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

Abstract

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 ${}^4{A}_2$ $(t_{2g}^3{e}_g^0)$ ground state lying 1.5$-$1.7 eV below the first excited state ${}^4{T}_2$ ($t_{2g}^2{e}_g^1$). CrCl${}_3$ exhibits a single-ion anisotropy $A_{\mathrm{sia}}=-0.02$ 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 $A_{\mathrm{sia}}=-0.08$ meV and $A_{\mathrm{sia}}=-0.12$ 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 $A_{\mathrm{sia}}$ and $A_{\mathrm{dip}}$ 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 ($A_{\mathrm{sia}}+A_{\mathrm{dip}}>0$) and easy-axis ($A_{\mathrm{sia}}+A_{\mathrm{dip}}<0$) 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.

arXiv comment9 pages, 2 figures, 5 tables, Supporting Information included as ancillary file

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