Highly frustrated magnetism in relativistic $\boldsymbol{d}^\mathbf{4}$ Mott insulators: Bosonic analog of Kitaev honeycomb model

TL;DR

This paper explores a bosonic analog of the Kitaev honeycomb model in spin-orbit coupled Mott insulators with a $t_{2g}^4$ configuration, revealing highly frustrated magnetic states with short-range correlations and no magnetic order.

Contribution

It introduces a flavor- and bond-selective triplon interaction model that parallels the Kitaev model, highlighting unique bosonic properties and their implications for frustrated magnetism.

Findings

Analogies with the Kitaev spin model including conserved quantities and short-range correlations.

Absence of gapless excitations within the spin gap due to bosonic triplons.

Ground state as a strongly correlated paramagnet with dense triplon pairs.

Abstract

We study the orbitally frustrated singlet-triplet models that emerge in the context of spin-orbit coupled Mott insulators with $t_{2g}^4$ electronic configuration. In these compounds, low-energy magnetic degrees of freedom can be cast in terms of three-flavor "triplon" operators describing the transitions between spin-orbit entangled $J=0$ ionic ground state and excited $J=1$ levels. In contrast to a conventional, flavor-isotropic O(3) singlet-triplet models, spin-orbit entangled triplon interactions are flavor-and-bond selective and thus highly frustrated. In a honeycomb lattice, we find close analogies with the Kitaev spin model -- an infinite number of conserved quantities, no magnetic condensation, and spin correlations being strictly short-ranged. However, due to the bosonic nature of triplons, there are no emergent gapless excitations within the spin gap, and ground state is a strongly correlated paramagnet of dense triplon pairs with no long-range entanglement. Using exact diagonalization, we study the bosonic Kitaev model and its various extensions, which break exact symmetries of the model and allow magnetic condensation of triplons. Possible implications for magnetism of ruthenium oxides are discussed.