Material realization of the non-Abelian Kitaev spin liquid phase—an example of Ising topological order (ITO)—has been the subject of intense research in recent years. The $4d$ honeycomb Mott insulator $\alpha \text{−}{\mathrm{RuCl}}_3$ has emerged as a leading candidate, as it enters a field-induced magnetically disordered state where a half-integer quantized thermal Hall conductivity ${\kappa }_{xy}$ was reported. Further, a recent report of a sign change in the quantized ${\kappa }_{xy}$ across a certain crystallographic direction is strong evidence for a topological phase transition between two ITOs with opposite Chern numbers. Although this is a fascinating result, independent verification remains elusive, and one may ask if there is a thermodynamic quantity sensitive to the phase transition. Here we propose that the magnetotropic coefficient $k$ would serve such a purpose. We report a singular feature in $k$ that indicates a topological phase transition across the $\widehat{\mathit{b}}$-axis where ITO is prohibited by a $C_2$ symmetry. If the transition in $\alpha \text{−}{\mathrm{RuCl}}_3$ is indeed a direct transition between ITOs, or is a more broad realization of a topological phase transition, then this feature in $k$ should be observable. Implications of $C_2$ symmetry on other experimental quantities are also discussed.

中文翻译：

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在平面磁场下测试Kitaev材料中的拓扑相变：在α-RuCl3中的应用

近年来，非阿贝尔Kitaev自旋液相的材料实现（伊辛拓扑顺序（ITO）的一个例子）一直是研究的主题。这$4d$ 蜂窝莫特绝缘子 $\alpha \text{-}{\mathrm{氯化钌}}_3$ 进入场致磁无序状态，其中半整数量化的热霍尔电导率已成为领先的候选者 ${\kappa }_{Xÿ}$已经报道。此外，最近的报告显示，量化后的符号变化${\kappa }_{Xÿ}$沿一定的晶体学方向的有力证据表明，两个Chern数相反的ITO之间存在拓扑相变。尽管这是一个令人着迷的结果，但是独立的验证仍然遥不可及，并且可能会问是否存在对相变敏感的热力学量。在这里，我们建议磁致系数$ķ$会达到这样的目的。我们在中报告了一个单一功能$ķ$ 表示整个网络的拓扑相变 $\widehat{\mathit{b}}$禁止使用ITO的轴 $C_2$对称。如果过渡在$\alpha \text{-}{\mathrm{氯化钌}}_3$ 确实是ITO之间的直接过渡，或者是拓扑相变的更广泛的实现，那么此功能 $ķ$应该是可观察的。的含义$C_2$ 还讨论了其他实验量的对称性。