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

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.

15 pages, 6 figures

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Cited by in corpus (16)

• Spin-orbit-entangled electronic phases in 4$d$ and 5$d$ transition-metal compounds
• Exchange interactions, Jahn-Teller coupling, and multipole orders in pseudospin one-half $5{\mathbf{d}}^2$ Mott insulators
• Nonmagnetic $J=0$ State and Spin-Orbit Excitations in K${}_2$RuCl${}_6$
• Vibronic excitations in resonant inelastic x-ray scattering spectra of K${}_2$RuCl${}_6$
• Competing spin-orbital singlet states in the 4$d^4$ honeycomb ruthenate Ag${}_3$LiRu${}_2$O${}_6$
• Correlated electron metal properties of the honeycomb ruthenate Na${}_2$RuO${}_3$
• MoP${}_3$SiO${}_{11}$: a $4d^3$ honeycomb antiferromagnet with disconnected octahedra
• Magnetic phases for two $t_{2g}$ holes with spin-orbit coupling and crystal field
• Two-triplon excitations of the Kitaev-Heisenberg-Bilayer
• Emergent transverse-field Ising model in ${\mathbf{d}}^4$ spin-orbit Mott insulators
• Evolution of Spin-Orbital Entanglement with Increasing Ising Spin-Orbit Coupling
• Fluctuation-induced first order phase transitions in Kitaev-like $d^4$ honeycomb magnet
• (H,Li)${}_6$Ru${}_2$O${}_6$ : a possible zero-field Ru${}^{3+}$-based Kitaev Quantum Spin Liquid
• Superconductivity in the spin-state crossover materials: Nickelates with planar-coordinated low-spin Ni${}^{2+}$ ions
• Geometrical frustration and incommensurate magnetic order in Na${}_3$RuO${}_4$ with two triangular motifs
• Formation of orbital molecules on a pyrochlore lattice induced by A-O bond covalency