In the down-spin DOS, a small gap state appears at the Fermi level, as indicated in Figure . This feature is likely due to the presence of minor defect-related states that involve a mixture of Ti 3+ and Ti 4+ sites. While the majority of the mid-gap states are localized in the up-spin channel, this small gap state suggests some degree of electronic interaction in the down-spin channel, which may be related to minor delocalized electronic activity near the surface or interactions with neighboring atoms .