Effective magnetic interactions in spin-orbit coupled $d^4$ Mott insulators

Abstract

Transition metal compounds with the $(t_{2g}{)}^4$ electronic configuration are expected to be nonmagnetic atomic singlets both in the weakly interacting regime due to spin-orbit coupling, as well as in the Coulomb dominated regime with oppositely aligned $L=1$ and $S=1$ angular momenta. However, starting with the full multi-orbital electronic Hamiltonian, we show the low energy effective magnetic Hamiltonian contains isotropic superexchange spin interactions but anisotropic orbital interactions. By tuning the ratio of superexchange to spin-orbit coupling $J_{\mathrm{SE}}/\lambda$, we obtain a phase transition from nonmagnetic atomic singlets to novel magnetic phases depending on the strength of Hund's coupling, the crystal structure and the number of active orbitals. Spin-orbit coupling plays a non-trivial role in generating a triplon condensate of weakly interacting excitations at antiferromagnetic ordering vector $\vec{k}=\vec{\pi }$, regardless of whether the local spin interactions are ferromagnetic or antiferromagnetic. In the large $J_{\mathrm{SE}}/\lambda$ regime, the localized spin and orbital moments produce anisotropic orbital interactions that are frustrated or constrained even in the absence of geometric frustration. Orbital frustration leads to frustration in the spin channel opening up the possibility of spin-orbital liquids with both spin and orbital entanglement.

11 pages, 9 figures; supplement: 4 pages and 1 figure

References in corpus (6)

• Strong electronic correlations from Hund's coupling
• Fingerprints of spin-orbital entanglement in transition metal oxides
• NaIrO3 - A pentavalent post-perovskite
• Lattice-Tuned Magnetism of Ru4+(4d4) Ions in Single-Crystals of the Layered Honeycomb Ruthenates: Li2RuO3 and Na2RuO3
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Cited by in corpus (6)

• Density matrix renormalization group study of a three-orbital Hubbard model with spin-orbit coupling in one dimension
• Unconventional magnetism in the 4d${}^4$ based ($S=1$) honeycomb system Ag${}_3$LiRu${}_2$O${}_6$
• Structural, thermodynamic, and local probe investigations of a honeycomb material Ag${}_3$LiMn${}_2$O${}_6$
• Correlated electron metal properties of the honeycomb ruthenate Na${}_2$RuO${}_3$
• Novel Block Excitonic Condensate at $n=3.5$ in a Spin-Orbit Coupled $t_{2g}$ Multiorbital Hubbard Model
• Evolution of Spin-Orbital Entanglement with Increasing Ising Spin-Orbit Coupling