| Summary: | 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 Sr_{2}(Ir_{1-x}Rh_{x})O_{4}, the emergence of a possible hidden-order phase with broken inversion symmetry has been suggested at T_{Ω} above the Néel temperature by optical second-harmonic-generation measurements. Moreover, polarized neutron diffraction measurements revealed broken time-reversal symmetry below T_{Ω}, 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_{Ω}, 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_{Ω}. 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 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.
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