  We study a change in the spin magnetization of a superconductor-ferromagnet
(SF) heterostructure, when temperature is lowered below the superconducting
transition temperature. It is assumed that the SF interface is smooth on the
atomic scale and the mean free path is not too short. Solving the Eilenberger
equation we show that the spin magnetic moment induced in the superconductor is
an oscillating sign-changing function of the product $hd$ of the exchange field
$h$ and the thickness $d$ of the ferromagnet. Therefore the total spin magnetic
moment of the system in the superconducting state can be not only smaller
(screening) but also greater (anti-screening) than that in the normal state, in
contrast with the case of highly disordered (diffusive) systems, where only
screening is possible. This surprising effect is due to peculiar periodic
properties of localized Andreev states in the system. It is most pronounced in
systems with ideal ballistic transport (no bulk disorder in the samples, smooth
ideally transparent interface), however these ideal conditions are not crucial
for the very existence of the effect. We show that oscillations exist (although
suppressed) even for arbitrary low interface transparency and in the presence
of bulk disorder, provided that $h \tau \gg 1$ ($\tau$ -- mean free path). At
low interface transparency we solve the problem for arbitrary strength of
disorder and obtain oscillating magnetization in ballistic regime ($h \tau \gg
1$) and nonoscillating magnetization in diffusive one ($h \tau \ll 1$) as
limiting cases of one formula.
