Bond Directional Anapole Order in a Spin-Orbit Coupled Mott Insulator Sr$_2$(Ir$_{1-x}$Rh$_x$)O$_{4}$

TL;DR

This study uncovers a hidden odd-parity anapole order with broken rotational symmetry in a spin-orbit coupled Mott insulator, Sr$_2$(Ir$_{1-x}$Rh$_x$)O$_{4}$, using high-precision magnetic and elastoresistance measurements.

Contribution

It provides bulk evidence for an odd-parity anapole state with broken rotational symmetry, revealing a new hidden order phase in a spin-orbit coupled Mott insulator.

Findings

Detection of a two-fold in-plane magnetic anisotropy below TΩ.

Absence of divergence in nematic susceptibility at TΩ.

Proposal of an intra-unit cell loop-current pattern along one diagonal direction.

Abstract

An anapole state that breaks inversion and time reversal symmetries with preserving translation symmetry of 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 \SIR, the emergence of a possible hidden order phase with broken inversion symmetry has been suggested at $T_{\Omega}$ above the N\'{e}el temperature by optical second harmonic generation measurements. Moreover, polarized neutron diffraction measurements revealed the broken time reversal symmetry below $T_{\Omega}$, 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 two-fold in-plane magnetic anisotropy along the [110] Ir-O-Ir bond direction sets in below $\sim T_{\Omega}$, 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 $T_{\Omega}$. 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 polar toroidal moment is induced by two current loops in each 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 IrO$_4$ square.