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The Hamiltonian of a two dimensional (2D) magnetic material in the strongcorrelation regime with a spin texture, for which both azimuthal and polarangle changes, is solved using $su(2)$ path integral method. The dependence ofthe Chern number on the atomic spin ($S$), azimuthal angle ($\vec{q}_{1}$) andpolar angle ($\vec{q}_{2}$) modulation vector of the spin texture on abipartite honeycomb lattice is found. For $S \leq 3$ it was found that Chernnumber depends strongly on $\vec{q}_{2}$ and $S$. We discuss applicability ofthe model to several van der Waals magnets. Experimentally, it is expectedthat, with increase in spin modulation vector the sign of the topological Hallconductivity changes, $+\sigma_{xy}^{THE} \to -\sigma_{xy}^{THE}$ orvice-versa, when $S$ is constant. We also propose several heterostrucures forexperimental realization of this effect.

Factors affecting the topological Hall effect in strongly correlated  layered magnets: spin of the magnetic atoms, polar and azimuthal angle  subtended by the spin texture