Related papers: Recent results for the Landau-Lifshitz equation
The Landau-Lifshitz-Gilbert equation yields a mathematical model to describe the evolution of the magnetization of a magnetic material, particularly in response to an external applied magnetic field. It allows one to take into account…
The dynamics of magnetization near a stable equilibrium in ferromagnetic nanomagnets are examined within the Landau--Lifshitz--Gilbert (LLG) framework. For a small angle precession, the dependence of ferromagnetic resonance (FMR) frequency,…
Propagating, solitary magnetic wave solutions of the Landau-Lifshitz equation with uniaxial, easy-axis anisotropy in thin (two-dimensional) magnetic films are investigated. These localized, nontopological wave structures, parametrized by…
The Landau-Lifshitz equation for the magnetization dynamics of a single-domain magnetic system is solved using the methods of self-organization. The description takes into account the torque due to spin transfer. The potential energy of the…
We consider the coupled system of the Landau--Lifshitz--Gilbert equation and the conservation of linear momentum law to describe magnetic processes in ferromagnetic materials including magnetoelastic effects in the small-strain regime. For…
We exhibit some large variations solutions of the Landau-Lifschitz equations as the exchange coefficient ε^2 tends to zero. These solutions are described by some asymptotic expansions which involve some internals layers by means of…
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.
We show that recently reported precessing solution of Landau-Lifshitz-Gilbert equations in ferromagnetic nanowires is stable under small perturbations of initial data, applied field and anisotropy constant. Linear stability is established…
The question of the uniqueness of energy-momentum tensors in the linearized general relativity and in the linear massive gravity is analyzed without using variational techniques. We start from a natural ansatz for the form of the tensor…
The stochastic Landau--Lifshitz--Gilbert (LLG) equation describes the behaviour of the magnetization under the influence of the effective field consisting of random fluctuations. We first reformulate the equation into an equation the…
The dynamics of magnetisation in a bounded ferromagnet in $\mathbb{R}^d$ ($d=1,2$) at high temperatures can be described by the stochastic Landau--Lifshitz--Bloch (sLLB) equation, which is a vector-valued quasilinear stochastic partial…
We obtain the equations of motion for a ferromagnetic Bose condensate of arbitrary spin in the long wavelength limit. We find that the magnetization of the condensate is described by a non-trivial modification of the Landau-Lifshitz…
We consider the time-dependent Landau-Lifshitz-Gilbert equation. We prove that each weak solution coincides with the (unique) strong solution, as long as the latter exists in time. Unlike available results in the literature, our analysis…
We consider the numerical approximation of a nonlinear system of partial differential equations modeling magnetostriction in the small-strain regime consisting of the Landau--Lifshitz--Gilbert equation for the magnetization and the…
Precise modeling of the magnetization dynamics of nanoparticles with finite size effects at fast varying temperatures is a computationally challenging task. Based on the Landau-Lifshitz-Bloch (LLB) equation we derive a coarse grained model…
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…
The Landau-Lifshitz-Gilbert equation for rigid and saturated ferromagnets is derived using a two-continuum model constructed by H.F. Tiersten for elastic and saturated ferromagnets. The relevant basic laws of physics are applied…
In this paper, we consider a model for the spin-magnetization system that takes into account the diffusion process of the spin accumulation. This model consists of the Landau-Lifshitz equation describing the precession of the magnetization,…
The Landau--Lifshitz--Bloch equation (LLBE) describes the evolution of the magnetic spin field in ferromagnets at high temperatures. In this paper, we study the numerical approximation of the LLBE on bounded polytopal domains in…
The Landau-Lifshitz-Gilbert-Slonczewski equation describes magnetization dynamics in the presence of an applied field and a spin polarized current. In the case of axial symmetry and with focus on one space dimension, we investigate the…