On-site and inter-site Hubbard corrections in magnetic monolayers: The case of FePS₃ and CrI₃

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 FePS₃ and ferromagnetic CrI₃, 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 FePS₃ 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. While empirical U can lead to an unstable ground-state (i.e. imaginary phonons), the system remains stable through the self-consistent process of calculating Hubbard parameters. For ferromagnetic CrI₃, 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.