Summary: Spin-polarized currents in ferromagnetic multilayers
Carlos J. GarciŽa-Cervera a,*, Xiao-Ping Wang b
Mathematics Department, University of California, Santa Barbara, CA 93106, United States
Mathematics Department, Hong Kong University of Science and Technology, Kowloong, Hong Kong
Received 20 March 2006; received in revised form 28 September 2006; accepted 17 October 2006
We present a semi-implicit numerical method for micromagnetics simulations, in the presence of spin-currents. The
dynamics of the magnetization are described by the LandauLifshitzGilbert equation, while the dynamics of the spin
are described by a diffusion equation with discontinuous coefficients. The complexity of the method presented is compa-
rable to that of solving the linear heat equation with the Backward Euler method. To illustrate the procedure, we carry out
three dimensional simulations of the magnetization reversal process in a magnetic multilayer when a current flows perpen-
dicular to the layers. Spin-polarized currents are shown to decrease the coercive field, and to induce magnetization reversal
even in the absence of external magnetic fields.
Ó 2006 Elsevier Inc. All rights reserved.
Keywords: Micromagnetics; Spin polarized transfer; LandauLifshitzGilbert
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. The discovery of the Giant Magneto-