Dependence of electronic structure of the Cr³⁺ substitutional defect in alpha-Al₂O₃ on the Hubbard U parameter

We explore how the density functional theory-calculated electronic structure of open-shell defects in wide-bandgap materials depends on the description of the electronic correlations in an open 3d shell, as well as the size of the supercells. We specifically study the Cr³⁺ substitutional defect in alpha-Al₂O₃ due to its promise for applications in quantum information. The intra-3d electronic correlation energies for the Cr³⁺ defect are estimated by the Hubbard model in the rotationally-invariant scheme, using a range of values for the effective interaction strength informed by the existing literature. In this work, we enumerate how both the supercell size as well as the strength of the Hubbard model parameter U impact the calculated atomic coordinates, the defect energy levels within the bulk band gap, the magnetocrystalline anisotropy energy, and other magnetic properties of the Cr³⁺ ion. These results are then compared to previous calculations using hybrid functionals.