few nanometers thick. The in-plane uniaxial anisotropy is usually also a shape anisotropy arising from an elongated cross section of the switching magnet [@albert]. We take the uniaxial anisotropy axis of the switching magnet to be parallel to the $z$-axis of the coordinate system shown in Fig. \[fig1\]. Since the switching magnet lies in the $xz$-plane, we can write the total anisotropy field as $$\label{hh}
{\bf H}_{\rm A}={\bf H}_{\rm u}+{\bf H}_{\rm p}$$ where ${\bf H}_{\rm u}$ and ${\bf H}_{\rm p}$ are given by $$\label{hu}
{\bf H}_{\rm u}= H_{\rm u0}({\bf m}\cdot{\bf e}_{z}){\bf e}_{z},$$

$$\label{hp}
{\bf H}_{\rm p}=-H_{\rm p0}({\bf m}\cdot{\bf e}_{y}){\bf e}_{y}.$$

Here ${\bf e}_x$, ${\bf e}_y$ and ${\bf e}_z$ are unit vectors in the directions of the axes shown in Fig. 1. If we write the energy of the switching magnet in the anisotropy field as $-{\bf H}_{\rm
A}\cdot\langle{\bf S}_{\rm tot}\rangle$, where $\langle{\bf S}_{\rm
tot}\rangle$ is the total spin angular momentum of the switching magnet, them $H_{\rm u0}$,$H_{\rm p0}$ which measure the strengths of the uniaxial and easy-plane anisotropies have dimensions of frequency. These quantities may be converted to a field in tesla by multiplying by $\hbar/2\mu_{\rm
  B}=5.69\times 10^{-12}$.

We are now ready to study the time evolution of the unit 