Exchange interactions, Jahn-Teller coupling, and multipole orders in pseudospin one-half $5{\mathbf{d}}^2$ Mott insulators

Abstract

We develop a microscopic theory of multipole interactions and orderings in 5$d^2$ transition metal ion compounds. In a cubic environment, the ground state of 5$d^2$ ions is a non-Kramers $E_g$ doublet, which is nonmagnetic but hosts quadrupole and octupole moments. We derive pseudospin one-half Hamiltonians describing various spin-orbital exchange processes between these ions. Direct overlap of the $t_{2g}$ orbitals results in bond-dependent pseudospin interactions similar to those for $e_g$ orbitals in manganites. The superexchange process via oxygen ions generates new types of pairwise interactions. In perovskites with 180${}^{\circ }$ bonding, we find nearly equal mixture of Heisenberg and $e_g$ orbital compass couplings. The 90${}^{\circ }$ superexchange in compounds with edge-shared octahedra is most unusual: despite highly anisotropic shapes of the $E_g$ wavefunctions, the pseudospin interactions have no bond dependence and show instead a hidden SU(2) symmetry, which equally supports quadrupole and octupole orders. We consider the $E_g$ pseudospin models on various lattices and obtain their ground state properties using analytical, classical Monte Carlo, and exact diagonalization methods. On the honeycomb lattice, we observe a duality with the extended Kitaev model, and uncover a critical point where the quadrupole and octupole states are exactly degenerate. On the triangular lattice, an exotic pseudospin state, corresponding to the coherent superposition of vortex-type quadrupole and ferri-type octupole orders, is realized due to geometrical frustration. We also consider Jahn-Teller coupling effects and lattice mediated interactions between $E_g$ pseudospins. Possible implications of the results for recent experiments on double perovskite osmates are discussed, including effects of local distortions on the pseudospin wavefunctions and interactions.

arXiv comment13 pages, 5 figures

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• Competing multipolar orders in a face-centered cubic lattice: Application to the osmium double perovskites
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• Spin-orbit coupling in a half-filled $t_{2g}$ shell: the case of $5d^3$ K${}_2$ReCl${}_6$
• Multipolar interactions and magnetic excitation gap in d${}^3$ spin-orbit Mott insulators
• Spin-orbit-entangled electronic structure of Ba${}_2$CaOsO${}_6$ studied by O $K$-edge resonant inelastic X-ray scattering
• Dynamic Jahn-Teller Phenomena in Heavy Transition Metal Compounds
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• Spin-orbit coupling induced orbital entanglement in a three-band Hubbard model
• Canted antiferromagnetism in a spin-orbit coupled $S_{\text{eff}}=3/2$ triangular-lattice magnet DyAuGe
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• Dipolar and quadrupolar correlations in the $5d^2$ Re-based double perovskites Ba${}_2$YReO${}_6$ and Ba${}_2$ScReO${}_6$
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• Possibility of ferro-octupolar order in Ba${}_2$CaOsO${}_6$ assessed by X-ray magnetic dichroism measurements
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