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 CrX3 (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 4A2 $$({t}_{2g}^{3}{e}_{g}^{0})$$ ground state lying 1.5–1.7 eV below the first excited state 4T2 ( $${t}_{2g}^{2}{e}_{g}^{1}$$ ). CrCl3 exhibits a single-ion anisotropy Asia = − 0.02 meV, while the Cr spin-3/2 moments are ferromagnetically coupled through bilinear and biquadratic exchange interactions of J1 = − 0.97 meV and J2 = − 0.05 meV, respectively. The corresponding values for CrBr3 and CrI3 increase to Asia = −0.08 meV and Asia= − 0.12 meV for the single-ion anisotropy, J1 = −1.21 meV, J2 = −0.05 meV and J1 = −1.38 meV, J2 = −0.06 meV for the exchange couplings, respectively. We find that the overall magnetic anisotropy is defined by the interplay between Asia and Adip 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 CrCl3 and CrI3 as the easy-plane (Asia + Adip >0) and easy-axis (Asia + Adip <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.