title: A three-dimensional spin-diffusion model for micromagnetics.
abstract: We solve a time-dependent three-dimensional spin-diffusion model coupled to the Landau-Lifshitz-Gilbert equation numerically. The presented model is validated by comparison to two established spin-torque models: The model of Slonzewski that describes spin-torque in multi-layer structures in the presence of a fixed layer and the model of Zhang and Li that describes current driven domain-wall motion. It is shown that both models are incorporated by the spin-diffusion description, i.e., the nonlocal effects of the Slonzewski model are captured as well as the spin-accumulation due to magnetization gradients as described by the model of Zhang and Li. Moreover, the presented method is able to resolve the time dependency of the spin-accumulation.
authors.affiliation: Christian Doppler Laboratory of Advanced Magnetic Sensing and Materials, Institute of Solid State Physics, Vienna University of Technology, Austria.
authors.forename: Claas
authors.initials: C
authors.lastname: Abert
authors.affiliation: Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria.
authors.forename: Michele
authors.initials: M
authors.lastname: Ruggeri
authors.affiliation: Christian Doppler Laboratory of Advanced Magnetic Sensing and Materials, Institute of Solid State Physics, Vienna University of Technology, Austria.
authors.forename: Florian
authors.initials: F
authors.lastname: Bruckner
authors.affiliation: Institute of Solid State Physics, Vienna University of Technology, Austria.
authors.forename: Christoph
authors.initials: C
authors.lastname: Vogler
authors.affiliation: College of Engineering, Mathematics and Physical Sciences, University of Exeter, United Kingdom.
authors.forename: Gino
authors.initials: G
authors.lastname: Hrkac
authors.affiliation: Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria.
authors.forename: Dirk
authors.initials: D
authors.lastname: Praetorius
authors.affiliation: Christian Doppler Laboratory of Advanced Magnetic Sensing and Materials, Institute of Solid State Physics, Vienna University of Technology, Austria.
authors.forename: Dieter
authors.initials: D
authors.lastname: Suess