Quantitatively separating superexchange and direct exchange interactions in 2D ferromagnetic materials

Two-dimensional (2D) ferromagnetic (FM) materials are promising candidates for emerging energy-efficient electronic devices. Various modulation strategies have been proposed to increase their rather low Curie temperatures, including ligand substitution, strain, and voltage control. Fundamentally, the improvement of the Curie temperature can be attributed to strengthened FM superexchange interactions, weakened direct exchange interactions, or both. With only a qualitative understanding, the effects of the modulation strategies on the entangled superexchange and direct exchange interactions, and hence on the Curie temperatures, often cannot be unambiguously determined. Therefore, we propose a descriptor-based computational approach to quantitatively separate the contributions of the superexchange and direct exchange interactions to each magnetic exchange parameter. The approach combines density-functional calculations with the exchange mechanisms, and we apply it to the archetypal 2D magnetic monolayers CrSX (X= Cl, Br, or I). This work provides a basis for rationally designing and modulating 2D FM materials to achieve high Curie temperatures.