Spin dynamics simulations of topological magnon insulators: From transverse current correlation functions to the family of magnon Hall effects

Abstract

We demonstrate theoretically that atomistic spin dynamics simulations of topological magnon insulators (TMIs) provide access to the magnon-mediated transport of both spin and heat. The TMIs, modeled by kagome ferromagnets with Dzyaloshinskii-Moriya interaction, exhibit nonzero transverse-current correlation functions from which conductivities are derived for the entire family of magnon Hall effects. Both longitudinal and transverse conductivities are studied in dependence on temperature and on an external magnetic field. A comparison between theoretical and experimental results for Cu(1,3-benzenedicarboxylate), a recently discovered TMI, is drawn.

Thermal Hall effect in square-lattice spin liquids: A Schwinger boson mean-field study

“…In previous literature, the thermal Hall effect has been widely investigated on the kagomé [15][16][17][18], pyrochlore [19], and honeycomb [20][21][22][23][24] lattices for insulating phases with and without long-range magnetic order and in the presence of additional electric field gradients [25]. However, it is strongly constrained by no-go theorems on the square lattice owing to the geometry thereof; the fluctuation of the scalar spin chirality averaged over nearby elementary plaquettes in the square lattice vanishes for a generic phase [26,27].…”

Topological Magnons and Edge States in Antiferromagnetic Skyrmion Crystals

“…This relevant distinction makes this AFM-SkX potentially more interesting for applications as small energies would be needed to excite magnonic edge states. More importantly, the higher the energy the more significant the magnon-magnon interactions become, resulting in linewidth broadening of high-energy magnon bands as confirmed by numerical calculations [38]. Therefore, the fact that the edge states emerge at low energies puts on a firmer footing the use of the noninteracting magnon approximation.…”

“…1. An important advantage of AFM-SkX's over previously considered antiferromagnets [36,37] is the possibility to obtain topologically-protected magnonic edge states at sufficiently low energies (where level broadening due to magnon-magnon interactions is minimal [38]). This results from the larger number of spins in the magnetic unit cell, thus accommodating more magnon bands at lower energies.…”

Thermal Hall Effect of Chiral Spin Fluctuations

“…[14] and evaluate the thermal Hall conductivity using classical Monte Carlo and stochastic spin dynamics simulations. Notably, our cal-culations feature the contribution due to the energy magnetization [15], which has not been included in previous numerical studies [16]. We show that this contribution is crucial to obtaining the correct behavior of the thermal Hall conductivity in the low-T and high field limits.…”