Green's function theory for a magnetic impurity layer in a ferromagnetic   Ising film with transverse field
  A Green's function formalism is used to calculate the spectrum of localized modes of an impurity layer implanted within a ferromagnetic thin film. The equations of motion for the Green's functions are determined in the framework of the Ising model in a transverse field. We show that depending on the thickness, exchange and effective field parameters, there is a ``crossover'' effect between the surface modes and impurity localized modes. For thicker films the results show that the degeneracy of the surface modes can be lifted by the presence of an impurity layer. 
R. V. Leite, B. T. F. Morais, J. Milton Pereira Jr., and R. N. Costa   Filho