A Realization of the Haldane-Kane-Mele Model in a System of Localized Spins

TL;DR

This paper demonstrates that magnon excitations in a spin-orbit-coupled honeycomb ferromagnet exhibit topological properties analogous to the Haldane and Kane-Mele models, suggesting potential for observing edge states and spin Nernst effects.

Contribution

It introduces a spin Hamiltonian on the honeycomb lattice whose magnon and spinon bands are topologically nontrivial, linking magnetic excitations to well-known topological electronic models.

Findings

Magnon bands are topologically nontrivial with edge states.

Spinon bands exhibit topological properties leading to spin Nernst effect.

Proposes an experimental setup to realize the model.

Abstract

We theoretically study a spin Hamiltonian for spin-orbit-coupled ferromagnets on the honeycomb lattice. We find that the effective Hamiltonian for magnons, a quanta of spin-wave excitations from ordered states, is equivalent to the Haldane model for electrons in the honeycomb lattice, which indicates the nontrivial topology of the magnon bands and the existence of the associated edge state. We also take the Schwinger boson (or bosonic spinon) representations of spins that are applicable both to ordered and disordered phases. We show that the spinon bands within the mean-field treatment are topologically nontrivial, which causes a spin Nernst effect, by adopting the properties of the Kane-Mele model. A feasible experimental realization of the spin Hamiltonian is proposed.