Theoretical design of the large topological magnetoelectric effect in the Co-intercalated NbS$_2$ structure

Abstract

A triangular Co-ion lattice intercalated between 1-H NbS$_2$ layers can exhibit a large anomalous Hall effect (AHE) due to the finite scalar spin chirality originating from the non-coplanar $3q$ ordering of Co spins. This large AHE occurs when the scalar spin chirality is uniform in all Co layers, as indeed found in the Co$_{1/3}$NbS$_2$ case [Phys. Rev. Mater. 6, 024201 (2022)]. However, if the spin chirality were staggered with the opposite signs in the adjacent Co layers, the net AHE would disappear, yielding instead the topological magneto-electric effect. Here, we theoretically verify that a transverse electric field generates a finite orbital magnetization under such conditions, consistent with the axion-like coupling. Using first-principles calculations, we show that the resulting magneto-electric coupling, $\alpha^{zz}$ can be as large as 0.9 $e^2/2h$. We also demonstrate that the inter-layer magnetic coupling in these materials can be tuned by strain, enabling the switching between the AHE and the axionic states.