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 $β$ and saturation magnetization $M_s$, and a pinned-layer material with high $β$ 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.