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.

Highlights

  • The strongly spin-orbit coupled orthorhomic structured 5d3 osmium compound NaOsO3, with nominally three electrons in the Os t2g sector, exhibits several novel electronic and magnetic properties

  • 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

  • These include a G-type antiferromagnetic (AFM) structure with spins oriented along the c axis,[1] a significantly reduced magnetic moment ∼ 1μB as measured from neutron scattering,[1] a continuous metal-insulator transition (MIT) that coincides with the AFM transition (TN = TMIT = 410 K) as seen in neutron and X-ray scattering,[1] and a large spin wave gap of 58 meV as seen in resonant inelastic X-ray scattering (RIXS) measurements indicating strong magnetic anisotropy.[2]

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Summary

INTRODUCTION

The strongly spin-orbit coupled orthorhomic structured 5d3 osmium compound NaOsO3, with nominally three electrons in the Os t2g sector, exhibits several novel electronic and magnetic properties These include a G-type antiferromagnetic (AFM) structure with spins oriented along the c axis,[1] a significantly reduced magnetic moment ∼ 1μB as measured from neutron scattering,[1] a continuous metal-insulator transition (MIT) that coincides with the AFM transition (TN = TMIT = 410 K) as seen in neutron and X-ray scattering,[1] and a large spin wave gap of 58 meV as seen in resonant inelastic X-ray scattering (RIXS) measurements indicating strong magnetic anisotropy.[2].

THREE ORBITAL MODEL AND MAGNETIC ORDERING
SOC INDUCED MAGNETIC ANISOTROPY
SPIN WAVE EXCITATIONS
EFFECT OF THE ORBITAL ENERGY OFFSET
CONCLUSIONS

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