Green's function theory for a magnetic impurity layer in a ferromagnetic Ising film with transverse field

TL;DR

This paper develops a Green's function approach within the Ising model to analyze localized magnetic impurity modes in ferromagnetic thin films, revealing a crossover effect and degeneracy lifting depending on film parameters.

Contribution

It introduces a Green's function formalism for impurity modes in ferromagnetic films with transverse field, highlighting the crossover and degeneracy effects based on film thickness and parameters.

Findings

Crossover effect between surface and impurity localized modes.

Degeneracy of surface modes can be lifted by impurities.

Results depend on film thickness, exchange, and field parameters.

Abstract

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.