Axion insulator state in ferromagnetically ordered Cr I 3 / B i 2 S e 3 / MnB i 2 S e 4 heterostructures

Ferromagnetic (FM) axion insulators may greatly simplify experimental explorations of the topological magnetoelectric effect, as the FM ordering can be stable in a broad range of magnetic field. Through density functional theory calculations and four-band model studies, we find that two-dimensional van der Waals FM $\mathrm{Cr}{\mathrm{I}}_{3}$ and $\mathrm{MnB}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{e}}_{4}$ overlayers induce opposite-sign exchange fields in the topological surface states of $\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{e}}_{3}$ film when they are ferromagnetically ordered. Consequently, the $\mathrm{Cr}{\mathrm{I}}_{3}/\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{e}}_{3}/\mathrm{MnB}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{e}}_{4}$ heterostructure is a robust FM axion insulator, according to surface-resolved Berry curvature calculations. Our work opens up opportunities for the design of materials with the topological magnetoelectric effect.