  We study the effect of free boundaries in finite magnetic systems of cubic
shape on the field and temperature dependence of the magnetization within the
isotropic model of D-component spin vectors in the limit D \to \infty. This
model is described by a closed system of equations and captures the
Goldstone-mode effects such as global rotation of the magnetic moment and
spin-wave fluctuations. We have obtained an exact relation between the
intrinsic (short-range) magnetization M = M(H,T) of the system and the
supermagnetization m = m(H,T) which is induced by the field. We have shown,
analytically at low temperatures and fields and numerically in a wide range of
these parameters, that boundary effects leading to the decrease of M with
respect to the bulk value are stronger than the finite-size effects making a
positive contribution to M. The inhomogeneities of the magnetization caused by
the boundaries are long ranged and extend far into the depth of the system.
