Spin-Polarized Orbitals for Localized States in Crystals

Using the concept of different orbitals for different spins, in conjunction with the tight-binding approximation, it is possible to construct a set of spin-polarized orbitals (SPO's) in which electrons with different spins are localized on different crystal atoms. Thus, SPO's allow for the correlation between electrons with different spins and, for a pure crystal, are very similar to Lowdin's alternant crystal orbitals. For one-dimensional crystals, an analysis which resembles that for linear mixed crystals reveals that, for alpha- or beta-spin electrons, the energy levels of the nonlocalized SPO's form two bands, while those of the localized SPO's lie either outside these bands or in the gap between them. Finally, Green's matrix method is employed to examine the effect on the SPO's of the perturbation produced by interior impurity atoms in the crystal, or chemisorbed atoms at the surface.