Chin. Phys. Lett.  2022, Vol. 39 Issue (2): 027501    DOI: 10.1088/0256-307X/39/2/027501
Evidence for Magnetic Fractional Excitations in a Kitaev Quantum-Spin-Liquid Candidate $\alpha$-RuCl$_3$
Kejing Ran1,2†, Jinghui Wang1,2†, Song Bao2, Zhengwei Cai2, Yanyan Shangguan2, Zhen Ma2,3, Wei Wang4, Zhao-Yang Dong5, P. Čermák6,7, A. Schneidewind6, Siqin Meng8,9, Zhilun Lu8,10, Shun-Li Yu2,11*, Jian-Xin Li2,11*, and Jinsheng Wen2,11*
1School of Physical Science and Technology, and ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 200031, China
2National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
3Institute for Advanced Materials, Hubei Normal University, Huangshi 435002, China
4School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
5Department of Applied Physics, Nanjing University of Science and Technology, Nanjing 210094, China
6Jülich Centre for Neutron Science (JCNS) at Heinz Maier-Leibnitz Zentrum (MLZ), Forschungszentrum Jülich GmbH, Lichtenbergstr. 1, 85748 Garching, Germany
7Charles University, Faculty of Mathematics and Physics, Department of Condensed Matter Physics, Ke Karlovu 5, 121 16, Praha, Czech Republic
8Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Hahn-Meitner-Platz 1D-14109, Berlin, Germany
9China Institute of Atomic Energy (CIAE), Beijing 102413, China
10The Henry Royce Institute and Department of Materials Science and Engineering, The University of Sheffield, Sir Robert Hadfield Building, Sheffield, S1 3JD, United Kingdom
11Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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Kejing Ran, Jinghui Wang, Song Bao et al  2022 Chin. Phys. Lett. 39 027501
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Abstract It is known that $\alpha$-RuCl$_3$ has been studied extensively because of its proximity to the Kitaev quantum-spin-liquid (QSL) phase and the possibility of approaching it by tuning the competing interactions. Here we present the first polarized inelastic neutron scattering study on $\alpha$-RuCl$_3$ single crystals to explore the scattering continuum around the $\varGamma$ point at the Brillouin zone center, which was hypothesized to be resulting from the Kitaev QSL state but without concrete evidence. With polarization analyses, we find that, while the spin-wave excitations around the $M$ point vanish above the transition temperature $T_{\rm N}$, the pure magnetic continuous excitations around the $\varGamma$ point are robust against temperature. Furthermore, by calculating the dynamical spin-spin correlation function using the cluster perturbation theory, we derive magnetic dispersion spectra based on the $K$–$\varGamma$ model, which involves with a ferromagnetic Kitaev interaction of $-7.2$ meV and an off-diagonal interaction of $5.6$ meV. We find this model can reproduce not only the spin-wave excitation spectra around the $M$ point, but also the non-spin-wave continuous magnetic excitations around the $\varGamma$ point. These results provide evidence for the existence of fractional excitations around the $\varGamma$ point originating from the Kitaev QSL state, and further support the validity of the $K$–$\varGamma$ model as the effective minimal spin model to describe $\alpha$-RuCl$_3$.
Received: 01 December 2021      Express Letter Published: 27 December 2021
PACS:  75.10.Kt (Quantum spin liquids, valence bond phases and related phenomena)  
  61.05.fg (Neutron scattering (including small-angle scattering))  
  75.30.Ds (Spin waves)  
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Kejing Ran
Jinghui Wang
Song Bao
Zhengwei Cai
Yanyan Shangguan
Zhen Ma
Wei Wang
Zhao-Yang Dong
P. Čermák
A. Schneidewind
Siqin Meng
Zhilun Lu
Shun-Li Yu
Jian-Xin Li
and Jinsheng Wen
[1] Anderson P W 1973 Mater. Res. Bull. 8 153
[2] Anderson P W 1987 Science 235 1196
[3] Balents L 2010 Nature 464 199
[4] Zhou Y, Kanoda K, and Ng T K 2017 Rev. Mod. Phys. 89 025003
[5] Savary L and Balents L 2017 Rep. Prog. Phys. 80 016502
[6] Wen J, Yu S L, Li S, Yu W, and Li J X 2019 npj Quantum Mater. 4 12
[7] Broholm C, Cava R J, Kivelson S A, Nocera D G, Norman M R, and Senthil T 2020 Science 367 eaay0668
[8] Kitaev A 2006 Ann. Phys. 321 2
[9] Trebst S 2017 arXiv:1701.07056 [cond-mat.str-el]
[10] Kitaev A Y 2003 Ann. Phys. 303 2
[11] Nayak C, Simon S H, Stern A, Freedman M, and Sarma S D 2008 Rev. Mod. Phys. 80 1083
[12] Barkeshli M, Berg E, and Kivelson S 2014 Science 346 722
[13] Jackeli G and Khaliullin G 2009 Phys. Rev. Lett. 102 017205
[14] Rau J G, Lee E K H, and Kee H Y 2016 Annu. Rev. Condens. Matter Phys. 7 195
[15] Chaloupka J, Jackeli G, and Khaliullin G 2010 Phys. Rev. Lett. 105 027204
[16] Kimchi I and You Y Z 2011 Phys. Rev. B 84 180407
[17] Singh Y, Manni S, Reuther J, Berlijn T, Thomale R, Ku W, Trebst S, and Gegenwart P 2012 Phys. Rev. Lett. 108 127203
[18] Chaloupka J, Jackeli G, and Khaliullin G 2013 Phys. Rev. Lett. 110 097204
[19] Rau J G, Lee E K H, and Kee H Y 2014 Phys. Rev. Lett. 112 077204
[20] Sizyuk Y, Price C, Wölfle P, and Perkins N B 2014 Phys. Rev. B 90 155126
[21] Chun S H, Kim J W, Kim J, Zheng H, Stoumpos C C, Malliakas C D, Mitchell J F, Mehlawat K, Singh Y, Choi Y, Gog T, Al-Zein A, Sala M M, Krisch M, Chaloupka J, Jackeli G, Khaliullin G, and Kim B J 2015 Nat. Phys. 11 462
[22] Winter S M, Tsirlin A A, Daghofer M, van den Brink J, Singh Y, Gegenwart P, and Valentí R 2017 J. Phys.: Condens. Matter 29 493002
[23] Winter S M, Li Y, Jeschke H O, and Valentí R 2016 Phys. Rev. B 93 214431
[24] Mazin I I, Jeschke H O, Foyevtsova K, Valentí R, and Khomskii D I 2012 Phys. Rev. Lett. 109 197201
[25] Foyevtsova K, Jeschke H O, Mazin I I, Khomskii D I, and Valentí R 2013 Phys. Rev. B 88 035107
[26] 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
[27] Sears J A, Songvilay M, Plumb K W, Clancy J P, Qiu Y, Zhao Y, Parshall D, and Kim Y J 2015 Phys. Rev. B 91 144420
[28] 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
[29] 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
[30] Cao H B, Banerjee A, Yan J Q, Bridges C A, Lumsden M D, Mandrus D G, Tennant D A, Chakoumakos B C, and Nagler S E 2016 Phys. Rev. B 93 134423
[31] 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
[32] Kim H S, Vijay S V, Catuneanu A, and Kee H Y 2015 Phys. Rev. B 91 241110
[33] Sandilands L J, Tian Y, Reijnders A A, Kim H S, Plumb K W, Kim Y J, Kee H Y, and Burch K S 2016 Phys. Rev. B 93 075144
[34] Kim H S and Kee H Y 2016 Phys. Rev. B 93 155143
[35] Wang W, Dong Z Y, Yu S L, and Li J X 2017 Phys. Rev. B 96 115103
[36] Janssen L, Andrade E C, and Vojta M 2017 Phys. Rev. B 96 064430
[37] Banerjee A, Yan J, Knolle J, Bridges C A, Stone M B, Lumsden M D, Mandrus D G, Tennant D A, Moessner R, and Nagler S E 2017 Science 356 1055
[38] Gohlke M, Wachtel G, Yamaji Y, Pollmann F, and Kim Y B 2018 Phys. Rev. B 97 075126
[39] Sears J A, Chern L E, Kim S, Bereciartua P J, Francoual S, Kim Y B, and Kim Y J 2020 Nat. Phys. 16 837
[40] Kubota Y, Tanaka H, Ono T, Narumi Y, and Kindo K 2015 Phys. Rev. B 91 094422
[41] Majumder M, Schmidt M, Rosner H, Tsirlin A A, Yasuoka H, and Baenitz M 2015 Phys. Rev. B 91 180401
[42] Sears J A, Zhao Y, Xu Z, Lynn J W, and Kim Y J 2017 Phys. Rev. B 95 180411
[43] Aoyama T, Hasegawa Y, Kimura S, Kimura T, and Ohgushi K 2017 Phys. Rev. B 95 245104
[44] Yu Y J, Xu Y, Ran K J, Ni J M, Huang Y Y, Wang J H, Wen J S, and Li S Y 2018 Phys. Rev. Lett. 120 067202
[45] 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
[46] Balz C, Lampen-Kelley P, Banerjee A, Yan J, Lu Z, Hu X, Yadav S M, Takano Y, Liu Y, Tennant D A, Lumsden M D, Mandrus D, and Nagler S E 2019 Phys. Rev. B 100 060405
[47] Cui Y, Zheng J, Ran K, Wen J, Liu Z X, Liu B, Guo W, and Yu W 2017 Phys. Rev. B 96 205147
[48] Bastien G, Garbarino G, Yadav R, Martinez-Casado F J, Rodríguez R B, Stahl Q, Kusch M, Limandri S P, Ray R, Lampen-Kelley P, Mandrus D G, Nagler S E, Roslova M, Isaeva A, Doert T, Hozoi L, Wolter A U B, Büchner B, Geck J, and van den Brink J 2018 Phys. Rev. B 97 241108
[49] Wang Z, Guo J, Tafti F F, Hegg A, Sen S, Sidorov V A, Wang L, Cai S, Yi W, Zhou Y, Wang H, Zhang S, Yang K, Li A, Li X, Li Y, Liu J, Shi Y, Ku W, Wu Q, Cava R J, and Sun L 2018 Phys. Rev. B 97 245149
[50] 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
[51] 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
[52] Liu Z X and Normand B 2018 Phys. Rev. Lett. 120 187201
[53] Kasahara Y, Ohnishi T, Mizukami Y, Tanaka O, Ma S, Sugii K, Kurita N, Tanaka H, Nasu J, Motome Y, Shibauchi T, and Matsuda Y 2018 Nature 559 227
[54] Winter S M, Riedl K, Maksimov P A, Chernyshev A L, Honecker A, and Valentí R 2017 Nat. Commun. 8 1152
[55] Sandilands L J, Tian Y, Plumb K W, Kim Y J, and Burch K S 2015 Phys. Rev. Lett. 114 147201
[56] Nasu J, Knolle J, Kovrizhin D L, Motome Y, and Moessner R 2016 Nat. Phys. 12 912
[57] Little A, Wu L, Lampen-Kelley P, Banerjee A, Patankar S, Rees D, Bridges C A, Yan J Q, Mandrus D, Nagler S E, and Orenstein J 2017 Phys. Rev. Lett. 119 227201
[58] Wang Z, Reschke S, Hüvonen D, Do S H, Choi K Y, Gensch M, Nagel U, Rõõm T, and Loidl A 2017 Phys. Rev. Lett. 119 227202
[59] Reschke S, Mayr F, Wang Z, Do S H, Choi K Y, and Loidl A 2017 Phys. Rev. B 96 165120
[60] Do S H, Park S Y, Yoshitake J, Nasu J, Motome Y, Kwon Y S, Adroja D T, Voneshen D J, Kim K, Jang T H, Park J H, Choi K Y, and Ji S 2017 Nat. Phys. 13 1079
[61] Nathans R, Shull C G, Shirane G, and Andresen A 1959 J. Phys. Chem. Solids 10 138
[62] Moon R M, Riste T, and Koehler W C 1969 Phys. Rev. 181 920
[63] Schneidewind A and Čermák P 2015 J. Large-Scale Res. Facil. 1 A12
[64] Schaerpf O and Capellmann H 1993 Phys. Status Solidi A 135 359
[65]Shirane G, Shapiro S M, and Tranquada J M 2002 Neutron Scattering with a Triple-Axis Spectrometer: Basic Techniques (Cambridge: Cambridge University Press)
[66] Li H, Qu D W, Zhang H K, Jia Y Z, Gong S S, Qi Y, and Li W 2020 Phys. Rev. Res. 2 043015
[67] Yu S L, Wang W, Dong Z Y, Yao Z J, and Li J X 2018 Phys. Rev. B 98 134410
[68] Schweika W 2010 J. Phys.: Conf. Ser. 211 012026
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