A self-consistent spin-diffusion model for micromagnetics.

Claas Abert,Christoph Vogler,Florian Bruckner,Aurelien Manchon,Dieter Suess,Michele Ruggeri,Dirk Praetorius

doi:10.1038/s41598-016-0019-y

Claas Abert, Christoph Vogler + Show 5 more

Open Access

https://doi.org/10.1038/s41598-016-0019-y

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Abstract

We propose a three-dimensional micromagnetic model that dynamically solves the Landau-Lifshitz-Gilbert equation coupled to the full spin-diffusion equation. In contrast to previous methods, we solve for the magnetization dynamics and the electric potential in a self-consistent fashion. This treatment allows for an accurate description of magnetization dependent resistance changes. Moreover, the presented algorithm describes both spin accumulation due to smooth magnetization transitions and due to material interfaces as in multilayer structures. The model and its finite-element implementation are validated by current driven motion of a magnetic vortex structure. In a second experiment, the resistivity of a magnetic multilayer structure in dependence of the tilting angle of the magnetization in the different layers is investigated. Both examples show good agreement with reference simulations and experiments respectively.

Highlights

Spin-tronic devices are versatile candidates for a variety of applications including sensors[1,2], storage devices[3], and frequency generators[4,5]
According to the micromagnetic model, the magnetization dynamics in a three-dimensional magnetic domain ω is described by the Landau-Lifshitz-Gilbert equation (LLG)
The resulting potential is compared to a sine parameterization a + b sin[2] (θ/2) that is often used to describe the giant magnetoresistance (GMR) effect in such a stack[18] in the presence of some in-plane current

Summary

In order to solve this problem with the self-consistent model the additional

The resistivity of this structure heavily depends on the tilting angle θ of the magnetization in ω1 and ω2. In order to calculate the electric resistivity with the diffusion model, the potential difference between the contacts Γ1 and Γ2 is computed for a given current inflow. The resulting potential is compared to a sine parameterization a + b sin[2] (θ/2) that is often used to describe the GMR effect in such a stack[18] in the presence of some in-plane current. The presented simulations, suggest that the potential and the resistivity of the stack in the presence of out-of-plane currents is not well described by a sine, but has a much narrower peak for certain choices of material parameters. With increasing β′ the perturbations of u gain influence on the solution of s which results in a distorsion of the sinusoidal response as seen in Figs 3 and 4

Conclusion

A Discretization