Magnetic excitations of diagonally coupled checkerboards

doi:10.1088/1674-1056/ac1b94

中国物理B ›› 2021, Vol. 30 ›› Issue (10): 107505-107505.doi: 10.1088/1674-1056/ac1b94

Magnetic excitations of diagonally coupled checkerboards

Tingting Yan(颜婷婷)¹, Shangjian Jin(金尚健)¹, Zijian Xiong(熊梓健)^1,3, Jun Li(李军)^1,2,†, and Dao-Xin Yao(姚道新)^1,‡

1 State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics, Sun Yat-Sen University, Guangzhou 510275, China;
2 Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, China;
3 Department of Physics, Chongqing University, Chongqing 401331, China

收稿日期:2021-07-12 修回日期:2021-07-30 接受日期:2021-08-07 出版日期:2021-09-17 发布日期:2021-09-30
通讯作者: Jun Li, Dao-Xin Yao E-mail:ljcj007@ysu.edu.cn;yaodaox@mail.sysu.edu.cn
基金资助:
Project supported by the National Key R&D Program of China (Grant Nos. 2018YFA0306001 and 2017YFA0206203), the National Natural Science Foundation of China (Grant No. 11974432), GBABRF-2019A1515011337, and Leading Talent Program of Guangdong Special Projects.

Magnetic excitations of diagonally coupled checkerboards

Tingting Yan(颜婷婷)¹, Shangjian Jin(金尚健)¹, Zijian Xiong(熊梓健)^1,3, Jun Li(李军)^1,2,†, and Dao-Xin Yao(姚道新)^1,‡

1 State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics, Sun Yat-Sen University, Guangzhou 510275, China;
2 Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, China;
3 Department of Physics, Chongqing University, Chongqing 401331, China

Received:2021-07-12 Revised:2021-07-30 Accepted:2021-08-07 Online:2021-09-17 Published:2021-09-30
Contact: Jun Li, Dao-Xin Yao E-mail:ljcj007@ysu.edu.cn;yaodaox@mail.sysu.edu.cn
Supported by:
Project supported by the National Key R&D Program of China (Grant Nos. 2018YFA0306001 and 2017YFA0206203), the National Natural Science Foundation of China (Grant No. 11974432), GBABRF-2019A1515011337, and Leading Talent Program of Guangdong Special Projects.

摘要/Abstract

摘要： By using quantum Monte Carlo based stochastic analytic continuation (QMC-SAC) and spin wave theory, we study magnetic excitations of Heisenberg models with diagonally coupled checkerboard structures. We consider three kinds of checkerboard models (DC 2×2, DC 3×3, and CDC 3×3) consisting nearest-neighbor strong J₁ and weak J₂ antiferromagnetic interactions. When the coupling ratio g=J₂/J₁ approaches 1, all three diagonal checkerboards have the same long-range antiferromagnetic Néel order at T=0. When g decreases, the quantum fluctuation can drive DC 2×2 model to quantum paramagnetic state, while DC 3×3 and CDC 3×3 models still have the long-range Néel order. By calculating the magnetic excitations at different coupling ratios, we find that the low-energy part of magnetic excitations calculated by QMC-SAC can be well explained by the spin wave theory. However, the high-energy parts even deep in the long-range antiferromagnetic phase are beyond the spin wave description. Compared to the g=1 uniform square lattice, the high-energy excitations are more rich in our models. Our study may also draw the attention to the high-energy exctitaions beyond the spin wave theory.

关键词: magnetic excitation, Heisenberg model, quantum Monte Carlo, spin wave

Abstract: By using quantum Monte Carlo based stochastic analytic continuation (QMC-SAC) and spin wave theory, we study magnetic excitations of Heisenberg models with diagonally coupled checkerboard structures. We consider three kinds of checkerboard models (DC 2×2, DC 3×3, and CDC 3×3) consisting nearest-neighbor strong J₁ and weak J₂ antiferromagnetic interactions. When the coupling ratio g=J₂/J₁ approaches 1, all three diagonal checkerboards have the same long-range antiferromagnetic Néel order at T=0. When g decreases, the quantum fluctuation can drive DC 2×2 model to quantum paramagnetic state, while DC 3×3 and CDC 3×3 models still have the long-range Néel order. By calculating the magnetic excitations at different coupling ratios, we find that the low-energy part of magnetic excitations calculated by QMC-SAC can be well explained by the spin wave theory. However, the high-energy parts even deep in the long-range antiferromagnetic phase are beyond the spin wave description. Compared to the g=1 uniform square lattice, the high-energy excitations are more rich in our models. Our study may also draw the attention to the high-energy exctitaions beyond the spin wave theory.

Key words: magnetic excitation, Heisenberg model, quantum Monte Carlo, spin wave

中图分类号: (Spin waves)

75.30.Ds

75.40.Gb (Dynamic properties?) 76.50.+g (Ferromagnetic, antiferromagnetic, and ferrimagnetic resonances; spin-wave resonance) 02.70.Uu (Applications of Monte Carlo methods)

Tingting Yan(颜婷婷), Shangjian Jin(金尚健), Zijian Xiong(熊梓健), Jun Li(李军), and Dao-Xin Yao(姚道新). Magnetic excitations of diagonally coupled checkerboards[J]. 中国物理B, 2021, 30(10): 107505-107505.

Tingting Yan(颜婷婷), Shangjian Jin(金尚健), Zijian Xiong(熊梓健), Jun Li(李军), and Dao-Xin Yao(姚道新). Magnetic excitations of diagonally coupled checkerboards[J]. Chin. Phys. B, 2021, 30(10): 107505-107505.

参考文献

[1] Manousakis E 1991 Rev. Mod. Phys. 63 1
[2] Barzykin V and Pines D 1995 Phys. Rev. B 52 13585
[3] Andersen B M and Hedegård P 2005 Phys. Rev. Lett. 95 037002
[4] Andersen B M, Hirschfeld P J, Kampf A P and Schmid M 2007 Phys. Rev. Lett. 99 147002
[5] Lee-Hone N R, Dodge J S and Broun D M 2017 Phys. Rev. B 96 024501
[6] Huang Q, Qiu Y, Bao W, Green M A, Lynn J W, Gasparovic Y C, Wu T, Wu G and Chen X H 2008 Phys. Rev. Lett. 101 257003
[7] Zhao J, Huang Q, de la Cruz C, Li S, Lynn J W, Chen Y, Green M A, Chen G F, Li G, Li Z, Luo J L, Wang N L and Dai P 2008 Nat. Mater. 7 953
[8] de la Cruz C, Huang Q, Lynn J W, Li J, Ⅱ W R, Zarestky J L, Mook H A, Chen G F, Luo J L, Wang N L and Dai P 2008 Nature 453 899
[9] Lumsden M D and Christianson A D 2010 J. Phys.: Condens. Matter 22 203203
[10] Dai P 2015 Rev. Mod. Phys. 87 855
[11] Wen J, Xu G, Gu G, Tranquada J M and Birgeneau R J 2011 Rep. Prog. Phys. 74 124503
[12] Máca F, Mašek J, Stelmakhovych O, Martí X, Reichlová H, Uhlířová K, Beran P, Wadley P, Novak V and Jungwirth T 2012 J. Magn. Magn. Mater. 324 1606
[13] Hu D, Lu X, Zhang W, Luo H, Li S, Wang P, Chen G, Han F, Banjara S R, Sapkota A, Kreyssig A, Goldman A I, Yamani Z, Niedermayer C, Skoulatos M, Georgii R, Keller T, Wang P, Yu W and Dai P 2015 Phys. Rev. Lett. 114 157002
[14] Baltz V, Manchon A, Tsoi M, Moriyama T, Ono T and Tserkovnyak Y 2018 Rev. Mod. Phys. 90 015005
[15] Manousakis E and Salvador R 1988 Phys. Rev. Lett. 60 840
[16] Singh R R P and Huse D A 1989 Phys. Rev. B 40 7247
[17] Greven M, Birgeneau R J, Endoh Y, Kastner M A, Keimer B, Matsuda M, Shirane G and Thurston T R 1994 Phys. Rev. Lett. 72 1096
[18] Wessel S, Jagannathan A and Haas S 2003 Phys. Rev. Lett. 90 177205
[19] Zhao B, Takahashi J and Sandvik A W 2020 Chin. Phys. B 29 057506
[20] Sun G, Ma N, Zhao B, Sandvik A W and Meng Z Y 2021 Chin. Phys. B 30 067505
[21] Liang S 1990 Phys. Rev. B 42 6555
[22] Read N and Sachdev S 1989 Phys. Rev. Lett. 62 1694
[23] Sandvik A W 2007 Phys. Rev. B 98 227202
[24] Anderson P W 1987 Science 235 1196
[25] Balents L 2010 Nature 464 199
[26] 2004 Phys. Rev. B 69 014424
[27] Campos I, Cotallo-Aban M, Martin-Mayor V, Perez-Gaviro S and Tarancon A 2006 Phys. Rev. Lett. 97 217204
[28] Guo H M 2016 Sci. China-Phys. Mech. Astron. 59 637401
[29] Guo J, Sun J, Zhu X, Li C A, Guo H and Feng S 2021 arXiv: 2010.05402
[30] Peng C, He R Q and Lu Z Y 2020 Phys. Rev. B 102 045110
[31] Coldea R, Hayden S M, Aeppli G, Perring T G, Frost C D, Mason T E, Cheong S W and Fisk Z 2001 Phys. Rev. Lett. 86 5377
[32] Headings N S, Hayden S M, Coldea R and Perring T G 2010 Phys. Rev. Lett. 105 247001
[33] Rønnow H M, McMorrow D F, Coldea R, Harrison A, Youngson I D, Perring T G, Aeppli G, Syljuåsen O, Lefmann K and Rischel C 2001 Phys. Rev. Lett. 87 037202
[34] Christensen N B, Rønnow H M, McMorrow D F, Harrison A, Perring T G, Enderle M, Coldea R, Regnault L P and Aeppli G 2007 Proc. Natl. Acad. Sci. USA 104 15264
[35] Dalla Piazza B, Mourigal M, Christensen N B, Nilsen G J, TregennaPiggott P, Perring T G, Enderle M, McMorrow D F, Ivanov D A and Rønnow H M 2015 Nat. Phys. 11 62
[36] Shao H, Qin Y Q, Capponi S, Chesi S, Meng Z Y and Sandvik A W 2017 Phys. Rev. X 7 041072
[37] Yu S L, Wang W, Dong Z Y, Yao Z J and Li J X 2018 Phys. Rev. B 98 134410
[38] Tennant D A, Broholm C, Reich D H, Nagler S E, Granroth G E, Barnes T, Damle K, Xu G, Chen Y and Sales B C 2003 Phys. Rev. B 67 054414
[39] Notbohm S, Ribeiro P, Lake B, Tennant D A, Schmidt K P, Uhrig G S, Hess C, Klingeler R, Behr G, Büchner B, Reehuis M, Bewley R I, Frost C D, Manuel P and Eccleston R S 2007 Phys. Rev. Lett. 98 027403
[40] Bera A K, Wu J, Yang W, Bewley R, Boehm M, Xu J, Bartkowiak M, Prokhnenko O, Klemke B, Islam A T M N, Law J M, Wang Z and Lake B 2020 Nat. Phys. 16 625
[41] Xu Y, Xiong Z, Wu H Q and Yao D X 2019 Phys. Rev. B 99 085112
[42] Hoffman J E, Hudson E W, Lang K M, Madhavan V, Eisaki H, Uchida S and Davis J C 2002 Science 295 466
[43] Hanaguri T, Lupien C, Kohsaka Y, Lee D H, Azuma M, Takano M, Takagi H and Davis J C 2004 Nature 430 1001
[44] Yao D X and Carlson E W 2008 Phys. Rev. B 77 024503
[45] Ran X X, Ma N and Yao D X 2019 Phys. Rev. B 99 174434
[46] Cheng J Q, Li J, Xiong Z, Wu H Q, Sandvik A W and Yao D X 2020 arxiV: 2011.02448
[47] Song Y, Yuan D, Lu X, Xu Z, Bourret-Courchesne E and Birgeneau R J 2019 Phys. Rev. Lett. 123 247205
[48] Góral K, Santos L and Lewenstein M 2002 Phys. Rev. Lett. 88 170406
[49] Ölschläger M, Wirth G, Kock T and Hemmerich A 2012 Phys. Rev. Lett. 108 075302
[50] Sandvik A W 1997 Phys. Rev. B 56 11678
[51] Wenzel S, Bogacz L and Janke W 2008 Phys. Rev. Lett. 101 127202
[52] Jiang F J 2012 Phys. Rev. B 85 014414
[53] Ma N, Sun G Y, You Y Z, Xu C, Vishwanath A, Sandvik A W and Meng Z Y 2018 Phys. Rev. B 98 174421
[54] Lin H Q 1990 Phys. Rev. B 42 6561
[55] Jeckelmann E 2002 Phys. Rev. B 66 045114
[56] Verstraete F and Cirac J I 2010 Phys. Rev. Lett. 104 190405
[57] Sandvik A W 1998 Phys. Rev. B 57 10287
[58] Syljuåsen O F 2008 Phys. Rev. B 78 174429
[59] Sandvik A W 2016 Phys. Rev. E 94 063308
[60] Shu Y R, Dupont M, Yao D X, Capponi S and Sandvik A W 2018 Phys. Rev. B 97 104424
[61] Sandvik A W 2010 AIP Conf. Proc. 1297 135
[62] des Cloizeaux J and Pearson J J 1962 Phys. Rev. 128 2131
[63] Melcher R L 1973 Phys. Rev. Lett. 30 125
[64] Locher P 1990 Phys. Rev. B 41 2537
[65] Wang L, Beach K S D and Sandvik A W 2006 Phys. Rev. B 73 014431
[66] Syljuåsen O F 2006 Phys. Rev. B 73 245105
[67] Yao D X, Gustafsson J, Carlson E W and Sandvik A W 2010 Phys. Rev. B 82 172409
[68] Fritz L, Doretto R L, Wessel S, Wenzel S, Burdin S and Vojta M 2011 Phys. Rev. B 83 174416
[69] Yasuda S and Todo S 2013 Phys. Rev. E 88 061301
[70] Wallace D J and Zia R K P 1975 Phys. Rev. B 12 5340
[71] Toth S and Lake B 2015 J. Phys.: Condens. Matter 27 166002
[72] Canali C M and Wallin M 1993 Phys. Rev. B 48 3264
[73] Lorenzana J, Seibold G and Coldea R 2005 Phys. Rev. B 72 224511
[74] Igarashi J I and Nagao T 2005 Phys. Rev. B 72014403
[75] Syromyatnikov A V 2010 J. Phys.: Condens. Matter 22 216003

Magnetic excitations of diagonally coupled checkerboards

Magnetic excitations of diagonally coupled checkerboards

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