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

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.