We present the application of the $\mathrm{SU}(N)$ spin-wave theory to spin-orbital Mott insulators whose ground states exhibit magnetic orders. When taking both spin and orbital degrees of freedom into account rather than projecting Hilbert space onto the Kramers doublet, which is the lowest spin-orbital locked energy levels, the $\mathrm{SU}(N)$ spin-wave theory should take the place of the $\mathrm{SU}(2)$ one due to the inevitable spin-orbital multipole exchange interactions. To implement the application, we introduce an efficient general local mean-field method, which involves all local fluctuations, and develop the $\mathrm{SU}(N)$ linear spin-wave theory. Our approach is tested firstly by calculating the multipolar spin-wave spectra of the $\mathrm{SU}(4)$ 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-$1/2$ picture when the spin-orbital coupling is not large enough. We further carry out the $\mathrm{SU}(N)$ spin-wave calculations of two materials, $\alpha \text{−}{\mathrm{RuCl}}_3$ and ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$, and find that the magnonic and spin-orbital excitations are consistent with experiments.

• Received 23 November 2017
• Revised 29 April 2018

DOI:https://doi.org/10.1103/PhysRevB.97.205106