Mechanism of ferro-octupolar interaction in Osmium double-perovskites

In 5d² Mott insulators with strong spin-orbit coupling, the lowest pseudospin states form a non-Kramers doublet which carries quadrupolar and octupolar moments. A family of double-perovskites, where the magnetic ions form a face-centered cubic (FCC) lattice, was suggested to unveil an octupolar order offering a rare example in d-orbital systems. The proposed order requires a ferromagnetic (FM) octupolar interaction, since the antiferromagnetic (AFM) Ising model is highly frustrated on the FCC lattice. Here we study a microscopic mechanism to generate a FM octupolar interaction. We find that the interference of two intra-orbital exchanges generates a FM octupolar interaction and higher order exchange processes connecting the non-Kramers doublet to an excited triplet further enhances the FM octupolar interaction. Applying the strong-coupling expansion results together with tight binding parameters obtained by density functional theory, we present the exchange interactions for several Osmium double-perovskites and discuss implications of our theory to experimental results.