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 a simple octahedral crystal field Hamiltonian for two electrons, incorporating spin-orbit coupling (SOC) and interactions. While the rotationally invariant Kanamori interaction in the t2g sector leads to a fivefold degenerate J=2 manifold, we find that either explicitly including the eg orbitals, or going beyond the rotationally invariant Coulomb interaction within the t2g sector, causes a degeneracy breaking of the J=2 levels. This can lead to a low-lying non-Kramers doublet carrying quadrupolar and octupolar moments and an excited triplet which supports magnetic dipole moments, bolstering our previous phenomenological proposal for the stabilization of ferro-octupolar order in heavy transition metal oxides. We show that the spontaneous time-reversal symmetry breaking due to ferro-octupolar ordering within the non-Kramers 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 Ba2ZnOsO6, Ba2CaOsO6, and Ba2MgOsO6, which were previously attributed to weak dipolar magnetism. We make further predictions for oxygen NMR experiments on these materials. We also study the reversed level scheme, where the J=2 multiplet splits into a low-lying magnetic triplet and excited non-Kramers doublet, presenting single-ion results for the magnetic susceptibility in this case, and pointing out its possible relevance for the rhenate Ba2YReO6. Our work highlights the intimate connection between the physics of heavy transition metal oxides and that of f-electron based heavy fermion compounds.