_{1}

The interaction between an electron with a three-dimensional domain wall was investigated using the Born’s expansion of the S scattering matrix. We obtain an influence of the scattering of the electron with the ferromagnetic domain wall in the spin wave function of the electron with the aim to generate the knowledge about the state of the electron spin after the scattering. It relates to the recent problem of generation of the spin polarized electric current. We also obtain the contribution of the electron-wall domain interaction on the electric conductivity , through the wall domain, where we have obtained a peak of resonance in the conductivity for one value of .

The study of the quantum matter is an important topic of research in modern physics [

The injection of a spin current in a magnetic film can generate a spin-transfer torque that acts on the magnetization collinearly to the damping torque [

The model that we are interesting is described by the following Hamiltonian

where

The purpose of this paper is to verify the influence of the scattering of electrons with the ferromagnetic domain wall on the spin wave function of the electron. We have employed the Borns approximation and the Matsubara’s Green’s function method to study the influence of the scattering of electron with the wall domain. The paper is divided in the following way. In Section 2, we discuss about the mechanism of electron scattering with the domain wall, in the Section 3, we verify the influence of electron-wall domain interaction in the current and finally, in the last section, Section 4, we present the final remarks.

We use the Born’s expansion of

where

where

as T is the transition matrix, given by the Lipmann-Schwinger’s equation

and

We consider J = 1.

as n being the number of times that the V operators enters,

and

where x' corresponds to the region of x into the ferromagnetic wall domain. We have that

where e is the electron charge and

The integral in the Equation (12) was solved approximately using the Maple program as

where

Such potential is plotted in

We obtain a very complicated expression for the wave function of the electron after the scattering with the ferromagnetic wall domain however, in a combination of two polarization states. The presence of the coefficient

The Hamiltonian of the electron that interacts with the domain wall can be written as [

where

V is given by Equation (10).

Making the transformation of the spin operators

we have for the Hamiltonian

where _{i} and A_{i}. The contribution of the interaction between electron with domain wall for the electric current operator

We use the Matsubara’s Green function method at finite temperature [

as

where v is the Fermi’s velocity.

In

In summary, we have studied the scattering between the electrons with the spherical domain wall. We have used the Born’s approximation for the S scattering matrix. We obtain a large influence of the scattering on the spin wave function of the electron. We also obtain the contribution of the electron-wall domain interaction on the electric conductivity where it is obtained a peak of resonance in the conductivity for one value of

From a general way, it is well known that the study of the electron scattering with the

wall domain can generate a different way to generate a spin current spin polarized based on the Hall effect of spin caused by spin-dependent scattering of electrons in thin films [

This work was partially supported by the Brazilian agencies FAPEMIG, CAPES, CNPq and CEFET-MG.

Lima, L.S. (2016) Electron-Domain Wall Interaction with a Ferromagnetic Spherical Domain Wall. Jour- nal of Modern Physics, 7, 1635-1643. http://dx.doi.org/10.4236/jmp.2016.713148