Spin-orbit and topological contributions to magnetic anisotropy in monolayer
Phys. Rev. B 113, 064419 – Published 13 February, 2026
DOI: https://doi.org/10.1103/ldvf-6qnr
Abstract
Two-dimensional magnetic topological insulators, such as monolayer , are promising platforms for realizing the quantum anomalous Hall (QAH) effect, with high Curie temperatures and large perpendicular magnetic anisotropy energies (MAEs). Using first-principles density functional theory calculations, we investigate the microscopic mechanism behind the large MAE in . The MAE arises from two key contributions: a spin-orbit coupling (SOC)-driven term, originating from the strong SOC of W orbitals, and a topology-assisted term near the band-inverted region. Both contributions favor out-of-plane magnetization, though they operate through different origins. The SOC-driven contribution arises from the intrinsic relativistic interaction, while the topology-assisted contribution is governed by the spin-orientation dependence of the electronic topology. Specifically, when the magnetization is in-plane, symmetry-protected nodal points near the Fermi level prevent the formation of a global gap. In contrast, out-of-plane magnetization lifts these degeneracies, opening a sizable topological gap with Chern number , leading to a greater energy separation between the two crossing bands and enhancing the MAE. Additionally, the energy and dispersion of these nodal points vary with the in-plane magnetization direction, introducing an additional anisotropy within the plane. As a result, the total MAE arises from the interplay between the SOC-driven and topology-assisted contributions, with the maximum MAE occurring when the system stabilizes the QAH insulating state with perpendicular magnetization.