On-site and intersite Hubbard corrections in magnetic monolayers: The case of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>FePS</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>CrI</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>
Fatemeh Haddadi, Edward Linscott, Iurii Timrov, Nicola Marzari, Marco Gibertini
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 $\mathrm{PBEsol}+U$ and its extensions $\mathrm{PBEsol}+U+V$ to investigate the electronic, structural, and vibrational properties of 2D antiferromagnetic ${\mathrm{FePS}}_{3}$ and ferromagnetic ${\mathrm{CrI}}_{3}$, and compare the monolayers with their bulk counterparts. Hubbard parameters (on-site $U$ and intersite $V$) are computed self-consistently using density-functional perturbation theory, thus avoiding any empirical assumptions. We show that for ${\mathrm{FePS}}_{3}$, the Hubbard corrections are crucial in obtaining the experimentally observed insulating state with the correct crystal symmetry, also providing vibrational frequencies in good agreement with Raman experiments. For ferromagnetic ${\mathrm{CrI}}_{3}$, 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.