Half metals at intermediate energy scales in Anderson-type insulators

Although quantum phase transitions involved with Anderson localization have been investigated for more than a half century, the role of spin polarization in these metal-insulator transitions has not been clearly addressed as a function of both the range of interactions and the range of energy scales. Based on the Anderson-Hartree-Fock study, we reveal that the spin polarization has nothing to do with Anderson metal-insulator transitions in three dimensions as long as effective interactions between electrons are long-ranged Coulomb type. On the other hand, we find that metal-insulator transitions appear with magnetism in the case of Hubbard-type local interactions. In particular, we show that the multifractal spectrum of spin-↑ electrons differs from that of spin-↓ electrons at the high-energy mobility edge, which indicates the existence of spin-dependent universality classes for metal-insulator transitions. One of the most fascinating and rather unexpected results is the appearance of half metals at intermediate energy scales above the high-energy mobility edge in Anderson-type insulators of the Fermi energy; that is, only spin-↑ electrons are delocalized, while spin-↓ electrons are Anderson type localized.