Surface Corrections to the Specific Heat of Ferromagnetic Films

The surface correction to the low-temperature form of the specific heat of ferromagnetic films is discussed. It is pointed out that the low-temperature form of the surface correction depends only on the curvature of the bulk spin-wave dispersion relation near $k=0\mathrm{}$, provided the exchange interactions between the spins are short-ranged in a sense described in the text. Hence, the surface correction to the magnon specific heat is insensitive to changes in the exchange constants in the film surfaces. We carry out the discussion with a simple method that does not require the use of Green's functions.