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(1,2) - that is, a literal transfer of charge to or from the atoms. Physical models have been founded on this charge- transfer paradigm(3-6), but first- principles quantum mechanical calculations show only negligible changes in the local transition-metal charge(7-12) 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(3,4,13-16) are instead a consequence of the negative- feedback charge regulation.