Intrinsic Spin Nernst Effect and Chiral Edge Modes in van der Waals Ferromagnetic Insulators: Dzyaloshinskii-Moriya vs. Kitaev Interactions

The thermomagnetic Nernst effect and chiral edge states are key signatures of nontrivial topology and emerging Berry curvature in magnonic systems. Implementing atomistic spin simulations, we theoretically demonstrate the emergence of chiral magnon edge states at the boundaries of a ferromagnetic hexagonal lattice in the presence of Dzyaloshinskii-Moriya and Kitaev interactions, which are robust against nonlinear magnon interactions. In our simulations, we consider the spin parameters of CrI${}_3$ as a prototype of van der Waals magnetic layers. We show that the spin accumulation is reduced in the presence of Kitaev spin interactions compared to systems governed by Dzyaloshinskii-Moriya interactions. This reduction stems from the breaking of the $U(1)$ symmetry, which leads to a shorter spin coherence length imposed by the Kitaev interaction. We propose that measuring the angular dependence of the Nernst signal in a magnetic field provides an effective indirect method for identifying the microscopic origin of topological magnons. Our findings hold promising potential for advancing next-generation energy-harvesting Nernst materials and facilitating the integration of topological magnetic materials with spintronic-based quantum technologies.