Magnetic anisotropy and electric field induced magnetic phase transition in the van der Waals antiferromagnet CrSBr

Magnetic anisotropy and the controllability of the magnetic order of two-dimensional magnetic materials are of great importance for the development of next-generation spintronics. Here, first-principles calculations are performed to study these two properties of a topical van der Waals antiferromagnetic (AFM) semiconductor CrSBr. Both the intralayer and interlayer exchange interactions are found nearly isotropic because of the weak $p\text{\ensuremath{-}}d$ hybridization between Cr and anion atoms. Magnetic anisotropy is determined by single-ion anisotropy, which is originated from the spin-orbit coupling of both Cr and Br atoms. Such results are distinct from previous works where anisotropic exchange interaction is supposed to be the origin of the exhibited uniaxial magnetic anisotropy in this material. Moreover, the AFM ground state of bilayer CrSBr is found to be originated from the competition between different orbital-dependent ferromagnetic (FM) and AFM exchange interactions via two inequivalent super-superexchange pathways. Importantly, the magnetic ground state of bilayer CrSBr can be switched from AFM to FM when the applied out-of-plane electric field exceeds a threshold value of 0.046 eV/\AA{}. This can be explained by the orbital overlap variation between interlayer nearest-neighbor Cr pairs upon application of the electric field. Our results will provide a comprehensive understanding of the magnetic behavior in layered CrSBr and suggest bilayer CrSBr as an appealing candidate for electric-field-driven miniaturized spintronic devices.