Collective excitations in Na${}_2$IrO${}_3$

Abstract

We study the collective excitations of Na${}_2$IrO${}_3$ in an itinerant electron approach. We consider a multi-orbital tight-binding model with the electron transfer between the Ir $5d$ states mediated via oxygen $2p$ states and the direct $d$-$d$ transfer on a honeycomb lattice. The one-electron energy as well as the ground state energy are investigated within the Hartree-Fock approximation. When the direct $d$-$d$ transfer is weak, we obtain nearly flat energy bands due to the formation of quasimolecular orbitals, and the ground state exhibits the zigzag spin order. The evaluation of the density-density correlation function within the random phase approximation shows that the collective excitations emerge as bound states. For an appropriate value of the direct $d$-$d$ transfer, some of them are concentrated in the energy region $\omega <$ 50 meV (magnetic excitations) while the others lie in the energy region $\omega >$ 350 meV (excitonic excitations). This behaviour is consistent with the resonant inelastic x-ray scattering spectra. We also show that the larger values of the direct $d$-$d$ transfer are unfavourable in order to explain the observed aspects of Na${}_2$IrO${}_3$ such as the ordering pattern of the ground state and the excitation spectrum. These findings may indicate that the direct $d$-$d$ transfer is suppressed by the structural distortions in the view of excitation spectroscopy, as having been pointed out in the \it{ab initio} calculation.

8 pages, 6 figures, Latex, Figures 5 and 6 have been replaced by those obtained for more appropriate parameter values. The concomitant descriptions have been also modified. To be published in Journal of Physics: Condensed Matter

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Cited by in corpus (4)

• From a quasimolecular band insulator to a relativistic Mott insulator in $t_{2g}^5$ systems with a honeycomb lattice structure
• Three-band Hubbard model for Na${}_2$IrO${}_3$: Topological insulator, zigzag antiferromagnet, and Kitaev-Heisenberg material
• On the multi-$\mathbf{q}$ characteristics of magnetic ground states of honeycomb cobalt oxides
• Non-local features of the spin-orbit exciton in Kitaev materials