Octupolar order in d-orbital Mott insulators

Motivated by experimental and theoretical interest in realizing multipolar orders in d-orbital materials, we discuss the quantum magnetism of J = 2 ions which can be realized in spin-orbit coupled oxides with 5d(2) transition metal ions. Based on the crystal-field environment, we argue for a splitting of the J = 2 multiplet, leading to a low-lying non-Kramers doublet which hosts quadrupolar and octupolar moments. We discuss a microscopic mechanism whereby the combined perturbative effects of orbital repulsion and antiferromagnetic Heisenberg spin interactions leads to ferro-octupolar coupling between neighboring sites, and stabilizes ferrooctupolar order for a face-centered cubic lattice. This same mechanism is also shown to disfavor quadrupolar ordering. We show that studying crystal field levels via Raman scattering in a magnetic field provides a probe of octupolar order. We study spin dynamics in the ferro-octupolar state using a slave-boson approach, uncovering a gapped and dispersive magnetic exciton. For sufficiently strong magnetic exchange, the dispersive exciton can condense, leading to conventional type-I antiferromagnetic (AFM) order which can preempt octupolar order. Our proposal for ferrooctupolar order, with specific results in the context of a model Hamiltonian, provides a comprehensive understanding of thermodynamics, mu SR, x-ray diffraction, and inelastic neutron-scattering measurements on a range of cubic 5d(2) double perovskite materials including Ba2ZnOsO6, Ba2CaOsO6, and Ba2MgOsO6. Our proposal for exciton condensation leading to type-I AFM order may be relevant to materials such as Sr2MgOsO6.