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 $〈S_z〉$ 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.