On the connection between magnetic interactions and the spin-wave gap of the insulating phase of NaOsO$_{3}$

TL;DR

This study derives an effective spin Hamiltonian for NaOsO3 using ab initio calculations and experimental data, revealing the interactions responsible for its magnon spectrum and spin-wave gap, supporting a local-moment magnetic description.

Contribution

The paper provides a microscopic derivation of the spin Hamiltonian for NaOsO3, with refined exchange interactions that accurately reproduce experimental magnon spectra and the spin-wave gap.

Findings

Heisenberg couplings are 45-63% smaller than previous estimates.

Dzyaloshinskii-Moriya interactions are about 15% of the Heisenberg exchange.

The spin-wave gap is explained by interplay of anisotropic interactions.

Abstract

The scenario of a metal-insulator transition driven by the onset of antiferromagnetic order in NaOsO$_3$ calls for a trustworthy derivation of the underlying effective spin Hamiltonian. To determine the latter we rely on {\it ab initio} electronic-structure calculations, linear spin-wave theory, and comparison to experimental data of the corresponding magnon spectrum. We arrive this way to Heisenberg couplings that are $\lesssim$45\% to$\lesssim$63\% smaller than values presently proposed in the literature and Dzyaloshinskii-Moriya interactions in the region of 15\% of the Heisenberg exchange $J$. These couplings together with the symmetric anisotropic exchange interaction and single-ion magnetocrystalline anisotropy successfully reproduce the magnon dispersion obtained by resonant inelastic X-ray scattering measurements. In particular, the spin-wave gap fully agrees with the measured one. We find that the spin-wave gap is defined from a subtle interplay between the single-ion anisotropy, the Dzyaloshinskii-Moriya exchange and the symmetric anisotropic exchange interactions. The results reported here underpin the local-moment description of NaOsO$_3$, when it comes to analyzing the magnetic excitation spectra. Interestingly, this comes about from a microscopic theory that describes the electron system as Bloch states, adjusted to a mean-field solution to Hubbard-like interactions.