Wannier functions and exchange integrals: The example of LiCu$_{2}$O$_{2}$

TL;DR

This paper develops explicit formulas for exchange integrals in metal oxides using Wannier functions and atomic parameters, applied to LiCu₂O₂, highlighting the importance of ligand contributions and the accuracy of ab-initio methods.

Contribution

It introduces a method to calculate exchange integrals considering ligand contributions using Wannier functions and compares it with ab-initio results for LiCu₂O₂.

Findings

Wannier functions reveal oxygen's significant role in exchange interactions.

Exchange integrals from Wannier functions agree with ab-initio LSDA+U calculations.

Precise Wannier functions are essential for accurate exchange estimates.

Abstract

Starting from a single band Hubbard model in the Wannier function basis, we revisit the problem of the ligand contribution to exchange and derive explicit formulae for the exchange integrals in metal oxide compounds in terms of atomic parameters that can be calculated with constrained LDA and LDA+U. The analysis is applied to the investigation of the isotropic exchange interactions of LiCu$_{2}$O$_{2}$, a compound where the Cu-O-Cu angle of the dominant exchange path is close to 90$^{\circ}$. Our results show that the magnetic moments are localized in Wannier orbitals which have strong contribution from oxygen atomic orbitals, leading to exchange integrals that considerably differ from the estimates based on kinetic exchange only. Using LSDA+U approach, we also perform a direct {\it ab-initio} determination of the exchange integrals LiCu$_{2}$O$_{2}$. The results agree well with those obtained from the Wannier function approach, a clear indication that this modelization captures the essential physics of exchange. A comparison with experimental results is also included, with the conclusion that a very precise determination of the Wannier function is crucial to reach quantitative estimates.