  We investigate equilibrium properties of an exchange-spring magnetic system
constituted of a soft layer (e.g. Fe) of a given thickness on top of a hard
magnetic layer (e.g. FePt). The magnetization profile M(z) as a function of the
atomic position ranging from the bottom of the hard layer to the top of the
soft layer is obtained in two cases with regard to the hard layer: i) in the
case of a rigid interface (the FePt layer is a single layer), the profile is
obtained analytically as the exact solution of a sine-Gordon equation with
Cauchy's boundary conditions. Additional numerical simulations also confirm
this result. Asymptotic expressions of M(z) show a linear behavior near the
bottom and the top of the soft layer. In addition, a critical value of the
number of atomic planes in the soft layer, that is necessary for the onset of
spin deviations, is obtained in terms of the anisotropy and exchange coupling
between the adjacent plane in the soft layer. ii) in the case of a relaxed
interface (the FePt layer is a multilayer), the magnetization profile is
obtained numerically for various Fe and FePt films thicknesses and applied
field.
