Harmonic voltage response to AC current in the nonlinear conductivity of iridium oxide Ca5Ir3O12

We have carried out harmonic voltage response experiments by application of AC current along the c-axis of Ca5Ir3O12, which has a nonlinear electrical conductivity in a non-ordered state. This AC current method can allow us to investigate a detail of the nonlinear conductivity by application of small current. We observed the harmonics up to 7th order below 200 K. The results reveal that the nonlinear conductivity exists even in application of current close to zero. In addition, the temperature dependence of the resistance R0 estimated at the zero current limit is expressed by ln R0 ∝T-2/3, which is explained by an adaptation of Efros-Shklovskii variable range hopping or Fogler-Teber-Shklovskii variable range hopping. As a field assisted motion of charge career occurs in hopping conduction, from this analysis result, the nonlinear conductivity comes form the field-assisted hopping conduction

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

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 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

Study of Phonon Dispersion of Iridium Oxide Ca5Ir3O12 with Strong Spin–Orbit Interaction

In this study, we report the results of experiments and calculations of phonon dispersion of iridium oxide with a strong spin–orbit interaction (SOI). Using inelastic X-ray scattering (IXS), we measured the IXS spectra of Ca5Ir3O12 along Γ–A, Γ–M, and Γ–K–M directions in the Brillouin zone of a hexagonal lattice at room temperature. We also show ab initio density-functional phonon dispersions based on local density approximation and generalized gradient approximation (GGA) considering SOI. By comparing the experimental and calculated results, we found that the GGA phonon dispersion with SOI is in very good agreement with the experimental results. The phonon calculation was performed for supercells of 1 × 1 × 3 and preliminary 2 × 2 × 1. We found no phonon instability within these supercells. Low-energy phonon properties such as Debye temperature, specific heat, and sound velocity are also discussed

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

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