superexchange interaction. Thus, when the applied magnetic field is parallel to the spiral axis (R), there are two branches; when it is perpendicular to the spiral axis, there is only one branch. By comparing the result of our theoretical calculation with that of experiment, we discuss the system properties, such as anisotropy and DM interaction. We also predict that the spiral axis will lies on a-b plane, and close to a +b, which is determined by the direction of the DM interaction. As a result of this work, we revealed the condition for spiral spin state to be the ground state in the zigzag spin chain, in which the DM interaction is very important. Furthermore, we understand the origin of ν1 in LiCu2O2 is from spin wave with wave vector q = Q. Then we obtain the system parameter, such as J, delta, D , spiral axis R and predict how the spiral ground state changes under applied magnetic field. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T23:40:31Z (GMT). No. of bitstreams: 1 ntu-101-D96222011-1.pdf: 5047210 bytes, checksum: b735248eb444cf5b427831b7eccefe6c (MD5) Previous issue date: 2012 | en |
| dc.description.tableofcontents | 口試委員會審定書. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii 中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v 英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii List of Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv List of Tables. . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi 1 Introduction. . . . . . . . . . . . . . . . . . . . . .. . . . . . .. . . . . . .. .. 1 1.1 Introduction to multiferroics . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Spiral spin state in multiferroics . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Spiral spin state in multiferroics . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 The origin of the spin interaction . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.1 Direct exchange and superexchange interaction . . . . . . . . . . . . . . . . . 6 1.3.2 Dzyaloshinskii-Moriya interaction . . . . . . . . . . . . . . . . . . . . . . . 13 1.3.3 The zigzag spin chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.4 The important property of LiCu2O2 . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4.1 The multiferroic property of LiCu2O2 . . . . . . . . . . . . . . . . . . . . . 19 1.4.2 The spin interaction in LiCu2O2 . . . . . . . . . . . . . . . . . . . . . . . . 24 I MODELING THE SYSTEM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2 Quantum critical surface of the XXZ zigzag spin chain with applied magnetic field . . 31 2.1 Quantum critical surface of the zigzag spin chain . . . . . . . . . . . . . . . . . 33 2.1.1 The quantum critical surface from local Hamiltonian . . . . . . . . . . . . . . . 35 2.1.2 Proof of the quantum critical surface by positive semi-definite matrix theorem . 37 2.1.3 Case outside the region of inequalities (2.18-2.19) . . . . . . . . . . . . . . . 39 2.2 The matrix product representation of the ground state . . . . . . . . . . . . . . . 45 3 The spiral spin state in a zigzag spin chain system. . . . . . . . . . . . . . . . . 53 3.1 Spiral spin state as an eigen state . . . . . . . . . . . . . .. . . . . . . . . . 54 3.2 Spiral state as the ground state . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.2.1 Isotropic exchange interaction . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.2.2 Without DM interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.2.3 Special case with φ′ = 50^0 . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.3 Symmetry properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.4 Extension of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.4.1 Coupled spin-1/2 zigzag spin system . . . . . . . . . . . . .. . . . . . . . . . 68 3.4.2 Two dimensional triangular spin-1/2 spin system with spiral state . . . . . . . . 74 3.5 Analysis and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 II LOOKING INTO THE EXPERIMENT. . . . . . . . . .. . . . . . . . . . . . . .. . . . . . 83 4 Analysis of the electron spin resonance of LiCu2O2 at low temperature . . . . . . . . 85 4.1 Experimental results of ESR in LiCu2O2 . . . . . . . . . . . . . . . . . . . . . . 86 4.2 Starting point of the spin wave theory . . . . . . . . . . . . . . . . . . . . . . 89 4.2.1 ESR resonance and relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.2.2 Physical picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.2.3 Classical ground state without applied magnetic field . . . . . . . . . . . . . 92 4.2.4 Classical ground state with applied magnetic field . . . . . . . . . . . . . . . 96 4.3 The model of spin wave excitation in LiCu2O2 . . . . . . . . . . . . . . . . . . . 97 4.3.1 Two branches case for the field applied on b axis . . . . . . . . . . . . . . . . 97 4.3.2 One branch case for h//c . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 4.4 Physical starting point for fitting . . . . . . . . . . . . . . . . . . . . . . . 104 4.4.1 Fitting equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4.4.2 Comparison of the result of fitting with experiment data . . . . . . . . . . . . 108 4.5 What can we see from analyzing delta h/ν? . . . . . . . . . . . . . . . . . . . . 111 5 Numerical analysis of the spin state, polarization and magnetization of LiCu2O2. . . 115 5.1 The response of the spiral axis to applied magnetic field . . . . . . . . . . . . 116 5.2 The case of D lying on the a-b plane make angle 45^0 with b-axis . . . . . . . . . 121 5.2.1 The spiral spin state change when the applied magnetic field is on the b-c plane 121 5.2.2 The state change when applied magnetic field lies on a-b plane. . . . . . . . . 125 5.2.3 The state change when the applied magnetic field lies on a-c plane . . . . . . . 128 5.3 Polarization P, Magnetization M and P × M . . . . . . . . . . . . . . . . . . . . 131 5.4 The chirality along a, b, and c-axis . . . . . . . . . . . . . . . . . . . . . . . 135 5.5 Summary of part II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 III CONCLUSIONS. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 139 Appendix. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 143 A Selected list of symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 B The important energy scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 C Introduction to the positive semi-definite theory. . . . . . . . . . . . . . . . . . 147 D Introduction of the Bethe ansatz . . . . . . . . . . . . . . . . . . . . . . . . . . 151 E Detailed derivation in Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . 155 E.1 Energy of the classical ground state . . . . . . . . . . . . . . . . . . . . . . . 156 E.2 Two branch case for the applied field on the b- c plane . . . . . . . . . . . . . 157 E.3 One branch case for h//c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 E.4 Definition of X_{q,r}, Y_{q,r}... . . . . . . . . . . . . . . . . . . . . . . . . 165 E.5 Formula to be use for Fourier transformation . . . . . . . . . . . . . . . . . . . 167 F The polarization change with applied different γ_h in Chapter 5 . . . . . . . . . . 168 F.1 The applied field on b-c plane . . . . . . . . . . . . . . . .. . . . . . . . . . 171 F.2 The field applied on the a-b plane . . . . . . . . . . . . . . . . . . . . . . . . 174 F.3 The field applied on the a-c plane . . . . . . . . . . . . . . . . . . . . . . . . 175 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 | |
| dc.language.iso | en | |
| dc.subject | Dzyaloshinskii-Moriya interaction | zh_TW |
| dc.subject | Zigzag 自旋鍊 | zh_TW |
| dc.subject | 電子自旋共振 | zh_TW |
| dc.subject | 鐵材料 | zh_TW |
| dc.subject | 螺旋自旋態 | zh_TW |
| dc.subject | 自旋波理論 | zh_TW |
| dc.subject | LiCu2O2 | zh_TW |
| dc.subject | positive semi-definite theorem | zh_TW |
| dc.subject | positive semi-definite theorem | en |
| dc.subject | spiral spin state | en |
| dc.subject | zigzag spin chain | en |
| dc.subject | electron spin resonance | en |
| dc.subject | spin wave theory | en |
| dc.subject | LiCu2O2 | en |
| dc.subject | multiferroic material | en |
| dc.subject | Dzyaloshinskii-Moriya interaction | en |
| dc.title | Z型自旋鍊的物理特性研究-量子相變面、螺旋自旋態及多鐵材料 | zh_TW |
| dc.title | Physical property of the zigzag spin chain: quantum critical surface, spiral spin state, and multiferroics | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 100-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 林昭吟,黃迪靖,郭光宇,吳文欽,張明哲 | |
| dc.subject.keyword | 鐵材料,螺旋自旋態,Zigzag 自旋鍊,電子自旋共振,自旋波理論,LiCu2O2,positive semi-definite theorem,Dzyaloshinskii-Moriya interaction, | zh_TW |
| dc.subject.keyword | multiferroic material,spiral spin state,zigzag spin chain,electron spin resonance,spin wave theory,LiCu2O2,positive semi-definite theorem,Dzyaloshinskii-Moriya interaction, | en |
| dc.relation.page | 182 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2012-07-25 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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