We show that repulsive local Coulomb interaction alone can drive valence-skipping charge disproportionation in the degenerate $d$-band, resulting in effective negative-$U$. This effect is shown to originate from anisotropic orbital-multipole scattering, and it occurs only for $d^1,d^4,d^6$, and $d^9$ fillings (and their immediate surroundings). Explicit boundaries for valence-skipping are derived, and the paramagnetic phase diagram for $d^4$ and $d^6$ is calculated. We also establish that the valence-skipping metal is very different, in terms of its local valence distribution, compared to the atomiclike Hund's metal. These findings explain why transition-metal compounds with the aforementioned $d$-band fillings are more prone to valence-skipping charge order and anomalous superconductivity.

• Received 4 February 2013
• Revised 5 August 2014

DOI:https://doi.org/10.1103/PhysRevB.90.155108