First-principles study on effects of local Coulomb repulsion and Hund's coupling in ferromagnetic semiconductor CrGeTe₃

Based on a first-principles computational method treating the local Coulomb repulsion of U and Hund's coupling of J separately, we investigate the effects of these important interactions on the electronic and magnetic structures of a layered ferromagnetic semiconductor CrGeTe₃. We show that explicit inclusion of a density functional for the coupling J is critical to obtain proper bandgaps of a single-layer and bulk systems with a reasonable U, unlike a usual approximation treating those together. After obtaining reliable U and J, we also study the effects of strain on its energy gap. Within 2% of tensile and compressive strains, respectively, there is no strain-induced semiconductor-to-metal transition, contrary to the results without J, thus highlighting important roles of exchange interactions.