Vector chirality for effective total momentum $J_{\text{eff}}$ in a nonfrustrated Mott insulator: Effects of strong spin-orbit coupling and broken inversion symmetry

Abstract

I propose the emergence of the spin-orbital-coupled vector chirality in a non-frustrated Mott insulator with the strong spin-orbit coupling due to $ab$-plane's inversion-symmetry (IS) breaking. I derive the superexchange interactions for a $t_{2g}$-orbital Hubbard model on a square lattice with the strong spin-orbit coupling and the IS-breaking-induced hopping integrals, and explain the microscopic origins of the Dzyaloshinsky-Moriya (DM) -type and the Kitaev-type interactions. Then, by adopting the mean-field approximation to a minimal model including only the Heisenberg-type and the DM-type nearest-neighbor interactions, I show that the IS breaking causes the spin-orbital-coupled chirality as a result of stabilizing the screw state. I also highlight the limit of the hard-pseudospin approximation in discussing the stability of the screw states in the presence of both the DM-type and the Kitaev-type interactions, and discuss its meaning. I finally discuss the effects of tetragonal crystal field and $J_{\text{eff}}=\frac{3}{2}$ states, and the application to the iridates near the $[001]$ surface of Sr${}_2$IrO${}_4$ and the interface between Sr${}_2$IrO${}_4$ and Sr${}_3$Ir${}_2$O${}_7$.

11 pages, 3 figures; published version

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• Inverse Faraday effect in Mott insulators
• Phase boundaries in alternating field quantum XY model with Dzyaloshinskii-Moriya interaction: Sustainable entanglement in dynamics
• Emergent orbital magnetization in Kitaev quantum magnets
• Polarization-dependent magnetic properties of periodically driven $\alpha$-RuCl${}_3$
• Inplane anisotropy of longitudinal thermal conductivities and weak localization of magnons in a disordered spiral magnet
• Possible superconductivity induced by a large spin-orbit coupling in carrier doped iridium oxide insulators: A weak coupling approach
• Effects of magnon-magnon interactions in a noncollinear magnet induced by combination of a symmetric and an antisymmetric exchange interaction
• Dzyaloshinskii-Moriya Interaction between Multipolar Moments in $5d^1$ Systems