# A simple treatment of the ''scattering-in'' term of the Boltzmann equation for multilayers

## Abstract

We present a simple approximation for treating anisotropic scattering within the semiclassical Boltzmann equation for current in plane geometry in magnetic multilayers. This approximation can be used to qualitatively account for the forward scattering that is neglected in the lifetime approximation, and requires only one additional parameter. For the case of a bulk material its effect is a simple renormalization of the scattering rate. The simplicity of this term has allowed quick and simple solution to the Boltzmann equation for magnetic multilayers using realistic band structures. When we use the band structures for Cu|Co multilayers obtained from first-principles calculations, we find an increase in the resistance of the multilayer, compared to the solution without the scattering-in term, due to the higher scattering rates needed to fit the same bulk conductivities. The giant-magnetoresistance ratio is also changed when the vertex corrections are included. (c) 2000 American Institute of Physics.

- Authors:

- Computational Physics and Engineering Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831-6114 (United States)
- Metals and Ceramics Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831-6114 (United States)

- Publication Date:

- OSTI Identifier:
- 20216230

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Applied Physics

- Additional Journal Information:
- Journal Volume: 87; Journal Issue: 9; Other Information: PBD: 1 May 2000; Journal ID: ISSN 0021-8979

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; BOLTZMANN EQUATION; LAYERS; COPPER; COBALT; SCATTERING; ELECTRONIC STRUCTURE; MAGNETORESISTANCE; ELECTRIC CONDUCTIVITY; THEORETICAL DATA

### Citation Formats

```
Zhang, X.-G., and Butler, W. H.
```*A simple treatment of the ''scattering-in'' term of the Boltzmann equation for multilayers*. United States: N. p., 2000.
Web. doi:10.1063/1.373286.

```
Zhang, X.-G., & Butler, W. H.
```*A simple treatment of the ''scattering-in'' term of the Boltzmann equation for multilayers*. United States. doi:10.1063/1.373286.

```
Zhang, X.-G., and Butler, W. H. Mon .
"A simple treatment of the ''scattering-in'' term of the Boltzmann equation for multilayers". United States. doi:10.1063/1.373286.
```

```
@article{osti_20216230,
```

title = {A simple treatment of the ''scattering-in'' term of the Boltzmann equation for multilayers},

author = {Zhang, X.-G. and Butler, W. H.},

abstractNote = {We present a simple approximation for treating anisotropic scattering within the semiclassical Boltzmann equation for current in plane geometry in magnetic multilayers. This approximation can be used to qualitatively account for the forward scattering that is neglected in the lifetime approximation, and requires only one additional parameter. For the case of a bulk material its effect is a simple renormalization of the scattering rate. The simplicity of this term has allowed quick and simple solution to the Boltzmann equation for magnetic multilayers using realistic band structures. When we use the band structures for Cu|Co multilayers obtained from first-principles calculations, we find an increase in the resistance of the multilayer, compared to the solution without the scattering-in term, due to the higher scattering rates needed to fit the same bulk conductivities. The giant-magnetoresistance ratio is also changed when the vertex corrections are included. (c) 2000 American Institute of Physics.},

doi = {10.1063/1.373286},

journal = {Journal of Applied Physics},

issn = {0021-8979},

number = 9,

volume = 87,

place = {United States},

year = {2000},

month = {5}

}