Effective model for rare-earth Kitaev materials and its classical Monte Carlo simulation

doi:10.1088/1674-1056/ac0a5d

中国物理B ›› 2021, Vol. 30 ›› Issue (8): 87503-087503.doi: 10.1088/1674-1056/ac0a5d

Effective model for rare-earth Kitaev materials and its classical Monte Carlo simulation

Mengjie Sun(孙梦杰)^1,2,†, Huihang Lin(林慧航)^1,†, Zheng Zhang(张政)^1,2, Yanzhen Cai(蔡焱桢)³, Wei Ren(任玮)³, Jing Kang(康靖)³, Jianting Ji(籍建葶)², Feng Jin(金峰)², Xiaoqun Wang(王孝群)^4,5, Rong Yu(俞榕)¹, Qingming Zhang(张清明)^3,2,‡, and Zhengxin Liu(刘正鑫)^1,§

1 Department of Physics, Renmin University of China, Beijing 100872, China;
2 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
3 School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China;
4 Key Laboratory of Artificial Structures and Quantum Control of MOE, Shenyang National Laboratory for Materials Science, Shenyang 110016, China;
5 School of Physics and Astronomy, Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China

收稿日期:2021-04-23 修回日期:2021-06-07 接受日期:2021-06-11 出版日期:2021-07-16 发布日期:2021-08-13
通讯作者: Qingming Zhang, Zhengxin Liu E-mail:qmzhang@ruc.edu.cn;liuzxphys@ruc.edu.cn
基金资助:
Project supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0302904 and 2016YFA0300504), the National Natural Science Foundation of China (Grant Nos. U1932215, 11774419, 11574392, and 11974421), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB33010100), the Fundamental Research Funds for the Central Universities, China, and the Research Funds of Renmin University of China (Grant No. 19XNLG11). Q. M. Z. acknowledges the support from Users with Excellence Program of Hefei Science Center and High Magnetic Field Facility, CAS.

Effective model for rare-earth Kitaev materials and its classical Monte Carlo simulation

1 Department of Physics, Renmin University of China, Beijing 100872, China;
2 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
3 School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China;
4 Key Laboratory of Artificial Structures and Quantum Control of MOE, Shenyang National Laboratory for Materials Science, Shenyang 110016, China;
5 School of Physics and Astronomy, Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China

Received:2021-04-23 Revised:2021-06-07 Accepted:2021-06-11 Online:2021-07-16 Published:2021-08-13
Contact: Qingming Zhang, Zhengxin Liu E-mail:qmzhang@ruc.edu.cn;liuzxphys@ruc.edu.cn
Supported by:
Project supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0302904 and 2016YFA0300504), the National Natural Science Foundation of China (Grant Nos. U1932215, 11774419, 11574392, and 11974421), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB33010100), the Fundamental Research Funds for the Central Universities, China, and the Research Funds of Renmin University of China (Grant No. 19XNLG11). Q. M. Z. acknowledges the support from Users with Excellence Program of Hefei Science Center and High Magnetic Field Facility, CAS.

摘要/Abstract

摘要： Recently, the family of rare-earth chalcohalides were proposed as candidate compounds to realize the Kitaev spin liquid (KSL) [Chin. Phys. Lett. 38 047502 (2021)]. In the present work, we firstly propose an effective spin Hamiltonian consistent with the symmetry group of the crystal structure. Then we apply classical Monte Carlo simulations to preliminarily study the model and establish a phase diagram. When approaching to the low temperature limit, several magnetic long range orders are observed, including the stripe, the zigzag, the antiferromagnetic (AFM), the ferromagnetic (FM), the incommensurate spiral (IS), the multi-Q, and the 120° ones. We further calculate the thermodynamic properties of the system, such as the temperature dependence of the magnetic susceptibility and the heat capacity. The ordering transition temperatures reflected in the two quantities agree with each other. For most interaction regions, the system is magnetically more susceptible in the ab-plane than in the c-direction. The stripe phase is special, where the susceptibility is fairly isotropic in the whole temperature region. These features provide useful information to understand the magnetic properties of related materials.

关键词: Monte Carlo methods, Kitaev materials, quantum spin liquids, rare-earth ions, DM interaction

Abstract: Recently, the family of rare-earth chalcohalides were proposed as candidate compounds to realize the Kitaev spin liquid (KSL) [Chin. Phys. Lett. 38 047502 (2021)]. In the present work, we firstly propose an effective spin Hamiltonian consistent with the symmetry group of the crystal structure. Then we apply classical Monte Carlo simulations to preliminarily study the model and establish a phase diagram. When approaching to the low temperature limit, several magnetic long range orders are observed, including the stripe, the zigzag, the antiferromagnetic (AFM), the ferromagnetic (FM), the incommensurate spiral (IS), the multi-Q, and the 120° ones. We further calculate the thermodynamic properties of the system, such as the temperature dependence of the magnetic susceptibility and the heat capacity. The ordering transition temperatures reflected in the two quantities agree with each other. For most interaction regions, the system is magnetically more susceptible in the ab-plane than in the c-direction. The stripe phase is special, where the susceptibility is fairly isotropic in the whole temperature region. These features provide useful information to understand the magnetic properties of related materials.

Key words: Monte Carlo methods, Kitaev materials, quantum spin liquids, rare-earth ions, DM interaction

中图分类号: (Applications of Monte Carlo methods)

02.70.Uu

71.70.Ej (Spin-orbit coupling, Zeeman and Stark splitting, Jahn-Teller effect) 75.10.Kt (Quantum spin liquids, valence bond phases and related phenomena)

Mengjie Sun(孙梦杰), Huihang Lin(林慧航), Zheng Zhang(张政), Yanzhen Cai(蔡焱桢), Wei Ren(任玮), Jing Kang(康靖), Jianting Ji(籍建葶), Feng Jin(金峰), Xiaoqun Wang(王孝群), Rong Yu(俞榕), Qingming Zhang(张清明), and Zhengxin Liu(刘正鑫). Effective model for rare-earth Kitaev materials and its classical Monte Carlo simulation[J]. 中国物理B, 2021, 30(8): 87503-087503.

参考文献

[1] Ji J, Sun M, Cai Y, Wang Y, Sun Y, Ren W, Zhang Z, Jin F and Zhang Q 2021 Chin. Phys. Lett. 38 047502
[2] AdyStern 2010 Nature 464 187
[3] Shimizu Y, Miyagawa K, Kanoda K, Maesato M and Saito G 2003 Phys. Rev. Lett. 91 107001
[4] Itou T, Oyamada A, Maegawa S and Kato R 2010 Nat. Phys. 6 673
[5] Han T H, Helton J S, Chu S, Nocera D G, Rodriguez-Rivera J A, Broholm C and Lee Y S 2012 Nature 492 406
[6] Depenbrock S, McCulloch I P and Schollwöck U 2012 Phys. Rev. Lett. 109 067201
[7] Chen G and Balents L 2008 Phys. Rev. B 78 094403
[8] Lawler M J, Kee H Y, Kim Y B and Vishwanath A 2008 Phys. Rev. Lett. 100 227201
[9] Micklitz T and Norman M R 2010 Phys. Rev. B 81 174417
[10] Kitaev A 2006 Ann. Phys 321 2
[11] Chaloupka J c v, Jackeli G and Khaliullin G 2010 Phys. Rev. Lett. 105 027204
[12] Nasu J, Knolle J, Kovrizhin D L, Motome Y and Moessner R 2016 Nat. Rev. Phys. 12 912
[13] Barkeshli M, Berg E and Kivelson S 2014 Science 346 722
[14] Shitade A, Katsura H, Kuneš J, Qi X L, Zhang S C and Nagaosa N 2009 Phys. Rev. Lett. 102 256403
[15] Choi S K, Coldea R, Kolmogorov A N, Lancaster T, Mazin I I, Blundell S J, Radaelli P G, Singh Y, Gegenwart P, Choi K R, Cheong S W, Baker P J, Stock C and Taylor J 2012 Phys. Rev. Lett. 108 127204
[16] Plumb K W, Clancy J P, Sandilands L J, Shankar V V, Hu Y F, Burch K S, Kee H Y and Kim Y J 2014 Phys. Rev. B 90 041112
[17] Liu X, Berlijn T, Yin W G, Ku W, Tsvelik A, Kim Y J, Gretarsson H, Singh Y, Gegenwart P and Hill J P 2011 Phys. Rev. B 83 220403
[18] Baek S H, Do S H, Choi K Y, Kwon Y S, Wolter A U B, Nishimoto S, van den Brink J and Büchner B 2017 Phys. Rev. Lett. 119 037201
[19] Takayama T, Kato A, Dinnebier R, Nuss J, Kono H, Veiga L S I, Fabbris G, Haskel D and Takagi H 2015 Phys. Rev. Lett. 114 077202
[20] Williams S C, Johnson R D, Freund F, Choi S, Jesche A, Kimchi I, Manni S, Bombardi A, Manuel P, Gegenwart P and Coldea R 2016 Phys. Rev. B 93 195158
[21] Knolle J, Moessner R and Perkins N B 2019 Phys. Rev. Lett. 122 047202
[22] Johnson R D, Williams S C, Haghighirad A A, Singleton J, Zapf V, Manuel P, Mazin I I, Li Y, Jeschke H O, Valentí R and Coldea R 2015 Phys. Rev. B 92 235119
[23] Liu Z X and Normand B 2018 Phys. Rev. Lett. 120 187201
[24] Zheng J, Ran K, Li T, Wang J, Wang P, Liu B, Liu Z X, Normand B, Wen J and Yu W 2017 Phys. Rev. Lett. 119 227208
[25] Wolter A U B, Corredor L T, Janssen L, Nenkov K, Schönecker S, Do S H, Choi K Y, Albrecht R, Hunger J, Doert T, Vojta M and Büchner B 2017 Phys. Rev. B 96 041405
[26] Yadav R, Bogdanov N A, Katukuri V M, Nishimoto S, van den Brink J and Hozoi L 2016 Sci. Rep. 6 37925
[27] Banerjee A, Lampen-Kelley P, Knolle J, Balz C, Aczel A A,Winn B, Liu Y, Pajerowski D, Yan J, Bridges C A, Savici A T, Chakoumakos B C, Lumsden M D, Tennant D A, Moessner R, Mandrus D G and Nagler S E 2018 npj Quantum Mater. 3 8
[28] Yao W and Li Y 2020 Phys. Rev. B 101 085120
[29] Ran K, Wang J, Wang W, Dong Z Y, Ren X, Bao S, Li S, Ma Z, Gan Y, Zhang Y, Park J T, Deng G, Danilkin S, Yu S L, Li J X and Wen J 2017 Phys. Rev. Lett. 118 107203
[30] Lin D, Ran K, Zheng H, Xu J, Gao L, Wen J, Yu S L, Li J X and Xi X 2020 Phys. Rev. B 101 045419
[31] Rau J G, Lee E K H and Kee H Y 2014 Phys. Rev. Lett. 112 077204
[32] Jackeli G and Khaliullin G 2009 Phys. Rev. Lett. 102 017205
[33] Birol T and Haule K 2015 Phys. Rev. Lett. 114 096403
[34] Banerjee A, Bridges C A, Yan J Q, Aczel A A, Li L, Stone M B, Granroth G E, Lumsden M D, Yiu Y, Knolle J, Bhattacharjee S, Kovrizhin D L, Moessner R, Tennant D A, Mandrus D G and Nagler S E 2016 Nat. Mater. 15 733
[35] Wang W, Dong Z Y, Yu S L and Li J X 2017 Phys. Rev. B 96 115103
[36] Laurell P and Okamoto S 2020 npj Quantum Mater. 5 2
[37] Wang J, Normand B and Liu Z X 2019 Phys. Rev. Lett. 123 197201
[38] Liu W, Zhang Z, Ji J, Liu Y, Li J, Wang X, Lei H, Chen G and Zhang Q 2018 Chin. Phys. Lett. 35 117501
[39] Zhang Z, Li J, Liu W, Zhang Z, Ji J, Jin F, Chen R, Wang J, Wang X, Ma J and Zhang Q 2021 Phys. Rev. B 103 184419
[40] Zhang Z, Ma X, Li J, Wang G, Adroja D T, Perring T P, Liu W, Jin F, Ji J, Wang Y, Kamiya Y, Wang X, Ma J and Zhang Q 2021 Phys. Rev. B 103 035144
[41] Song K and Kauzlarich S M 1994 Chem. Mater. 6 386
[42] Li Y, Chen G, Tong W, Pi L, Liu J, Yang Z, Wang X and Zhang Q 2015 Phys. Rev. Lett. 115 167203
[43] Li Y, Liao H, Zhang Z, Li S, Jin F, Ling L, Zhang L, Zou Y, Pi L, Yang Z, Wang J, Wu Z and Zhang Q 2015 Sci. Rep. 5 16419
[44] Li Y, Adroja D, Biswas P K, Baker P J, Zhang Q, Liu J, Tsirlin A A, Gegenwart P and Zhang Q 2016 Phys. Rev. Lett. 117 097201
[45] Shen Y, Li Y D, Wo H, Li Y, Shen S, Pan B, Wang Q, Walker H C, Steffens P, Boehm M, Hao Y, Quintero-Castro D L, Harriger L W, Frontzek M D, Hao L, Meng S, Zhang Q, Chen G and Zhao J 2016 Nature 540 559
[46] Xu Y, Zhang J, Li Y S, Yu Y J, Hong X C, Zhang Q M and Li S Y 2016 Phys. Rev. Lett. 117 267202
[47] Li Y, Adroja D, Bewley R I, Voneshen D, Tsirlin A A, Gegenwart P and Zhang Q 2017 Phys. Rev. Lett. 118 107202
[48] Luo Q, Hu S, Xi B, Zhao J and Wang X 2017 Phys. Rev. B 95 165110
[49] Lu Y M and Ran Y 2011 Phys. Rev. B 84 024420
[50] You Y Z, Kimchi I and Vishwanath A 2012 Phys. Rev. B 86 085145
[51] Luo Z X and Chen G 2020 SciPost Phys. Core 3 4
[52] Ross K A, Savary L, Gaulin B D and Balents L 2011 Phys. Rev. X 1 021002
[53] Rau J G and Gingras M J P 2018 Phys. Rev. B 98 054408
[54] Li Y D, Wang X and Chen G 2016 Phys. Rev. B 94 035107
[55] Luo Q, Zhao J, Kee H Y and Wang X 2020 Preprint 1910.01562
[56] Luo Q, Hu S, Zhao J, Metavitsiadis A, Eggert S andWang X 2018 Phys. Rev. B 97 214433
[57] Winter S M, Li Y, Jeschke H O and Valentí R 2016 Phys. Rev. B 93 214431
[58] Suzuki T and Suga S I 2018 Phys. Rev. B 97 134424
[59] Kanki K, Loison D and Schotte K D 2005 Eur. Phys. J. B 44 309
[60] Gohlke M, Wachtel G, Yamaji Y, Pollmann F and Kim Y B 2018 Phys. Rev. B 97 075126
[61] Janssen L, Andrade E C and Vojta M 2017 Phys. Rev. B 96 064430
[62] Joshi D G 2018 Phys. Rev. B 98 060405
[63] Gotfryd D, Rusnačko J, Wohlfeld K, Jackeli G, Chaloupka J C V and Oleś A M 2017 Phys. Rev. B 95 024426
[64] Liu K, Sadoune N, Rao N, Greitemann J and Pollet L 2021 Phys. Rev. Research 3 023016
[65] Rao N, Liu K, Machaczek M and Pollet L 2021 Preprint 2102.01103
[66] Wang S, Qi Z, Xi B, Wang W, Yu S L and Li J X 2021 Phys. Rev. B 103 054410
[67] Park S, Nagaosa N and Yang B J 2020 Nano Lett. 20 2741
[68] Gao Y H and Chen G 2020 SciPost Phys. Core 2 4
[69] VillalbaME, Gómez Albarracín F A, Rosales H D and Cabra D C 2019 Phys. Rev. B 100 245106
[70] Moriya T 1960 Phys. Rev. 120 91

Effective model for rare-earth Kitaev materials and its classical Monte Carlo simulation

Effective model for rare-earth Kitaev materials and its classical Monte Carlo simulation

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