Quantum oscillations of the spin density in magnetic multilayers

An asymptotic stationary phase formula is derived for the oscillatory spin density induced in a nonmagnetic spacer sandwiched between two semi-infinit e ferromagnets. It gives an explicit dependence for the polarization on the spacer layer thickness and on the distance from the ferromagnet-spacer int erface. Both dependences are shown to oscillate with thr same periods as th e exchange coupling between the ferromagnetic layers. The magnitude of the polarization is governed by the degree of confinement of carriers in the sp acer quantum well and by the curvature of the spacer Fermi surface. The for mula is applied to a Co/Cu/Co (001) trilayer described by tight-binding ban ds fitted to an ab initio band structure. Its validity is tested against a fully numerical calculation using the same band structure. As in the case o f the oscillatory exchange coupling, the induced polarization is dominated by the contribution of the Cu Fermi surface neck extrema leading to a short period oscillation of 2.6 atomic planes. An interesting non-Ruderman-Kitte l-Kasuya-Yosida initial decay of the induced polarization is discussed. [S0 163-1829 (99)06309-2].