On-site and inter-site Hubbard corrections in magnetic monolayers: The case of FePS_3 and CrI_3

Hubbard-corrected density-functional theory has proven to be successful in addressing self-interaction errors in 3D magnetic materials. However, the effectiveness of this approach for 2D magnetic materials has not been extensively explored. Here, we use PBEsol+U and its extensions PBEsol+U+V to investigate the electronic, structural, and vibrational properties of 2D antiferromagnetic FePS_3 and ferromagnetic CrI_3, and compare the monolayers with their bulk counterparts. Hubbard parameters (on-site U and inter-site V) are computed self-consistently using density-functional perturbation theory, thus avoiding any empirical assumptions. We show that for FePS_3 the Hubbard corrections are crucial in obtaining the experimentally observed insulating state with the correct crystal symmetry, providing also vibrational frequencies in good agreement with Raman experiments. For ferromagnetic CrI_3, we discuss how a straightforward application of Hubbard corrections worsens the results and introduces a spurious separation between spin-majority and minority conduction bands. Promoting the Hubbard U to be a spin-resolved parameter - that is, applying different (first-principles) values to the spin-up and spin-down manifolds - recovers a more physical picture of the electronic bands and delivers the best comparison with experiments.