Charge self-regulation upon changing the oxidation state of transition metals in insulators.

Transition-metal atoms embedded in an ionic or semiconducting crystal can exist in various oxidation states that have distinct signatures in X-ray photoemission spectroscopy and 'ionic radii' which vary with the oxidation state of the atom. These oxidation states are often tacitly associated with a physical ionization of the transition-metal atoms--that is, a literal transfer of charge to or from the atoms. Physical models have been founded on this charge-transfer paradigm, but first-principles quantum mechanical calculations show only negligible changes in the local transition-metal charge as the oxidation state is altered. Here we explain this peculiar tendency of transition-metal atoms to maintain a constant local charge under external perturbations in terms of an inherent, homeostasis-like negative feedback. We show that signatures of oxidation states and multivalence--such as X-ray photoemission core-level shifts, ionic radii and variations in local magnetization--that have often been interpreted as literal charge transfer are instead a consequence of the negative-feedback charge regulation.