state. This interesting case is implicit in the phenomenological LLG treatment and we shall discuss it in detail later.

In describing the switching magnet by a unique unit vector ${\bf m}$, we assume that it remains uniformly magnetised during the switching process. This is only strictly true when the exchange stiffness of the switching magnet is infinitely large. It is generally a good approximation as long as the switching magnet is small enough to remain single domain, so that the switching occurs purely by rotation of the magnetisation as in the Stoner-Wohlfarth theory [@17] of field switching. This seems to be the case in many experiments [@albert; @16; @18; @19]

Before we can apply the LLG equation to study the time evolution of the unit vector ${\bf m}$ in the direction of the magnetisation of the switching magnet, we need to determine all the contributions to the torque acting on the switching magnet. Firstly, there is the spin-transfer torque ${\bf T}^{\rm s-t}$ which we discussed in Section \[due\]. Secondly, there is a torque due to the uniaxial in-plane and easy plane (shape) anisotropies. The easy-plane shape anisotropy torque arises because the switching magnet is a thin layer typically only a 