Tight-binding theory of tunneling giant magnetoresistance

A unified theory of the tunneling magnetoresistance (TMR) and of the ballistic-current perpendicular-to-plane giant magnetoresistance (CPP GMR) is developed. It is based on the Kubo-Landauer formula and fully realistic tight-binding bands fitted to an ab initio band structure. The theory is first applied to a single-orbital tight-binding model to investigate analytically a continuous transition from the CPP GMR of a metallic system to the TMR of a tunneling junction. The transition takes place when either hopping of electrons between the ferromagnetic electrodes is gradually turned off or the on-site potentials in the nonmagnetic spacer are varied so that the Fermi level in the spacer moves into the band gap. It is shown that the TMR approaches rapidly the same saturation value when either the interelectrode hopping decreases or the height of the insulating barrier increases. When the insulating barrier is high (band gap is large), the TMR depends only weakly on the thickness of the insulating layer. However, when the band gap is small compared to the conduction band width, the TMR decreases rapidly with increasing thickness of the insulator. The numerical results for a Co(001) junction, based on a fully realistic band structure of the Co electrodes, show a very similar behavior. As the tight-binding hopping matrix between the Co electrodes is gradually turned off, the TMR ratio drops initially very rapidly from its value of 280% in the metallic regime to about 40% but then stabilizes in the range 40-65%. This is in a very good agreement with the observed value of 40%. The polarization of the current flowing across the Co junction in the metallic regime is negative (antiparallel to the magnetization) but becomes positive in the tunneling regime. The sign of the calculated polarization is, therefore, in agreement with the sign observed in all the experiments on tunneling from transition-metal ferromagnets. [S0163-1829(97)01141-7].