Exotic phases induced by strong spin-orbit coupling in ordered double perovskites

Abstract

We construct and analyze a microscopic model for insulating rocksalt ordered double perovskites, with the chemical formula ${A}_{2}B{B}^{\ensuremath{'}}{\text{O}}_{6}$, where the ${B}^{\ensuremath{'}}$ atom has a $4{d}^{1}$ or $5{d}^{1}$ electronic configuration and forms a face-centered-cubic lattice. The combination of the triply degenerate ${t}_{2g}$ orbital and strong spin-orbit coupling forms local quadruplets with an effective spin moment $j=3/2$. Moreover, due to strongly orbital-dependent exchange, the effective spins have substantial biquadratic and bicubic interactions (fourth and sixth order in the spins, respectively). This leads, at the mean-field level, to three main phases: an unusual antiferromagnet with dominant octupolar order, a ferromagnetic phase with magnetization along the [110] direction, and a nonmagnetic but quadrupolar ordered phase, which is stabilized by thermal fluctuations and intermediate temperatures. All these phases have a two-sublattice structure described by the ordering wave vector $\mathbit{Q}=2\ensuremath{\pi}(001)$. We consider quantum fluctuations and argue that in the regime of dominant antiferromagnetic exchange, a nonmagnetic valence-bond solid or quantum-spin-liquid state may be favored instead. Candidate quantum-spin-liquid states and their basic properties are described. We also address the effect of single-site anisotropy driven by lattice distortions. Existing and possible future experiments are discussed in light of these results.