Magnetic anisotropy of the two-dimensional ferromagnetic insulator MnBi2Te4

Abstract

Magnetic anisotropy is vital for establishing the long-range magnetic order in two-dimensional systems. Here, based on the density functional theory calculation, we systematically study the magnetic anisotropy of monolayer ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$, a ferromagnetic insulator. We find that the exchange interaction in monolayer ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ is nearly isotropic and almost has no contribution to the magnetic anisotropy, as a result of the weak $p\ensuremath{-}d$ hybridization between Mn and Te atoms. We further reveal that magnetic anisotropy originates from single-ion anisotropy, leading to a ferromagnetic Curie temperature of about 20 K. Interestingly, the emergence of single-ion anisotropy cannot be induced solely by the spin-orbit coupling of Mn atoms, but also involves the spin-orbit coupling of ligand Te, as the spin-orbit coupling of Te atoms can induce changes in the local Mn-$d$ states. This behavior is very different from that in monolayer ${\mathrm{CrI}}_{3}$ and ${\mathrm{CrGeTe}}_{3}$, where the anisotropy of the exchange interaction is critical for long-range magnetic order. Our findings may provide a comprehensive understanding of the magnetic behavior in monolayer ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ and motivate further research on its potential applications.