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We present efficient numerical methods for the simulation of small magnetization oscillations in three-dimensional micromagnetic systems. Magnetization dynamics is described by the Landau-Lifshitz-Gilbert (LLG) equation, linearized in the…

Computational Physics · Physics 2023-01-18 Massimiliano d'Aquino , Riccardo Hertel

In this paper we present an overview of recent progress made in the understanding of the spin-torque induced magnetization dynamics in nanodevices using mesoscopic micromagnetic simulations. We first specify how a spin-torque term may be…

Mesoscale and Nanoscale Physics · Physics 2009-11-13 D. V. Berkov , J. Miltat

Magnetic Skyrmions belong to the most interesting spin structures for the development of future information technology as they have been predicted to be topologically protected. To quantify their stability, we use an innovative multiscale…

Materials Science · Physics 2017-07-19 Andrea De Lucia , Kai Litzius , Benjamin Krüger , Oleg A. Tretiakov , Mathias Kläui

The Landau-Lifshitz equation governing magnetization dynamics is written in terms of the amplitudes of normal modes associated with the micromagnetic system's appropriate ground state. This results in a system of nonlinear ordinary…

Other Condensed Matter · Physics 2022-01-19 S. Perna , F. Bruckner , C. Serpico , D. Suess , M. d'Aquino

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…

Micromagnetics depends on high-fidelity numerical methods for magnetization dynamics. This work proposes a third-order temporal accuracy scheme for the Landau-Lifshitz-Gilbert equation, addressing accuracy-efficiency trade-offs in existing…

Mathematical Physics · Physics 2025-11-17 Changjian Xie , Cheng Wang

We consider a multiscale strategy addressing the disparate scales in the Landau-Lifschitz equations in micro-magnetism. At the microscopic scale, the dynamics of magnetic moments are driven by a high frequency field. On the macroscopic…

Numerical Analysis · Mathematics 2017-03-16 Doghonay Arjmand , Stefan Engblom , Gunilla Kreiss

Crystallographic lattice defects strongly influence dynamical properties of magnetic materials at both microscopic and macroscopic length scales. A multi-scale approach to magnetisation dynamics, which is presented in this paper, accurately…

Materials Science · Physics 2020-02-05 É. Méndez , M. Poluektov , G. Kreiss , O. Eriksson , M. Pereiro

Magnetization reversal in magnetic nanostructures is investigated numerically over time-scales ranging from fast switching processes on a picosecond scale to thermally activated reversal on a microsecond time-scale. A simulation of the…

Statistical Mechanics · Physics 2015-06-24 D. Hinzke , U. Nowak

Numerical integration of a stochastic Landau-Lifshitz-Gilbert equation is used to study dynamic processes in single-domain nanoscale magnets at nonzero temperatures. Special attention is given to including thermal fluctuations as a Langevin…

Materials Science · Physics 2009-10-31 Gregory Brown , M. A. Novotny , Per Arne Rikvold

Micromagnetics simulation based on the classical Landau-Lifshitz-Gilbert (LLG) equation has long been a powerful method for modeling magnetization dynamics and reversal of three-dimensional (3D) magnets. For two-dimensional (2D) magnets,…

Mesoscale and Nanoscale Physics · Physics 2022-09-13 Essa M. Ibrahim , Shufeng Zhang

A composite multiferroic chain with an interfacial linear magneto-electric coupling is used to study the magnetic and electric responses to an external magnetic or electric field. The simulation uses continuous spin dynamics through the…

Mesoscale and Nanoscale Physics · Physics 2015-08-25 Zidong Wang , Malcolm J. Grimson

Magnetic skyrmions widely exist in a diverse range of magnetic systems, including chiral magnets with a non-centrosymmetric structure characterized by Dzyaloshinkii-Moriya interaction~(DMI). In this study, we propose a generalized…

Numerical Analysis · Mathematics 2023-04-13 Panchi Li , Shuting Gu , Jin Lan , Jingrun Chen , Weiqing Ren , Rui Du

High-fidelity numerical simulation serves as a cornerstone for exploring magnetization dynamics in micromagnetics. This work introduces a novel third-order temporally accurate and stable numerical scheme for the Landau-Lifshitz-Gilbert…

Mathematical Physics · Physics 2025-11-27 Changjian Xie

We present a simple and fast method to simulate spin-torque driven magnetisation dynamics in nano-pillar spin-valve structures. The approach is based on the coupling between a spin transport code based on random matrix theory and a…

Mesoscale and Nanoscale Physics · Physics 2017-09-27 Simone Borlenghi , M. R. Mahani , Hans Fangohr , Matteo Franchin , Anna Delin , Jonas Fransson

The current-induced magnetization dynamics of a spin valve are studied using a macrospin (single domain) approximation and numerical solutions of a generalized Landau-Lifshitz-Gilbert equation. For the purpose of quantitative comparison…

Mesoscale and Nanoscale Physics · Physics 2009-11-11 Jiang Xiao , A. Zangwill , M. D. Stiles

We present a method for performing atomistic spin dynamic simulations. A comprehensive summary of all pertinent details for performing the simulations such as equations of motions, models for including temperature, methods of extracting…

Materials Science · Physics 2014-04-04 B. Skubic , J. Hellsvik , L. Nordström , O. Eriksson

Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…

Numerical Analysis · Mathematics 2012-01-18 A. J. Roberts , Tony MacKenzie , J. E. Bunder

Atomistic-continuum multiscale modelling is becoming an increasingly popular tool for simulating the behaviour of materials due to its computational efficiency and reliable accuracy. In the case of ferromagnetic materials, the atomistic…

Computational Physics · Physics 2019-02-01 Doghonay Arjmand , Mikhail Poluektov , Gunilla Kreiss

Various applications ranging from spintronic devices, giant magnetoresistance sensors, and magnetic storage devices, include magnetic parts on very different length scales. Since the consideration of the Landau-Lifshitz-Gilbert equation…

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