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 …