Spin drift diffusion studies of magnetoresistance effects in current-perpendicular-to-plane spin valves with half-metallic insertions

Abstract

We present a theoretical analysis of spin transport and magnetoresistance (MR) of a penta-layer device, consisting of a basic pseudo-spin-valve trilayer with half-metallic (HM) insertions. Our analysis is based on two models, i.e., the Fert-Valet equation in the limit of infinite spin relaxation length $\ensuremath{\lambda}$, and the spin-dependent drift-diffusion equation, with finite $\ensuremath{\lambda}$. In both cases, we found that MR decreases with increasing HM or ferromagnetic (FM) layer resistivity, when the spin polarization of the HM or FM material is lower than some critical value. We derived the critical value analytically, and explained the MR effect in terms of the relative contribution of FM and HM layers in providing spin-dependent scattering. More interestingly, the presence of spin relaxation causes MR to be always suppressed at high HM/FM resistivity, irrespective of the spin polarization of the HM/FM layers. This phenomenon may be explained by introducing an effective spin-flip resistance, which provides a less resistive path to minority spin electrons via spin flipping. Finally, we show the validity of our analysis in the presence of realistically long contact leads, provided the lead conductivity is sufficiently high. Thus, the insertion of the HM layers results in an interplay between the resistivities of the HM/FM and spacer layers, and the effects of spin relaxation, leading to a MR behavior which is hitherto undescribed.