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All-optical switching of the magnetization in magnetic nanostructures by femtosecond circularly polarized laser pulses has been demonstrated in several systems. We present a Landau-Lifshitz-Lambda (LLL) model which describes the…

Optics · Physics 2020-11-23 Marco Menarini , Vitaliy Lomakin

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 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

The nonlinearity of magnetization precession and spin waves is a cornerstone of contemporary magnonics. We investigate nonlinear magnetization dynamics in a thin epitaxial iron film driven by femtosecond laser pulses in regimes of…

Materials Science · Physics 2026-05-28 P. I. Gerevenkov , L. A. Shelukhin , Ia. A. Filatov , P. A. Dvortsova , A. M. Kalashnikova

Dynamic relaxation for nonlinear magnetization excitation is analyzed. For direct processes, such as magnon-electron scattering and two-magnon scattering, the relaxation rate is determined from the linear case simply by utilizing the…

Materials Science · Physics 2009-11-07 Vladimir L. Safonov , H. Neal Bertram

The ability to experimentally map the three-dimensional structure and dynamics in bulk and patterned three-dimensional ferromagnets is essential both for understanding fundamental micromagnetic processes, as well as for investigating…

We consider the Landau-Lifshitz-Gilbert equation (LLG) that models time-dependent micromagnetic phenomena. We propose a full discretization that employs first-order finite elements in space and a BDF2-type two-step method in time. In each…

Numerical Analysis · Mathematics 2026-02-11 Michele Aldé , Michael Feischl , Dirk Praetorius

We consider a lowest-order finite element discretization of the nonlinear system of Maxwell's and Landau-Lifshitz-Gilbert equations (MLLG). Two algorithms are proposed to numerically solve this problem, both of which only require the…

Numerical Analysis · Mathematics 2017-01-30 L'ubomir Banas , Marcus Page , Dirk Praetorius

When nano-magnets are coupled to random external sources, their magnetization becomes a random variable, whose properties are defined by an induced probability density, that can be reconstructed from its moments, using the Langevin…

Statistical Mechanics · Physics 2017-03-21 Stam Nicolis , Pascal Thibaudeau , Julien Tranchida

The paper is concerned with the analysis of an evolutionary model for magnetoviscoelastic materials in two dimensions. The model consists of a Navier-Stokes system featuring a dependence of the stress tensor on elastic and magnetic terms, a…

Analysis of PDEs · Mathematics 2019-04-16 Martin Kalousek , Joshua Kortum , Anja Schlömerkemper

We examine a stochastic Landau-Lifshitz-Gilbert equation for a frustrated ferromagnet with competing first and second order exchange interactions exposed to deterministic and random spin transfer torques in form of transport noise. We prove…

Probability · Mathematics 2023-06-29 Beniamin Goldys , Chunxi Jiao , Christof Melcher

In this paper, we first prove the local-in-time existence of the evolutionary model for magnetoelasticity with finite initial energy by employing the nonlinear iterative approach given in \cite{Jiang-Luo-2019-SIAM} to deal with the…

Analysis of PDEs · Mathematics 2019-04-23 Ning Jiang , Hui Liu , Yi-Long Luo

A new way of magnetization switching employing both the spin-transfer torque and the torque by a magnetic field is proposed. The solution of the Landau-Lifshitz-Gilbert equation shows that the dynamics of the magnetization in the initial…

Mesoscale and Nanoscale Physics · Physics 2009-11-11 Hirofumi Morise , Shiho Nakamura

Recent theoretical and experimental advances show that the inertia of magnetization emerges at sub-picoseconds and contributes to the ultrafast magnetization dynamics which cannot be captured intrinsically by the LLG equation. Therefore, as…

Numerical Analysis · Mathematics 2021-08-09 Panchi Li , Lei Yang , Jin Lan , Rui Du , Jingrun Chen

We propose a novel model which efficiently describes the magnetization dynamics in a magnetic bilayer system. By applying a particular gauge transformation to the Landau-Lifshitz-Gilbert (LLG) equation, we successfully convert the model…

Mesoscale and Nanoscale Physics · Physics 2024-05-01 Xin-Wei Jin , Zhan-Ying Yang , Zhimin Liao , Guangyin Jing , Wen-Li Yang

We demonstrate the existence of stable time dependent solutions of the Landau-Lifshitz model with a constant external magnetic field. We find such solutions in all topological sectors, including N=0. We discuss some of their properties.

High Energy Physics - Theory · Physics 2009-10-30 B. Piette , W. J. Zakrzewski

In this paper, we first derive the compressible Navier-Stokes/Landau-Lifshitz-Gilbert (NS-LLG) model for magnetoelastic materials via the energetic variational approach (EnVarA). It is important to emphasize that the manner in which the…

Analysis of PDEs · Mathematics 2026-04-23 Boling Guo , Ning Jiang , Hui Liu , Yi-Long Luo , Teng-Fei Zhang

We develop an analytical model for describing the magnetization dynamics in ferromagnetic metal nanoparticles, which is based on the coupled system of the Landau-Lifshitz-Gilbert (LLG) and Maxwell equations. By solving Maxwell's equations…

Mesoscale and Nanoscale Physics · Physics 2014-07-29 S. I. Denisov , T. V. Lyutyy , B. O. Pedchenko , H. V. Babych

The numerical approximation for the Landau-Lifshitz equation, the dynamics of magnetization in a ferromagnetic material, is taken into consideration. This highly nonlinear equation, with a non-convex constraint, has several equivalent…

Analysis of PDEs · Mathematics 2019-07-05 Jingrun Chen , Cheng Wang , Changjian Xie

We present an eigenvalue-based approach for studying the magnetization dynamics in magnetic nanostructures driven by spintronic excitations, such as spin transfer torque and spin orbit torque. The approach represents the system dynamics in…

Applied Physics · Physics 2022-03-25 Zhuonan Lin , Iana Volvach , Xueyang Wang , Vitaliy Lomakin