SU($N$) spin-wave theory: Application to spin-orbital Mott insulators

TL;DR

This paper develops an SU(N) spin-wave theory for spin-orbital Mott insulators, incorporating both spin and orbital degrees of freedom, and demonstrates its effectiveness through theoretical calculations and first-principles material analysis.

Contribution

It introduces an efficient local mean field approach for SU(N) spin-wave theory applicable to spin-orbital Mott insulators, extending beyond traditional SU(2) models.

Findings

Successfully calculates multipolar spin-wave spectra for SU(4) model

Reveals Hund's coupling impacts isospin-1/2 representation effectiveness

Qualitatively depicts low-energy magnons in $$-RuCl$_3$ and Sr$_2$IrO$_4$

Abstract

We present the application of the SU($N$) ($N>2$) spin-wave theory to spin-orbital Mott insulators whose ground states exhibit magnetic orders. When taking both the spin and orbital degrees of freedom into account rather than projecting onto the Kramers doublet, the lowest spin-orbital locking energy levels, due to the inevitable spin-orbital multipole exchange interactions, the SU($N$) spin-wave theory should take the place of the SU($2$) one. To implement the application, we introduce an efficient general local mean field approach which involves all the local fluctuations into the SU($N$) linear spin-wave theory. Our approach is tested firstly by calculating the multipolar spin-wave spectra of the SU($4$) antiferromagnetic model. Then we apply it to spin-orbital Mott insulators. It is revealed that the Hund's coupling would influence the effectiveness of the isospin-$1/2$ representation when the spin orbital coupling is not large enough. Besides, we also calculate the spin-wave spectra based on the first principle calculations for two concrete materials, $\alpha$-RuCl$_3$ and Sr$_2$IrO$_4$. The SU($N$) spin-wave theory appropriately depicts the low-energy magnons and the spin-orbital excitations qualitatively.