A three-dimensional spin-diffusion model for micromagnetics

Claas Abert; Michele Ruggeri; Florian Bruckner; Christoph Vogler; Gino Hrkac; Dirk Praetorius; Dieter Suess

doi:10.1038/srep14855

A three-dimensional spin-diffusion model for micromagnetics

Claas Abert^*
, Michele Ruggeri
, Florian Bruckner
, Christoph Vogler
, Gino Hrkac
, Dirk Praetorius
, Dieter Suess

^*Corresponding author for this work

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

58 Citations (Scopus)

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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.

Original language	English
Article number	14855
Number of pages	11
Journal	Scientific Reports
Volume	5
DOIs	https://doi.org/10.1038/srep14855
Publication status	Published - 7 Oct 2015

Funding

The financial support by the Austrian Federal Ministry of Science, Research and Economy and the National Foundation for Research, Technology and Development as well as the Austrian Science Fund (FWF) under grant W1245 and F4102 SFB ViCoM, the innovative projects initiative of Vienna University of Technology, the Vienna Science and Technology Fund (WWTF) under grant MA14-044, and the Royal Society under UF080837 is gratefully acknowledged.

Keywords

micromagnetics
three-dimensional spin-diffusion model
Landau-Lifshitz-Gilbert equation
spin-accumulation

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10.1038/srep14855Licence: CC BY 4.0

Abert-etal-SR2015-A-three-dimensional-spin-diffusion model-micromagneticsFinal published version, 860 KBLicence: CC BY 4.0

Cite this

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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.",

keywords = "micromagnetics, three-dimensional spin-diffusion model, Landau-Lifshitz-Gilbert equation, spin-accumulation",

author = "Claas Abert and Michele Ruggeri and Florian Bruckner and Christoph Vogler and Gino Hrkac and Dirk Praetorius and Dieter Suess",

note = "Funding Information: The financial support by the Austrian Federal Ministry of Science, Research and Economy and the National Foundation for Research, Technology and Development as well as the Austrian Science Fund (FWF) under grant W1245 and F4102 SFB ViCoM, the innovative projects initiative of Vienna University of Technology, the Vienna Science and Technology Fund (WWTF) under grant MA14-044, and the Royal Society under UF080837 is gratefully acknowledged.",

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doi = "10.1038/srep14855",

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T1 - A three-dimensional spin-diffusion model for micromagnetics

AU - Abert, Claas

AU - Ruggeri, Michele

AU - Bruckner, Florian

AU - Vogler, Christoph

AU - Hrkac, Gino

AU - Praetorius, Dirk

AU - Suess, Dieter

N1 - Funding Information: The financial support by the Austrian Federal Ministry of Science, Research and Economy and the National Foundation for Research, Technology and Development as well as the Austrian Science Fund (FWF) under grant W1245 and F4102 SFB ViCoM, the innovative projects initiative of Vienna University of Technology, the Vienna Science and Technology Fund (WWTF) under grant MA14-044, and the Royal Society under UF080837 is gratefully acknowledged.

PY - 2015/10/7

Y1 - 2015/10/7

N2 - 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.

AB - 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.

KW - micromagnetics

KW - three-dimensional spin-diffusion model

KW - Landau-Lifshitz-Gilbert equation

KW - spin-accumulation

UR - https://www.scopus.com/pages/publications/84943328508

U2 - 10.1038/srep14855

DO - 10.1038/srep14855

M3 - Article

AN - SCOPUS:84943328508

SN - 2045-2322

VL - 5

JO - Scientific Reports

JF - Scientific Reports

M1 - 14855

ER -

A three-dimensional spin-diffusion model for micromagnetics

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