An anapole state that breaks inversion and time-reversal symmetries while preserving translation symmetry of an underlying lattice has aroused great interest as a new quantum state, but only a few candidate materials have been reported. Recently, in a spin-orbit coupled Mott insulator ${\mathrm{Sr}}_2({\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x){\mathrm{O}}_4$, the emergence of a possible hidden-order phase with broken inversion symmetry has been suggested at $T_{\mathrm{\Omega }}$ above the Néel temperature by optical second-harmonic-generation measurements. Moreover, polarized neutron diffraction measurements revealed broken time-reversal symmetry below $T_{\mathrm{\Omega }}$, which was supported by subsequent muon spin relaxation experiments. However, the nature of this mysterious phase remains largely elusive. Here, we investigate the hidden-order phase through the combined measurements of the in-plane magnetic anisotropy with exceptionally high-precision magnetic torque and the nematic susceptibility with elastoresistance. A distinct twofold in-plane magnetic anisotropy along the [110] Ir-O-Ir bond direction sets in below about $T_{\mathrm{\Omega }}$, providing thermodynamic evidence for a nematic phase transition with broken $C_4$ rotational symmetry. However, in contrast to the even-parity nematic transition reported in other correlated electron systems, the nematic susceptibility exhibits no divergent behavior towards $T_{\mathrm{\Omega }}$. These results provide bulk evidence for an odd-parity order parameter with broken rotational symmetry in the hidden-order state. We discuss the hidden order in terms of an anapole state, in which the polar toroidal moment is induced by two current loops in each ${\mathrm{IrO}}_6$ octahedron of opposite chirality. Contrary to the simplest loop-current pattern previously suggested, the present results are consistent with a pattern in which the intra-unit cell loop current flows along only one of the diagonal directions in the ${\mathrm{IrO}}_4$ square.

中文翻译：

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自旋轨道耦合Mott绝缘子Sr2（Ir1-xRhx）O4的键方向性偶极子阶

作为一种新的量子态，打破了反演和时间反转对称性同时保留了下层晶格的平移对称性的偶极子态引起了人们极大的兴趣，但仅报道了少数几种候选材料。最近，在自旋轨道耦合的莫特绝缘子中$r_2（{铱}_{\mathrm{1个}-X}{铑}_X）{\mathrm{Ø}}_4$，已经有人提出可能存在具有颠倒反对称性的隐藏阶相位 ${Ť}_{\mathrm{\Omega }}$通过光学二次谐波测量可以使温度高于Néel温度。此外，极化中子衍射测量结果显示破损的时间反转对称性在下面${Ť}_{\mathrm{\Omega }}$，随后的muon自旋弛豫实验对此提供了支持。但是，这个神秘阶段的本质仍然难以捉摸。在这里，我们通过面内磁各向异性与异常高精度磁矩和向列磁化率的弹性结合测量，来研究隐阶相。沿[110] Ir-O-Ir键方向的独特的双重平面内磁各向异性在下面大约设置${Ť}_{\mathrm{\Omega }}$，为断裂向列相转变提供热力学证据 $C_4$旋转对称。但是，与其他相关电子系统中报道的偶数奇偶性向列相变相反，向列相的磁化率对${Ť}_{\mathrm{\Omega }}$。这些结果为隐藏顺序状态下具有旋转对称性破坏的奇偶校验顺序参数提供了大量证据。我们以偶极状态讨论了隐藏顺序，在该状态中，极环面磁矩由两个电流环感应而来${\mathrm{氧化铁}}_6$相反的八面体。与先前提出的最简单的回路电流模式相反，本结果与以下模式一致：在这种模式中，单元内单元回路电流仅沿对角线方向中的一个方向流动。${\mathrm{氧化铁}}_4$ 广场。