[论文解读] Evidence for the topological order in a kagome antiferromagnet

Wei Yuan, Zili Feng+20 more|arXiv (Cornell University)|Oct 9, 2017

Advanced Condensed Matter Physics参考文献 50被引用 13

一句话总结

本研究通过非弹性中子散射和比热测量，首次在kagome晶格反铁磁体Cu₃Zn(OH)₆FBr中识别出具有能隙的自旋子和任何任何任何子激发，为Z₂拓扑序提供了强有力的实验证据。第一性原理计算证实了主要的面内自旋耦合，观测到的动量依赖自旋能隙以及磁场不敏感的低温磁熵被解释为Z₂量子自旋液体中分数化任意子激发的特征。

ABSTRACT

A Z2 quantum spin liquid hosts one of the simplest topological orders and exhibits many exotic properties due to long-range quantum entanglements. Its elementary excitations are anyons such as spinons carrying fractionalized spin quantum number and visons carrying emergent Z2 gauge flux. However, experimental detection of these anyons remains elusive. The difficulties lie not only in the fact that there exists few candidates for Z2 quantum spin liquids but also in that visons are magnetically inert hence immune to available experimental techniques. Here we have studied the spin excitations and specific heats of kagome-lattice antiferromagnet Cu$_4$(OH)$_6$FBr and Cu$_3$Zn(OH)$_6$FBr, which consists of two-dimensional Cu$^{2+}$ kagome layers with either Cu$^{2+}$ or Zn$^{2+}$ ions in between. By combining the first principle calculations and inelastic neutron scattering data in the former, we show that the dominate couplings in Cu$_4$(OH)$_6$FBr are between the nearest neighbor spins within the kagome planes, and the kagome and interlayer spin systems are essentially decoupled above the antiferromagnetic transition temperature. The intrinsic spin excitations and specific heats of the kagome layers for Cu$_3$Zn(OH)$_6$FBr are thus derived by removing the contributions from the residual interlayer Cu$^{2+}$ magnetic impurities. Accordingly, the kagome spin system exhibits spin continuum with momentum-dependent spin gap and a large magnetic entropy at low temperature that is insensitive to magnetic field, which can be understood as the evidences of spinons and visons in this kagome quantum spin liquid candidate. Our results suggest the existence of the Z2 anyons in the material, and therefore provide a comprehensive set of evidences for the Z2 topological order in kagome quantum spin liquid and bring their choreographed entanglement dances to the stage of real materials.

研究动机与目标

• 在kagome晶格量子自旋液体中识别Z₂拓扑序的实验特征。
• 区分Cu₃Zn(OH)₆FBr中本征kagome层激发与层间杂质贡献。
• 为受挫量子磁体中分数化自旋子与任何子激发提供一致的实验与理论证据。
• 评估局部扰动（如kagome平面中的Zn掺杂）对拓扑序的鲁棒性影响。
• 探索通过量子临界性在拓扑序与对称性破缺相之间实现调控的潜力。

提出的方法

• 对Cu₄(OH)₆FBr进行第一性原理计算，以确定主导自旋交换耦合并确认面内主导特性。
• 利用多晶Cu₃Zn(OH)₆FBr的非弹性中子散射（INS）探测自旋激发，并提取动量依赖的自旋能隙。
• 测量比热以检测低温磁熵，解释为具有能隙的单重态-单重态任何子激发的证据。
• 系统性地减去残余层间Cu²⁺杂质的贡献，以分离本征kagome层物理。
• 将INS数据与Z₂量子自旋液体的理论预期进行比较，包括自旋子连续谱和任何子能隙特征。
• 分析自旋激发的动量依赖性，以评估在布里渊区边界附近自旋子-任何子束缚态的可能性。

实验结果

研究问题

• RQ1 能否在kagome反铁磁体中实验识别出具有能隙的自旋子与任何子激发？
• RQ2 所观测到的自旋激发与磁熵在多大程度上与Z₂量子自旋液体基态一致？
• RQ3 Zn掺杂等局部扰动对拓扑序的鲁棒性如何？
• RQ4 动量依赖的自旋激发谱中是否存在自旋子-任何子耦合的证据？
• RQ5 该体系是否可能经历从拓扑序到对称性破缺相的量子临界转变？

主要发现

• Cu₃Zn(OH)₆FBr中的自旋激发谱表现出动量依赖的自旋能隙，其中Q = 0处的能隙约为NMR测得的自旋子能隙的两倍，证实连续谱源于自旋子。
• 比热测量显示在低温下存在一个大而与磁场无关的磁熵，与具有能隙的单重态-单重态任何子激发一致。
• 第一性原理计算表明，在Cu₄(OH)₆FBr中，主导自旋耦合位于kagome平面内，且在Néel转变温度以上层间耦合可忽略。
• 在扣除残余层间Cu²⁺杂质贡献后，本征kagome层表现出自旋连续谱与自旋能隙，支持Z₂量子自旋液体基态。
• 观测到的自旋激发动量依赖性与自旋子与任何子之间束缚态的存在一致，特别是在布里渊区边界如Q = (2,0,0)或(1,1,0)附近。
• 该体系对局部扰动表现出显著的鲁棒性，表现为即使在kagome平面中掺杂约5%的Zn后，自旋动力学与比热特征仍保持不变。