Multipolar magnetism in d-orbital systems: Crystal field levels, octupolar order, and orbital loop currents

Quantum magnets with spin J=2, which arise in spin-orbit coupled Mott insulators, can potentially display multipolar orders. Motivated by gaining a better microscopic understanding of the local physics of such d-orbital quantum magnets, we carry out an exact diagonalization study of an octahedral crystal field Hamiltonian for two electrons, incorporating spin-orbit coupling and interactions. While the rotationally invariant Kanamori interaction in the t_2g sector leads to a five-fold degenerate J=2 manifold, we propose two mechanisms which cause a degeneracy breaking of the J=2 levels. This can lead to a low-lying non-Kramers doublet carrying quadrupolar and octupolar moments, where spontaneous time-reversal symmetry breaking due to ferro-octupolar ordering within the doublet leads to electronic orbital loop currents. The resulting internal magnetic fields can potentially explain the small fields inferred from muon-spin relaxation (μSR) experiments on cubic 5d² Osmate double perovskites. Our work highlights the intimate connection between the physics of heavy transition metal oxides and that of f-electron based heavy fermion compounds.