A triangular Co-ion lattice intercalated between 1-H ${\mathrm{NbS}}_2$ layers can exhibit a large anomalous Hall effect (AHE) due to the finite scalar spin chirality originating from the noncoplanar $3q$ ordering of Co spins. This large AHE occurs when the scalar spin chirality is uniform in all Co layers, as indeed found in the ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$ 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 magnetoelectric effect. Here, we theoretically verify that a transverse electric field generates a finite orbital magnetization under such conditions, consistent with the axionlike coupling. Using first-principles calculations, we show that the resulting magnetoelectric coupling, ${\alpha }^{zz}$ can be as large as 0.9 $e^2/2h$. We also demonstrate that the interlayer magnetic coupling in these materials can be tuned by strain, enabling the switching between the AHE and the axionic states.

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• Berry curvature
• Exchange interaction
• Intercalation
• Strain
• Noncollinear magnets
• Topological materials
• Density functional calculations