Lone octupole and bulk magnetism in osmate 5d2 double perovskites

Exchange interactions, Jahn-Teller coupling, and multipole orders in pseudospin one-half $5\boldsymbol{d}^\mathbf{2}$ Mott insulators

We develop a microscopic theory of multipole interactions and orderings in 5$d^2$ transition metal ion compounds. In a cubic environment, the ground state of 5$d^2$ ions is a non-Kramers $E_g$ doublet, which is nonmagnetic but hosts quadrupole and octupole moments. We derive pseudospin one-half Hamiltonians describing various spin-orbital exchange processes between these ions. Direct overlap of the $t_{2g}$ orbitals results in bond-dependent pseudospin interactions similar to those for $e_g$ orbitals in manganites. The superexchange process via oxygen ions generates new types of pairwise inter…