Triaxial magnetic anisotropy in two-dimensional ferromagnetic semiconductor CrSBr

Two-dimensional (2D) ferromagnets have recently drawn extensive attention, and here we study the electronic structure and magnetic properties of the bulk and monolayer of CrSBr, using first-principles calculations and Monte Carlo simulations. Our results show that bulk CrSBr is a magnetic semiconductor and has the easy magnetization b-axis, hard c-axis, and intermediate a-axis. Thus, the experimental triaxial magnetic anisotropy (MA) is well reproduced here, and it is identified to be the joint effects of spin-orbit coupling (SOC) and magnetic dipole-dipole interaction. We find that bulk CrSBr has a strong ferromagnetic (FM) intralayer coupling but a marginal interlayer one. We also study CrSBr monolayer in detail and find that the intralayer FM exchange persists and the shape anisotropy has a more pronounced contribution to the MA. Using the parameters of the FM exchange and the triaxial MA, our Monte Carlo simulations show that CrSBr monolayer has Curie temperature Tc = 175 K. Moreover, we find that a uniaxial tensile (compressive) strain along the a (b) axis would further increase the Tc.