Oscillations of Andreev States in Clean Ferromagnetic Films

We investigate the influence of the exchange field on the Andreev bound states in a ferromagnetic ( $F$) film backed on one side by a superconductor ( $S$). Our model accounts for diffusive reflection at the outer surface and possible backscattering at the $\mathrm{FS}$ interface. Phase shifting of the Andreev level by the exchange field results in an oscillatory behavior of the density of states of $F$ as a function of the layer thickness. We show that our results agree quantitatively with recent experiments.