Antiferro octupolar order in the 5d$^1$ double perovskite Sr$_2$MgReO$_6$ and its spectroscopic signatures

Abstract: "Hidden"-order phases with high-rank multipolar order parameters have been recently detected in several cubic double perovskites of 5$d$ transition metals. Here, by constructing and solving an ab initio low-energy Hamiltonian, we show that an antiferroic order of magnetic octupoles also forms in the tetragonal 5d$^1$ double perovskite Sr$_2$MgReO$_6$. The low-temperature order in this material is determined by a tetragonal crystal field dominating over exchange interactions. This results in a well isolated crystal-field doublet ground state hosting octupolar low-energy degrees of freedom. Very weak dipole moments entangled with the primary octupole order parameters are induced by admixture of the excited $j1/2$ spin-orbit multiplet. We show that the octupolar order leads to characteristic quasi-gapless magnetic excitation spectra as well as to the intensity of superstructural neutron diffraction reflexes peaking at large scattering momenta.