Orbital-polarization terms: from a phenomenological to a first-principles description of orbital magnetism in density-functional theory

TL;DR

This paper links phenomenological orbital-polarization terms in density-functional theory to first-principles current-density-functional theory, providing a theoretical foundation and new approximations that improve the description of orbital magnetism in transition metal systems.

Contribution

It demonstrates that orbital-polarization terms can be derived as approximations to the exchange-correlation vector potential in CDFT, bridging empirical methods and first-principles theory.

Findings

Orbital-polarization terms are connected to the exchange-correlation vector potential in CDFT.

New simple approximations to the CDFT potential A_xc are proposed.

The approach offers features absent in traditional electron-gas-based functionals.

Abstract

Phenomenological orbital-polarization (OP) terms have been repeatedly introduced in the single-particle equations of spin-density-functional theory, in order to improve the description of orbital magnetic moments in systems containing transition metal ions. Here we show that these ad hoc corrections can be interpreted as approximations to the exchange-correlation vector potential A_xc of current-density-functional theory (CDFT). This connection provides additional information on both approaches: Phenomenological OP terms are connected to first-principles theory, leading to a rationale for their empirical success and a reassessment of their limitations and the approximations made in their derivation. Conversely, the connection of OP terms with CDFT leads to a set of simple approximations to the CDFT potential A_xc, with a number of desirable features that are absent from electron-gas-based functionals.