  The effect of undesirable high-frequency free-layer switching in magnetic
multilayer systems, referred to as back hopping, is investigated by means of
the spin-diffusion model. A possible origin of the back-hopping effect is found
to be the destabilization of the pinned layer which leads to perpetual
switching of both layers. The influence of different material parameters on the
critical switching currents for the free and pinned layer is obtained by
micromagnetic simulations. It is found that the choice of a free-layer material
with low polarization $\beta$ and saturation magnetization $M_s$, and a
pinned-layer material with high $\beta$ and $M_s$ leads to a low free-layer
critical current and a high pinned-layer critical current and hence reduces the
likelihood of back hopping. While back hopping was observed in various types of
devices, there are only few experiments that exhibit this effect in
perpendicularly magnetized systems. However, our simulations suggest, that this
is likely to change due to loss of pinned-layer anisotropy when decreasing
device sizes.
