Abstract
We consider a superconductor-ferromagnet (S/F) structure and assume that above the superconducting transition temperature $T_{c}$ the magnetic moment exists only in F. {In a simple model of the ferromagnet (the exchange field is of the ferromagnetic type for all energies)}we show by an explicit calculation that below $T_{c}$ the magnetic moment may penetrate the superconductor. {In this model} its direction in S is opposite {to the magnetization of free electrons} in the ferromagnet. The magnetization spreads over a large distance which is of the order of the superconducting coherence length $\xi_{S}$ and can much exceed the ferromagnet film thickness. At the same time the magnetic moment in the ferromagnet is reduced. This inverse proximity effect may explain the reduction in magnetization observed in recent experiments and may lead to a strong interaction between the ferromagnetic layers in F/S/F structures.
Highlights
Penetration of the superconducting condensate into a normal metal in the superconductorS-normal metalNheterostructures is a well established proximity effect
At the same time the magnetic moment in the ferromagnet is reduced. This inverse proximity effect may explain the reduction in magnetization observed in recent experiments and may lead to a strong interaction between the ferromagnetic layers in F/S/F structures
While the superconducting condensate consists of paired electrons with opposite spins, the exchange field J in the ferromagnet tends to align them and break the Cooper pairs
Summary
Where the exchange energy is assumed to be positive for all energiesthe ferromagnetic type of interaction, n is the unit vector parallel to the magnetization of the ferromagnet. A constant J1 is related to J via the equation: JϭJ1nMS0, where nM is the concentration of magnetic ions and S0 is a maximum value of Sawe consider these spins as classical vectors; see Ref. 16͒. In this case the magnetization is a sum: MϭMlocϩMe , and the magnetization Me may be aligned parallel The function K(x) contains the correction ␦⌬(x) to the order parameter ⌬ This term is not relevant in our calculations since only the component off proportional to ˆ 0 contributes to the magnetizationsee below, Eq ͑17͔͒. Equations9͒ and10͒ should be complemented by the boundary conditions that can be written for smallf S,F as x
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