Chin. Phys. Lett.  2021, Vol. 38 Issue (9): 097501    DOI: 10.1088/0256-307X/38/9/097501
Nonlocal Effects of Low-Energy Excitations in Quantum-Spin-Liquid Candidate Cu$_3$Zn(OH)$_6$FBr
Yuan Wei1,2, Xiaoyan Ma1,2, Zili Feng1,3, Yongchao Zhang1,2, Lu Zhang1,2, Huaixin Yang1,2,4, Yang Qi5, Zi Yang Meng1,6, Yan-Cheng Wang7*, Youguo Shi1,8*, and Shiliang Li1,2,8*
1Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
2School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
3Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
4Yangtze River Delta Physics Research Center Co., Ltd., Liyang 213300, China
5State Key Laboratory of Surface Physics, Department of Physics, Fudan University, Shanghai 200433, China
6Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
7School of Materials Science and Physics, China University of Mining and Technology, Xuzhou 221116, China
8Songshan Lake Materials Laboratory, Dongguan 523808, China
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Yuan Wei, Xiaoyan Ma, Zili Feng et al  2021 Chin. Phys. Lett. 38 097501
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Abstract We systematically study the low-temperature specific heats for the two-dimensional kagome antiferromagnet, Cu$_{3}$Zn(OH)$_6$FBr. The specific heat exhibits a $T^{1.7}$ dependence at low temperatures and a shoulder-like feature above it. We construct a microscopic lattice model of $Z_2$ quantum spin liquid and perform large-scale quantum Monte Carlo simulations to show that the above behaviors come from the contributions from gapped anyons and magnetic impurities. Surprisingly, we find the entropy associated with the shoulder decreases quickly with grain size $d$, although the system is paramagnetic to the lowest temperature. While this can be simply explained by a core-shell picture in that the contribution from the interior state disappears near the surface, the 5.9-nm shell width precludes any trivial explanations. Such a large length scale signifies the coherence length of the nonlocality of the quantum entangled excitations in quantum spin liquid candidate, similar to Pippard's coherence length in superconductors. Our approach therefore offers a new experimental probe of the intangible quantum state of matter with topological order.
Received: 12 July 2021      Express Letter Published: 10 August 2021
PACS:  75.10.Kt (Quantum spin liquids, valence bond phases and related phenomena)  
  75.10.Jm (Quantized spin models, including quantum spin frustration)  
  75.40.-s (Critical-point effects, specific heats, short-range order)  
Fund: Supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0302900, 2016YFA0300500, and 2020YFA0406003), the National Natural Science Foundation of China (Grant Nos. 11874401, 11674406, 11961160699, 11774399, and 11804383), the Strategic Priority Research Program(B) of the Chinese Academy of Sciences (Grant Nos. XDB33000000, XDB28000000, XDB25000000, and XDB07020000), the K. C. Wong Education Foundation (Grant Nos. GJTD-2020-01 and GJTD-2018-01), and the Beijing Natural Science Foundation (Grant No. Z180008).
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Yuan Wei
Xiaoyan Ma
Zili Feng
Yongchao Zhang
Lu Zhang
Huaixin Yang
Yang Qi
Zi Yang Meng
Yan-Cheng Wang
Youguo Shi
and Shiliang Li
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