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A spin wave is the disturbance of intrinsic spin order in magnetic materials. In this paper, a spin wave in the Landau-Lifshitz-Gilbert equation is obtained based on the assumption that the spin wave maintains its shape while it propagates…

Mesoscale and Nanoscale Physics · Physics 2019-10-25 Zhiwei Sun , Jingrun Chen

The precession and damping of a collinear magnetization displaced from its equilibrium are described by the Landau-Lifshitz-Gilbert equation. For a noncollinear magnetization, it is not known how the damping should be described. We use…

Materials Science · Physics 2015-02-09 Zhe Yuan , Kjetil M. D. Hals , Yi Liu , Anton A. Starikov , Arne Brataas , Paul J. Kelly

We discuss the dissipative diffusion-type term of the form $\mathbf{m}\times\nabla^2\partial_t\mathbf{m}$ in the phenomenological Landau-Lifshitz equation of ferromagnetic precession, which describes enhanced Gilbert damping of…

Mesoscale and Nanoscale Physics · Physics 2009-11-13 Yaroslav Tserkovnyak , E. M. Hankiewicz , Giovanni Vignale

The stochastic Landau-Lifshitz equation is used to investigate the relaxation process and equilibrium magnetization of interacting assembly of superparamagnetic nanoparticles uniformly distributed in a nonmagnetic matrix. For weakly…

Mesoscale and Nanoscale Physics · Physics 2021-01-01 N. A. Usov , O. N. Serebryakova

Here we report the possibility to excite ultra-short spin waves in ferromagnetic thin-films by using time-harmonic electromagnetic fields with terahertz frequency. Such ultra-fast excitation requires to include inertial effects in the…

Mesoscale and Nanoscale Physics · Physics 2024-04-11 Massimiliano d'Aquino , Salvatore Perna , Matteo Pancaldi , Riccardo Hertel , Stefano Bonetti , Claudio Serpico

Quasi particle based (e.g. Boltzmann equation) studies of spin wave transport often assume that their scattering rates follow the simple form $\eta=\alpha \omega$, with the Gilbert damping $\alpha$ and frequency $\omega$. In this work, we…

Mesoscale and Nanoscale Physics · Physics 2026-05-11 Mexx. E. Y. Regout , Bertrand Dupé , Matthieu J. Verstraete

A keen interest towards technological implications of spin-orbit driven magnetization dynamics requests a proper theoretical description, especially in the context of a microscopic framework, to be developed. Indeed, magnetization dynamics…

Mesoscale and Nanoscale Physics · Physics 2018-11-22 Anastasiia A. Pervishko , Mikhail I. Baglai , Olle Eriksson , Dmitry Yudin

Thermal fluctuations of nanomagnets driven by spin-polarized currents are treated via the Landau-Lifshitz-Gilbert equation as generalized to include both the random thermal noise field and Slonczewski spin-transfer torque terms. The…

Statistical Mechanics · Physics 2017-09-26 Y. P. Kalmykov , D. Byrne , W. T. Coffey , W. J. Dowling , S. V. Titov , J. E. Wegrowe

The magnetization dynamics of ferromagnets are often formulated in terms of the Landau-Lifshitz-Gilbert (LLG) equation. The reactive part of this equation describes the response of the magnetization in terms of effective fields, whereas the…

Mesoscale and Nanoscale Physics · Physics 2015-05-27 Arne Brataas , Yaroslav Tserkovnyak , Gerrit E. W. Bauer

The phenomenological Landau-Lifshitz-Gilbert (LLG) equation of motion remains as the cornerstone of contemporary magnetisation dynamics studies, wherein the Gilbert damping parameter has been attributed to first-order relativistic effects.…

Other Condensed Matter · Physics 2018-06-28 Ritwik Mondal , Marco Berritta , Peter M. Oppeneer

Using first-principles electronic structure calculation, we demonstrate the spin dissipation process in bulk Fe by orbital excitations within the energy bands of pure spin character. The variation of orbitals in the intraband transitions…

Mesoscale and Nanoscale Physics · Physics 2025-04-02 Yue Chen , Haoran Chen , Xi Shen , Weizhao Chen , Yi Liu , Yizheng Wu , Zhe Yuan

The deterministic Landau-Lifshitz-Gilbert equation has been used to investigate the nonlinear dynamics of magnetization and the specific loss power in magnetic nanoparticles with uniaxial anisotropy driven by a rotating magnetic field,…

Mesoscale and Nanoscale Physics · Physics 2012-12-13 I. Nandori , J. Racz

In this paper, we consider spin-diffusion Landau-Lifshitz-Gilbert equations (SDLLG), which consist of the time-dependent Landau-Lifshitz-Gilbert (LLG) equation coupled with a time-dependent diffusion equation for the electron spin…

Analysis of PDEs · Mathematics 2020-10-01 Giovanni Di Fratta , Ansgar Jüngel , Dirk Praetorius , Valeriy Slastikov

Spin precession in magnetic materials is commonly modelled with the classical phenomenological Landau-Lifshitz-Gilbert (LLG) equation. Based on a quantized spin+environment Hamiltonian, we here derive a general spin operator equation of…

Quantum Physics · Physics 2022-11-02 J. Anders , C. R. J. Sait , S. A. R. Horsley

Ferromagnetic materials tend to develop very complex magnetization patterns whose time evolution is modeled by the so-called Landau-Lifshitz-Gilbert equation (LLG). In this paper, we construct time-periodic solutions for LLG in the regime…

Analysis of PDEs · Mathematics 2010-06-25 Alexander Huber

Films of metal-insulator nanogranular composites M$_x$D$_{100-x}$ with different compositions and atomic percentage of metal and dielectric phases (M = Fe, Co, Ni, CoFeB; D = Al$_2$O$_3$, SiO$_2$, ZrO$_2$; x $\approx$ 15-60 at.%) are…

Materials Science · Physics 2024-07-26 A. B. Drovosekov , M. Yu. Dmitrieva , A. V. Sitnikov , S. N. Nikolaev , V. V. Rylkov

Nonlinear magnetization dynamics excited by spin-transfer effect with feedback current is studied both numerically and analytically. The numerical simulation of the Landau-Lifshitz-Gilbert equation indicates the positive Lyapunov exponent…

Mesoscale and Nanoscale Physics · Physics 2019-11-27 Tomohiro Taniguchi , Nozomi Akashi , Hirofumi Notsu , Masato Kimura , Hiroshi Tsukahara , Kohei Nakajima

Using a scattering matrix approach, the precession of the magnetization of a ferromagnet is shown to transfer spins into adjacent normal metal layers. This ``pumping'' of spins slows down the precession corresponding to an enhanced Gilbert…

Mesoscale and Nanoscale Physics · Physics 2009-11-07 Yaroslav Tserkovnyak , Arne Brataas , Gerrit E. W. Bauer

Numerical integration of the Landau-Lifshitz-Gilbert equation with thermal fluctuations is used to study the dynamic response of single-domain nanomagnets to rapid changes in the applied magnetic field. The simulation can resolve…

Materials Science · Physics 2007-05-23 G. Brown , M. A. Novotny , P. A. Rikvold

Energy dissipation via spin excitations is investigated for a hard ferromagnetic tip scanning a soft magnetic monolayer. We use the classical Heisenberg model with Landau-Lifshitz-Gilbert (LLG)-dynamics including a stochastic field…

Other Condensed Matter · Physics 2009-08-03 Martin P. Magiera , Lothar Brendel , Dietrich E. Wolf , Ulrich Nowak