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 CrX 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 $$ ground state lying 1.5-1.7 eV below the first excited state ⁴ T ₂ ( $$ ). CrCl₃ 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 CrBr₃ and CrI₃ 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 CrCl₃ and CrI₃ 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.