Finite Element Modeling of Charge- and Spin-Currents in Magnetoresistive Pillars With Current Crowding Effects

Charge- and spin-diffusion equations, taking into account spin-diffusion and spin-transfer torque, were numerically solved using a finite element method in complex noncollinear geometry. As an illustration, this approach was used to study the spin-dependent transport in a two-dimensional model giant magnetoresistance metallic pillar sandwiched between extended electrodes as is the case in magnetoresistive heads for hard disk drives. In this model system, the charge current crowding around the boundaries between the electrodes and the pillar has a quite significant influence on the spin current within the magnetoresistive pillar.