A MEAN-FIELD MODEL FOR SPIN DYNAMICS IN MULTILAYERED FERROMAGNETIC MEDIA

In this paper, we develop a mean-field model for describing the dynamics of spin-transfer torque in multilayered ferromagnetic media. Specifically, we use the techniques of Wigner transform and moment closure to connect the underlying physics at different scales and reach a macroscopic model for the dynamics of spin coupled with the magnetization within the material. This provides a further understanding of the linear response model proposed by Zhang, Levy, and Fert [Phys. Rev. Lett., 88 (2002), 236601], and in particular we get an extra relaxation term which helps to stabilize the system. We develop efficient numerical methods to overcome the stiffness appearing in this new mean-field model and present several examples to analyze and show its validity.