It is well known that two-dimensional spin-wave excitations result in a linear temperature dependence of the magnetization in a quasi-two-dimensional ferromagnetic system. However, it has been shown also that magnetic relaxation from small islands inside a film can also result in a similar linear temperature dependence. In this paper, it is found that comparative Mossbauer measurements with and without a weak magnetic field can clearly distinguish these two different mechanisms: The linear temperature dependence of the magnetization is unaffected by the external field if 2D spin-wave excitations are responsible for the linear behavior, while the linear slope of the temperature dependence of the magnetization is reduced by the external field if magnetic relaxation is involved.