Young Researchers Workshop:
Multiscale phenomena: modeling, analysis and computation

Spin-polarized transport in ferromagnetic materials

Jingrun Chen

University of California Santa Barbara

Magnetic storage devices rely on the fact that ferromagnetic materials are typically bistable, and that it is possible to switch between different states by applying a magnetic field. Recent developments include magnetoresistance random access memories and race-track memories, with the underlying mechanism known as spin transfer torque, proposed by Slonczweski and Berger independently. In this talk we will discuss the connection between several models for the description of the spin transfer torque at different physical scales. Specifically, we connect the quantum and kinetic descriptions via the Wigner transform, and the kinetic and diffusion models using a moment closure technique. A non-isotropic diffusion term is obtained, independent of the closure assumption. Simulation results will be presented to illustrate the applicability and limit of the different models for magnetic bilayers and domain wall motions. Under certain conditions, we prove that the Boltzmann equation for spin is the semicalssical limit of the Schrodinger equation in the Spinor form.