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

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.