Spin-orbit coupling induced magnetic anisotropy and large spin wave gap in $\rm Na Os O_3$

TL;DR

This study investigates how spin-orbit coupling and Hund's rule coupling influence magnetic properties, anisotropy, and excitations in Na Os O_3, revealing the importance of hopping asymmetry and electronic density changes.

Contribution

It introduces a minimal three-orbital model that explains the large magnetic anisotropy and spin wave gap in Na Os O_3 due to SOC and structural asymmetries.

Findings

Hopping asymmetry from octahedral tilting affects magnetic moments.

SOC induces significant magnetic anisotropy and a large spin wave gap.

Electronic density changes under magnetic rotation contribute to anisotropy energy.

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 $5d^3$ compound $\rm Na Os O_3$. Asymmetry between the magnetic moments for the $xy$ and $xz,yz$ orbitals, arising from the hopping asymmetry generated by the $\rm Os O_6$ 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.