Module: FM|NM Interface
The page is under development.
FM||NM module models the interface between a ferromagnet and a non-magnet, capturing the spin-torque on the magnet at the interface.
Model Description
The FM|NM module is modeled with a series and shunt conductances as shown below:
Where the shunt is on the "NM" side and the spin current flowing through it is the spin-torque, which can be provided to an LLG module.
Parameters
| Parameter | Symbol | Units |
| Conductance | ||
| Polarization | - | |
| Slonczewski like torque coeff. | - | |
| FIeld like torque coeff. | - |
Model Conductance Matrices
Magnet Rotation
The matrices above are for magnet in +z direction. To obtain conductances matrices for a magnet is any general direction "m",we need to basis transformation these matrix, the transformation matrix being obtained by Rodrigues formula. The rotation matrix is given as:
where, and
are equatorial and azimuthal angles referenced from the
direction. This information is provided to the module using the third terminal "m".
The matrices can then be rotated using the transformation formula:
Download
The module, as a part of the library, can be downloaded here.
References
- A. Brataas, G. E. W. Bauer, and P. J. Kelly, “Non-collinear magnetoelectronics,” Phys. Rep., vol. 427, no. 4, pp. 157–255, Apr. 2006
- S. Srinivasan, V. Diep, B. Behin-Aein, A. Sarkar, and S. Datta, “Modeling Multi-Magnet Networks Interacting Via Spin Currents,” ArXiv13040742 Cond-Mat, Apr. 2013