Size-dependent indirect exchange

The size dependence of the indirect exchange in small particles and thin films has been investigated theoretically. The surface contribution to the effective exchange integral is found, as well as renormalization of the bulk indirect exchange due to the surface shift of the Fermi momentum. In typical cases the decay of the surface indirect exchange with the inter-spin distance is essentially slower than the decay of the bulk exchange. The critical carrier density up to which the ferromagnetic ordering is stable is higher for small samples than for bulk samples.