Dependence of topological phase on nuclear spin $S$ and spin modulation vector in van der Waals Magnets

Kaushal K. Kesharpu

Published 2023-05-22Version 1

Recently non-chiral spin structures on the surface of the van der Waals (vdW) magnets have been observed down to monolayers. We provide a Hamiltonian to analyze the electronic properties of these materials. The Hamiltonian takes into account the arbitrary background spin structures and large atomic spin $S$ of the materials. The large spin-\emph{S} treatment is necessary as magnetic atoms of the vdW magnets can have spin $S > 1/2$. In this work the Hamiltonian is solved for the spin spirals with azimuthal and polar degrees of freedom -- this spin structure was recently observed in Fe$_{3}$GeTe$_{2}$. We methodically analyze the Hamiltonian for both integer and half-integer spins in the honeycomb lattice. It shows emerging topological hall effect emerges irrespective of the spin. The Chern number, hence the topological phase, depends on the spin \emph{S}, and interestingly only on the azimuthal angle of the spin vector. These results will be useful for the design of the topological electronics devices based on vdW magnets.