Cluster Toroidal Multipoles Formed by Electric-Quadrupole and Magnetic-Octupole Trimers: A Possible Scenario for Hidden Orders in Ca$_5$Ir$_3$O$_{12}$

Abstract

Cluster multipole orderings composed of atomic high-rank multipole moments are theoretically investigated with a 5d-electron compound Ca5Ir3O12 in mind. Ca5Ir3O12 exhibits two hidden orders: One is an intermediate-temperature phase with time-reversal symmetry and the other is a low-temperature phase without time-reversal symmetry. By performing the symmetry and augmented multipole analyses for a d-orbital model under the hexagonal point group D 3h , we find that the 120 • -type ordering of the electric quadrupole corresponds to cluster electric toroidal dipole ordering with the electric ferroaxial moment, which can become the microscopic origin of the intermediate-temperature phase in Ca5Ir3O12. Furthermore, based on 193 Ir synchrotron-radiation-based Mössbauer spectroscopy, we propose that the low-temperature phase in Ca5Ir3O12 is regarded as a coexisting state with cluster electric toroidal dipole and cluster magnetic toroidal quadrupole, the latter of which is formed by the 120 • -type ordering of the magnetic octupole and accompanies a small uniform magnetization as a secondary effect. Our results provide a clue to two hidden phases in Ca5Ir3O12.