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Strain-induced phase transition in CrI$_{3}$ bilayers

A monolayer of CrI$_3$ is a two-dimensional crystal that in its equilibrium configuration is a ferromagnetic semiconductor, however, two coupled layers can be ferromagnetic or antiferromagnetic depending on the stacking. We study the magnetic phase diagram upon the strain of the antiferromagnetically coupled bilayer with C2/m symmetry. We found that strain may be an efficient tool to tune the magnetic phase of the structure. A tensile strain stabilizes the antiferromagnetic phase, while a compressive strain turns the system ferromagnetic. We understood that behavior by looking at the relative displacement between layers due to the strain. We also study the evolution of the magnetic anisotropy, the magnetic exchange coupling between Cr atoms, and how the Curie temperature is affected by the strain.