Effect of Surface Pinning Fields on the Properties of the Heisenberg Ferromagnet

We consider the effect of a surface pinning field on the thermodynamic properties of the semi-infinite Heisenberg ferromagnet. For a simple cubic lattice of spins coupled via nearest-neighbor exchange, we derive the low-temperature form of the specific heat and the variation of 〈Sz〉 with distance from the surface by an elementary method, for zero and infinite pinning fields. For general values of the pinning field, we derive a form for the surface specific heat valid in the spin-wave regime by employing a Green's-function technique.