Curved Magnetism in CrI₃

Strain gradients or curvature are ubiquitous at the nanoscale and can have tremendous effects on material properties. Micromagnetic modeling has shown how curved magnets can exhibit unusually rich phase diagrams, including chiral or topological spin states. This is particularly important in relation to the recent finding of ferromagnetism in 2D monolayers, such as CrI₃, given their extreme flexibility and natural tendency to rippling. Nevertheless, a thorough, quantitative, understanding of such effects in real materials, from first principles theory, is challenging and still lacking. Here, we use non-collinear-spin density-functional theory to study the (flexomagnetic) coupling between magnetism and curvature in monolayer CrI₃. We find a crossover from a magnetization normal to the surface at small curvatures, to a cycloidal spin state at larger curvatures. We show that this cycloidal state is stabilized by curvature induced, effective anisotropy and Dzyaloshinskii–Moriya type contributions to the magnetic energy. While the latter appears to be dominated by non-relativistic effects, in line with earlier predictions, our results reveal an unexpectedly large impact of spin-orbit coupling on the curvature dependence of the former, qualitatively different from the purely geometric effect discussed in earlier theory.