Oscillations of Induced Magnetization in Superconductor-Ferromagnet Heterostructures

We study a change in the spin magnetization of a superconductor-ferromagnet $(\mathit{SF})$ heterostructure, when temperature is lowered below the superconducting transition temperature. It is assumed that the $\mathit{SF}$ 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 (antiscreening) 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 $h\ensuremath{\tau}⪢1$ ($\ensuremath{\tau}$ is the mean free path). At low interface transparency we solve the problem for arbitrary strength of disorder and obtain oscillating magnetization in ballistic regime $(h\ensuremath{\tau}⪢1)$ and nonoscillating magnetization in diffusive one $(h\ensuremath{\tau}⪡1)$ as limiting cases of one formula.