Singularity of the surface magnetization in anisotropic Heisenberg ferromagnets

The surface-magnetization singularity at the bulk critical temperature is studied within the context of the Green-function formalism. We take a pure Heisenberg model on the bulk of a semi-infinite lattice and the surface is described by an anisotropic Heisenberg model, whose anisotropy parameter ${\mathrm{\epsilon }}_{\mathit{s}}$ permits us to consider a sequence of models from pure Heisenberg to Ising. We show that the slope of the surface magnetization is discontinuous at the bulk critical temperature and that the discontinuity increases when the model on the surface varies from Ising to Heisenberg. This result could indicate that the exchange coupling on the surface of Gd is highly anisotropic.