Strain-tunable magnetic anisotropy in monolayer CrCl3, CrBr3, and CrI3

Recent observation of intrinsic ferromagnetism in two-dimensional (2D)\nCrI$_3$ is associated with the large magnetic anisotropy due to strong\nspin-orbit coupling (SOC) of I. Magnetic anisotropy energy (MAE) defines the\nstability of magnetization in a specific direction with respect to the crystal\nlattice and is an important parameter for nanoscale applications. In this work\nwe apply the density functional theory to study the strain dependence of MAE in\n2D monolayer chromium trihalides CrX$_3$ (with X = Cl, Br, and I). Detailed\ncalculations of their energetics, atomic structures and electronic structures\nunder the influence of a biaxial strain $\\varepsilon$ have been carried out. It\nis found that all three compounds exhibit ferromagnetic ordering at the ground\nstate (with $\\varepsilon$=0) and upon applying a compressive strain, phase\ntransition to antiferromagnetic state occurs. Unlike in CrCl$_3$ and CrBr$_3$,\nthe electronic band gap in CrI$_3$ increases when a tensile strain is applied.\nThe MAE also exhibits a strain dependence in the chromium trihalides: it\nincreases when a compressive strain is applied in CrI$_3$, while an opposite\ntrend is observed in the other two compounds. In particular, the MAE of CrI$_3$\ncan be increased by 47\\% with a compressive strain of $\\varepsilon$ = 5\\%.\n