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

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.

9 pages, 5 figures

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• Order-by-Disorder from Bond-Dependent Exchange and Intensity Signature of Nodal Quasiparticles in a Honeycomb Cobaltate
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• Metastable antiphase boundary ordering in CaFe${}_2$O${}_4$
• Magnon Condensation in Dimerized Antiferromagnets with Spin-Orbit Coupling
• Excitonic transverse and amplitude fluctuations in the noncollinear and charge-ordered RbFe${}^{2+}$Fe${}^{3+}$F${}_6$
• Dynamics of a single hole in the Heisenberg-Kitaev model: a self-consistent Born approximation study
• Anisotropic excitonic magnetism from discrete ${\mathrm{C}}_4$ symmetry in CeRhIn${}_5$
• Spectrum of the hole excitation in spin-orbit Mott insulator Na${}_2$IrO${}_3$
• Defect-induced edge ferromagnetism and fractional spin excitations of the SU(4) $\pi$-flux Hubbard model on honeycomb lattice
• Ligand-SOC enhanced $4f^5$ Kitaev antiferromagnet: Application to ${\mathrm{SmI}}_3$