Topological Hall effect in strongly correlated layered magnets: The effect of the spin of the magnetic atoms and of the polar and azimuthal angles subtended by the spin texture

The topological properties are investigated for strongly correlated materials having honeycomb lattice structures and spin texture ${P}{S}=S[sin({{P}{q}}₁{P}{r})cos({{P}{q}}₂{P}{r}),sin({{P}{q}}₁{P}{r})sin({{P}{q}}₂{P}{r}),cos({{P}{q}}₁{P}{r})]$; here, ${{P}{q}}₁$ (polar) and ${{P}{q}}₂$ (azimuthal) are the spin modulating vectors and $S$ is the spin (total angular momentum) of the magnetic atoms. The results can be applied to materials showing the Kondo lattice behavior within the strong Kondo coupling regime. The explicit dependence of the Chern number on Pq₁, Pq₂ for S=1,4pt0ex2,4pt0ex3 and S=1/2,4pt0ex3/2,4pt0ex5/2 (in limiting cases) is derived. We find that for S=1,4pt0ex2,4pt0ex3, the Chern number depends strongly on Pq₂ and S; and for S=1/2,4pt0ex3/2,4pt0ex5/2, the same dependence is expected. The main physical effect of our result is the change in the direction of the topological Hall resistivity (+ρxyTHE→-ρxyTHE or vice versa, THE stands for the topological Hall effect) when $S>2$ as the wave vectors are modulated. We propose heterostructures involving the iron based van der Waals magnet FeN=3,4,5GeTe₂, because in this material both the investigated spin texture and Kondo lattice behavior were observed. Our method can also be applied to materials with higher spin $S>3$ to investigate topological properties.