Cluster Toroidal Multipoles Formed by Electric-Quadrupole and Magnetic-Octupole Trimers: A Possible Scenario for Hidden Orders in Ca<sub>5</sub>Ir<sub>3</sub>O<sub>12</sub>

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  • Cluster Toroidal Multipoles Formed by Electric-Quadrupole and Magnetic- Octupole Trimers : A Possible Scenario for Hidden Orders in Ca5Ir3O12

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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 D3h, we find that the 120 degrees-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 193Ir synchrotron-radiation-based Mossbauer 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 degrees-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.

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