Boundary and finite-size effects in small magnetic systems

We study the effect of free boundaries in finite magnetic systems of cubic shape on the field and temperature dependence of the magnetisation within the isotropic model of D-component spin vectors in the limit D → ∞. 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) magnetisation M=M(H,T) of the system and the induced magnetisation 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 rendering a positive contribution to M. The inhomogeneities of the magnetisation caused by the boundaries are long ranged and extend far into the depth of the system.