Difference in magnetic anisotropy of the ferromagnetic monolayers VI3 and CrI3

Concerning the magnetic anisotropy and magnetic moments of the M3+ (M = V, Cr) ions in ferromagnetic (FM) MI3 monolayers, which have a honeycomb pattern of edge-sharing MI6 octahedra, conflicting observations have been reported in experimental and theoretical studies. We resolve these conflicts by determining the magnetic anisotropy energies for the M3+ ions of MI3 monolayers, by analyzing their preferred spin orientations in terms of the selection rules based on the highest occupied molecular orbital-lowest unoccupied molecular orbital interactions of the MI6 octahedra, and by discussing whether or not the M3+ ions are uniaxial. Here we show that the FM monolayer VI3 is uniaxial, but that of CrI3 is not. The magnetic anisotropy energy for the V3+ (d(2), S = 1) ion of VI3 is greater than that for the Cr3+ (d(3), S = 3/2) ion of CrI3 by more than an order of magnitude (i.e., similar to 8 vs similar to 0.6 meV). The V3+ ion exhibits uniaxial magnetism because its orbital quantum number L is not zero (L = 1), in contrast to the Cr3+ ion (L = 0).