On-site and inter-site Hubbard corrections in magnetic monolayers: The case of FePS$_3$ and CrI$_3$

TL;DR

This study evaluates the effectiveness of on-site and inter-site Hubbard corrections in 2D magnetic monolayers, specifically FePS3 and CrI3, revealing their impact on electronic, structural, and vibrational properties and proposing spin-resolved Hubbard parameters for improved accuracy.

Contribution

It introduces a first-principles approach to compute Hubbard parameters in 2D magnetic materials and demonstrates the importance of spin-resolved Hubbard U for accurate electronic structure predictions.

Findings

Hubbard corrections are essential for accurately modeling FePS3's insulating state.

Applying Hubbard U to CrI3 without modifications can worsen results.

Spin-resolved Hubbard U improves agreement with experimental electronic band structures.

Abstract

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+$\textit{U}$ and its extensions PBEsol+$\textit{U}$+$\textit{V}$ 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 $\textit{U}$ and inter-site $\textit{V}$) 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 $\textit{U}$ 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.