First Observation of Superlattice Reflections in the Hidden Order at 105 K of Spin–Orbit Coupled Iridium Oxide Ca₅Ir₃O₁₂

Abstract

We report the inelastic X-ray scattering (IXS) experimental results of iridium oxide Ca5Ir3O12 with a strong spin–orbit interaction, showing the hidden order at 105 K where no superlattice reflections were observed so far. We measured the IXS spectra of Ca5Ir3O12 along Γ–A, Γ–M, Γ–K–M, M–L, and K–H directions in the Brillouin zone of a hexagonal lattice down to 20 K. The obtained phonon spectra show almost no change on cooling; there are no soft phonon modes. However, the superlattice reflections specified by wavevector \(\textbf{q} = (1/3,1/3,1/3)\) are observed below 105 K. For the order parameter in the hidden order, the characteristic on intensity for observed superlattice reflections can lead to the irreducible representation A2 order parameter in the point group 31m. Furthermore, the theoretical study indicates that the hidden order at 105 K comes from an electric toroidal dipole or higher-order multipole ordering.