suitable strength and methods have been proposed [@2] for providing such a local field by currents in a criss-cross array of conducting strips. However an alternative, and potentially more efficient method, proposed by Slonczewski [@3] makes use of a current passing up the pillar itself. Slonczewski’s effect relies on “spin transfer” and not on the magnetic field produced by the current which in the nanopillar geometry is ineffective. The idea of spin-transfer is as follows. In a ferromagnet there are more electrons of one spin orientation than of the other so that current passing through the thick magnetic layer (the polarising magnet) becomes spin-polarised. In general its state of spin-polarisation changes as it passes through the second (switching) magnet so that spin angular momentum is transferred to the switching magnet. This transfer of spin angular momentum is called spin-transfer torque and, if the current exceeds a critical value, it may be sufficient to switch the direction of magnetisation of the switching magnet. This is called current-induced switching.

In the next section we show how to calculate the spin-transfer torque for a simple model.

Spin-transfer torque in a simple model {#due}
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For simplicity we consider a structure of the type 