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用于现代磁阻随机存取存储器(MRAM)器件模拟的有限元方法

Finite Element Approach for the Simulation of Modern MRAM Devices.

作者信息

Fiorentini Simone, Jørstad Nils Petter, Ender Johannes, de Orio Roberto Lacerda, Selberherr Siegfried, Bendra Mario, Goes Wolfgang, Sverdlov Viktor

机构信息

Christian Doppler Laboratory for Nonvolatile Magnetoresistive Memory and Logic at the Institute for Microelectronics, TU Wien, Gußhausstraße 27-29/E360, 1040 Vienna, Austria.

Institute for Microelectronics, TU Wien, Gußhausstraße 27-29/E360, 1040 Vienna, Austria.

出版信息

Micromachines (Basel). 2023 Apr 22;14(5):898. doi: 10.3390/mi14050898.

DOI:10.3390/mi14050898
PMID:37241522
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10221272/
Abstract

Because of their nonvolatile nature and simple structure, the interest in MRAM devices has been steadily growing in recent years. Reliable simulation tools, capable of handling complex geometries composed of multiple materials, provide valuable help in improving the design of MRAM cells. In this work, we describe a solver based on the finite element implementation of the Landau-Lifshitz-Gilbert equation coupled to the spin and charge drift-diffusion formalism. The torque acting in all layers from different contributions is computed from a unified expression. In consequence of the versatility of the finite element implementation, the solver is applied to switching simulations of recently proposed structures based on spin-transfer torque, with a double reference layer or an elongated and composite free layer, and of a structure combining spin-transfer and spin-orbit torques.

摘要

由于其非易失性和简单的结构,近年来对磁阻随机存取存储器(MRAM)器件的兴趣一直在稳步增长。可靠的模拟工具能够处理由多种材料组成的复杂几何形状,为改进MRAM单元的设计提供了有价值的帮助。在这项工作中,我们描述了一种基于朗道-里夫希茨-吉尔伯特方程有限元实现的求解器,该方程与自旋和电荷漂移-扩散形式主义相结合。从一个统一的表达式计算出不同贡献在所有层中作用的转矩。由于有限元实现的通用性,该求解器被应用于基于自旋转移转矩的最近提出的结构的开关模拟,这些结构具有双参考层或细长复合自由层,以及一种结合了自旋转移和自旋轨道转矩的结构。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b46f/10221272/fbe9f114d693/micromachines-14-00898-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b46f/10221272/8be6dc605ed6/micromachines-14-00898-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b46f/10221272/d648e8ea8eea/micromachines-14-00898-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b46f/10221272/f44e923bdbf8/micromachines-14-00898-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b46f/10221272/7f6d819e771c/micromachines-14-00898-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b46f/10221272/35e90e6b28e1/micromachines-14-00898-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b46f/10221272/fbe9f114d693/micromachines-14-00898-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b46f/10221272/8be6dc605ed6/micromachines-14-00898-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b46f/10221272/d648e8ea8eea/micromachines-14-00898-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b46f/10221272/f44e923bdbf8/micromachines-14-00898-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b46f/10221272/7f6d819e771c/micromachines-14-00898-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b46f/10221272/35e90e6b28e1/micromachines-14-00898-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b46f/10221272/fbe9f114d693/micromachines-14-00898-g006.jpg

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本文引用的文献

1
Spin and charge drift-diffusion in ultra-scaled MRAM cells.超小型 MRAM 单元中的自旋和电荷输运。
Sci Rep. 2022 Dec 5;12(1):20958. doi: 10.1038/s41598-022-25586-4.
2
Nonresonant amplification of spin waves through interface magnetoelectric effect and spin-transfer torque.通过界面磁电效应和自旋转移矩实现自旋波的非共振放大。
Sci Rep. 2021 Aug 3;11(1):15692. doi: 10.1038/s41598-021-95267-1.
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Single-shot dynamics of spin-orbit torque and spin transfer torque switching in three-terminal magnetic tunnel junctions.三端磁性隧道结中自旋轨道转矩和自旋转移转矩切换的单次动力学
Micromachines (Basel). 2023 Aug 11;14(8):1581. doi: 10.3390/mi14081581.
Nat Nanotechnol. 2020 Feb;15(2):111-117. doi: 10.1038/s41565-019-0607-7. Epub 2020 Jan 27.
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A cryogenic spin-torque memory element with precessional magnetization dynamics.
Sci Rep. 2019 Jan 28;9(1):803. doi: 10.1038/s41598-018-37204-3.
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Unified treatment of spin torques using a coupled magnetisation dynamics and three-dimensional spin current solver.使用耦合磁化动力学和三维自旋电流求解器对自旋扭矩进行统一处理。
Sci Rep. 2017 Oct 11;7(1):12937. doi: 10.1038/s41598-017-13181-x.
6
A self-consistent spin-diffusion model for micromagnetics.用于磁动力学的自洽自旋扩散模型。
Sci Rep. 2016 Dec 21;6(1):16. doi: 10.1038/s41598-016-0019-y.
7
Spin-polarized transport in ferromagnetic multilayers: An unconditionally convergent FEM integrator.铁磁多层膜中的自旋极化输运:一种无条件收敛的有限元积分器。
Comput Math Appl. 2014 Sep;68(6):639-654. doi: 10.1016/j.camwa.2014.07.010.
8
A three-dimensional spin-diffusion model for micromagnetics.一种用于微磁学的三维自旋扩散模型。
Sci Rep. 2015 Oct 7;5:14855. doi: 10.1038/srep14855.
9
Unified drift-diffusion theory for transverse spin currents in spin valves, domain walls, and other textured magnets.用于自旋阀、畴壁和其他织构磁体中横向自旋电流的统一漂移-扩散理论。
Phys Rev Lett. 2012 Sep 14;109(11):117204. doi: 10.1103/PhysRevLett.109.117204. Epub 2012 Sep 13.
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Electric manipulation of spin relaxation using the spin Hall effect.利用自旋霍尔效应进行自旋弛豫的电操控。
Phys Rev Lett. 2008 Jul 18;101(3):036601. doi: 10.1103/PhysRevLett.101.036601.