Abstract
The spin diffusion and charge equations in Levy-Fert and Waintal models were numerically solved, using finite element method in complex non-collinear geometry with strongly inhomogeneous current flow. As an illustration, spin-dependent transport through a magnetic pillar and nonmagnetic spacer separating two magnetic layers was investigated. It is shown, that the structure with number of pillars gives a higher value of Giant Magnetoresistance (GMR) effect rather than a structure with one pillar of equivalent diameter. The inhomogeneity of spin currents, which has one of the strongest impacts on GMR effect value leads to the occurrence of spin-current vortices. Introduction of lT and lL lengths in Waintal model gives a better description of angular dependence of GMR effect rather than Levy-Fert model.
Highlights
Discovery of the effect of giant magnetoresistance (GMR) was a first step which allowed spintronics to become a very promising field of studies [1,2]
We show that inhomogeneity of current flows, appearing in Giant Magnetoresistance (GMR) structures leads to creation of vortices in distribution of spin currents and compare angular dependence of GMR for Levy-Fert and Waintal models
The first one has long paramagnetic electrodes with long and thin ferromagnetic layers connected with a thin paramagnetic spacer
Summary
Discovery of the effect of giant magnetoresistance (GMR) was a first step which allowed spintronics to become a very promising field of studies [1,2]. One of the ground theories introduces the concept of spin accumulation and spin diffusion length as key parameters to describe the diffusive transport in CPP metallic multilayers, which were generalized for both collinear and non-collinear cases. Another model was proposed by Waintal et al [9] which generalizes Valet-Fert theory, involving two new coherence and Larmor lengths. All these theoretical models were applied for simple geometries with homogeneous current flow so far. We show that inhomogeneity of current flows, appearing in GMR structures leads to creation of vortices in distribution of spin currents and compare angular dependence of GMR for Levy-Fert and Waintal models
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