Is Hund's Second Rule Responsible for the Orbital Magnetism in Solids?

We argue that the key parameter responsible for the exchange-correlation enhancement of the orbital magnetic moments in solids is “Hubbard $U$” rather than the intra-atomic Hund's second rule coupling, being consistent with a more general concept of the orbital polarization. This leads us to a unified rotationally invariant local density approximation $\left(\mathrm{LDA}\right)+U$ prescription for the orbital magnetism. Validity of the present theory is demonstrated by numerical calculations, which perfectly account for the orbital magnetism as well as the canted magnetic structure in CoO.