The importance of anisotropic Coulomb interaction in LaMnO$_{3}$

TL;DR

This paper demonstrates that incorporating explicit intra-orbital exchange corrections in DFT+U calculations is essential for accurately modeling the electronic, magnetic, and structural properties of LaMnO$_{3}$, highlighting the role of Hund's coupling.

Contribution

The study introduces a reformulation of the DFT+U functional emphasizing intra-orbital exchange, improving the description of LaMnO$_{3}$ by capturing anisotropic Coulomb interactions.

Findings

DFT+U with explicit exchange corrections matches experimental observations.

Hund's coupling is crucial for Jahn-Teller distortion and band gap opening.

Optimal parameters for LaMnO$_{3}$ are U=8 eV and J=1.9 eV.

Abstract

In low-temperature anti-ferromagnetic LaMnO$_{3}$, strong and localized electronic interactions among Mn 3d electrons prevent a satisfactory description from standard local density and generalized gradient approximations in density functional theory calculations. Here we show that the strong on-site electronic interactions are described well only by using direct and exchange corrections to the intra-orbital Coulomb potential. Only DFT+U calculations with explicit exchange corrections produce a balanced picture of electronic, magnetic and structural observables in agreement with experiment. To understand the reason, a rewriting of the functional form of the +U corrections is presented that leads to a more physical and transparent understanding of the effect of these correction terms. The approach highlights the importance of Hund's coupling (intra-orbital exchange) in providing anisotropy across the occupation and energy eigenvalues of the Mn d states. This intra-orbital exchange is the key to fully activating the Jahn-Teller distortion, reproducing the experimental band gap and stabilizing the correct magnetic ground state in LaMnO$_{3}$. The best parameter values for LaMnO$_{3}$ within the DFT (PBEsol) +U framework are determined to be U = 8 eV and J = 1.9 eV.