  The charge and spin diffusion equations taking into account spin-flip and
spin-transfer torque were numerically solved using a finite element method in
complex non-collinear geometry. This approach was used to study the
spin-dependent transport in giant magnetoresistance metallic pillars sandwiched
between extended electrodes as in magnetoresistive heads for hard disk drives.
The charge current crowding around the boundaries between the electrodes and
the pillar has a quite significant influence on the spin current.
