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ISBN: 3110307103 9783110307108 3110307111 9783110307115 3110306999 9783110306996 9781306462488 1306462487 Year: 2014 Publisher: Berlin : Walter de Gruyter GmbH & Co. KG,
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This monograph examines magnetization dynamics at elevated temperatures which can be described by the stochastic Landau-Lifshitz-Gilbert equation (SLLG). The first part of the book studies the role of noise in finite ensembles of nanomagnetic particles: we show geometric ergodicity of a unique invariant measure of Gibbs type and study related properties of approximations of the SLLG, including time discretization and Ginzburg-Landau type penalization. In the second part we propose an implementable space-time discretization using random walks to construct a weak martingale solution of the corresponding stochastic partial differential equation which describes the magnetization process of infinite spin ensembles. The last part of the book is concerned with a macroscopic deterministic equation which describes temperature effects on macro-spins, i.e. expectations of the solutions to the SLLG. Furthermore, comparative computational studies with the stochastic model are included. We use constructive tools such as e.g. finite element methods to derive the theoretical results, which are then used for computational studies. The numerical experiments motivate an interesting interplay between inherent geometric and stochastic effects of the SLLG which still lack a rigorous analytical understanding: the role of space-time white noise, possible finite time blow-up behavior of solutions, long-time asymptotics, and effective dynamics.
Book
ISBN: 3036557741 3036557733 Year: 2022 Publisher: Basel MDPI - Multidisciplinary Digital Publishing Institute
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The Special Issue on Recent Advances in Nanomagnetism is a compilation of articles, addressing various aspects of magnetic properties and behaviour in low dimensional magnetic materials. One contribution addresses the novel magnetic properties in a nanohybrid of iron oxide and carbide nanoparticles grown in diamond. Magnetic textures, such as skyrmion structures, form an important area of research in nanomagnetism, this forms the topic of another contribution. Several aspects of magnetisation dynamics are addressed in other contributions and relate to the developments of microresonators and microantennas applied to the study of magnetic nanostructures; the ferromagnetic resonance behaviour in nanodot systems are also considered. Materials development forms an important area of study in nanomagnetism, and, as such, the preparation conditions, such as annealing under an applied field, can have important effects on the magnetic properties of thin films and low dimensional structures. Such considerations form the study of one of the contributions. Perpendicular magnetic anisotropy has a number of important applications in magnetic storage materials; this is the subject of two further contributions.
Information technology industries --- Computer science --- magnetic nanohybrid materials --- nanodiamonds --- nanoparticles --- iron carbides --- Fe3C --- spinel-type iron oxide --- Mössbauer spectroscopy --- skyrmions --- micromagnetic simulations --- geometric pinning --- finite-element modelling --- ferromagnetic resonance --- microantenna --- microresonator --- magnetic relaxation --- thin films --- nanostructures --- [Co/Ni]2/PtMn multilayers --- magnetic field annealing --- hysteresis loop vertical shift --- exchange coupling --- nanomagnetism --- magnetic multilayers --- micromagnetism --- magnetization dynamics --- magnetic nanodots --- coupled magnetic thin films --- perpendicular magnetic anisotropy --- n/a --- Mössbauer spectroscopy
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