Bond Directional Anapole Order in a Spin-Orbit Coupled Mott Insulator Sr2 (Ir1-xRhx) O4

Abstract

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 Sr2(Ir1-xRhx)O4, the emergence of a possible hidden-order phase with broken inversion symmetry has been suggested at Tω above the Néel temperature by optical second-harmonic-generation measurements. Moreover, polarized neutron diffraction measurements revealed broken time-reversal symmetry below Tω, 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 Tω, providing thermodynamic evidence for a nematic phase transition with broken C4 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 Tω. 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 IrO6 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 IrO4 square.