Ferro-octupolar order in d^2 double perovskites of Osmium from first principles

Conflicting interpretations of experimental data have challenged the understanding of the quantum magnetic phase of spin-orbit coupled $d^2$ double pervoskites. Whether the ground state is a Janh-Teller-distorted order of electric quadrupoles with antiferromagnetic arrangement of magnetic dipoles or the hitherto elusive magnetic octupolar order remains debated. We resolve this uncertainty through direct calculations of all-rank inter-site exchange interactions and inelastic neutron scattering cross-section including octupolar contributions for the $d^2$ double perovskite series Ba$_2M$OsO$_6$ ($M$= Zn, Mg, Ca) using advanced many-body first principles methods.

We investigate the magnetic properties of such compounds both by means of Density Functional Theory (DFT) + dynamical mean field theory (DMFT) and by purely DFT calculations with a new approach that consists in the constrain of the onsite density matrix, as obtained via DFT + DMFT solution, in order to mimic the octupolar order of magnetic multipoles. We observe a ground state formed by ferro-ordered octupoles coupled within the ground-state E$_g$ doublet and compare this result to conventional type-a antiferrromagnetic phase. Furthemore, we compute the ordering temperature of the single second-order phase-transition and of
the gapped excitation spectra, which are proven to be fully consistent and in agreement with experimental observations. Finally, we studied, within the DFT framework, the possibility of these systems to undergo a cubic-to-tetragonal transition, finding no such evidence.