In-plane epitaxy-strain-tuning intralayer and interlayer magnetic coupling in CrSe2 and CrTe2 monolayers and bilayers

Mismatched lattice constants at a van der Waals epitaxy interface often introduce in-plane strains to the lattice of the epitaxial layer, termed epitaxy strain, wherein the strains do not follow the intralayer Poisson's relation. In this study, we obtained the magnetic phase diagrams of ${\mathrm{CrSe}}_{2}$ and ${\mathrm{CrTe}}_{2}$ mono- and bilayers under epitaxy strain up to 8%, as predicted using density functional theory calculations. The magnetic phase diagrams indicate that the in-plane epitaxy strain manipulates either the intra- or interlayer magnetism. The in-plane strain varies the interlayer distance, defined using an interlayer Poisson's ratio, which determines whether the interlayer magnetism follows a Bethe--Slater curve-like (BSC-like) or a reversed BSC-like behavior, depending on the in-plane magnetism. The tunability of the intralayer magnetism is a result of competing intralayer Cr--Cr superexchange interactions. A graphene substrate was introduced to examine the validity of our diagrams in practice. This study also afforded a tentative explanation on the previously reported magnetizations in ${\mathrm{CrSe}}_{2}$ and ${\mathrm{CrTe}}_{2}$ epitaxial mono- or bilayers under epitaxy strains, which had given rise to some controversy.