Electronic excitations and spin interactions in chromium trihalides from embedded many-body wavefunctions.

Although chromium trihalides are widely regarded as a promising class of two-dimensional magnets for next-generation devices, an accurate description of their electronic structure and magnetic interactions has proven challenging to achieve. Here, we quantify electronic excitations and spin interactions in Cr X 3 ( X = Cl, Br, I) using embedded many-body wavefunction calculations and fully generalized spin Hamiltonians. We find that the three trihalides feature comparable d -shell excitations, consisting of a high-spin 4 A 2 ( t 2 g 3 e g 0 ) ground state lying 1.5-1.7 eV below the first excited state 4 T 2 ( t 2 g 2 e g 1 ). CrCl 3 exhibits a single-ion anisotropy A sia  = - 0.02 meV, while the Cr spin-3/2 moments are ferromagnetically coupled through bilinear and biquadratic exchange interactions of J 1  = - 0.97 meV and J 2  = - 0.05 meV, respectively. The corresponding values for CrBr 3 and CrI 3 increase to A sia  = -0.08 meV and A sia = - 0.12 meV for the single-ion anisotropy, J 1  = -1.21 meV, J 2  = -0.05 meV and J 1  = -1.38 meV, J 2  = -0.06 meV for the exchange couplings, respectively. We find that the overall magnetic anisotropy is defined by the interplay between A sia and A dip due to magnetic dipole-dipole interaction that favors in-plane orientation of magnetic moments in ferromagnetic monolayers and bulk layered magnets. The competition between the two contributions sets CrCl 3 and CrI 3 as the easy-plane ( A sia + A dip >0) and easy-axis ( A sia + A dip <0) ferromagnets, respectively. The differences between the magnets trace back to the atomic radii of the halogen ligands and the magnitude of spin-orbit coupling. Our findings are in excellent agreement with recent experiments, thus providing reference values for the fundamental interactions in chromium trihalides.