Spin-orbit coupling induced magnetic anisotropy and large spin wave gap in NaOsO3

Abstract

The role of spin–orbit coupling and Hund’s rule coupling on magnetic ordering, anisotropy, and excitations are investigated within a minimal three-orbital model for the 5d3 compound NaOsO3. Small asymmetry between the magnetic moments for the xy and xz, yz orbitals, arising from the hopping asymmetry generated by OsO6 octahedral tilting and rotation, together with the weak correlation effect, are shown to be crucial for the large SOC induced magnetic anisotropy and spin wave gap observed in this compound. Due to the intrinsic SOC-induced changes in the electronic densities under rotation of the staggered field, their coupling with the orbital energy offset is also found to contribute significantly to the magnetic anisotropy energy.