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

摘要

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