We use time-dependent spin-density-functional theory to study dynamical magnetic phenomena. First, we recall that the local-spindensity approximation (LSDA) fails to account correctly for magnetic fluctuations in the paramagnetic state of iron and other itinerant ferromagnets. Next, we construct a gradient-dependent density functional that does not suffer from this problem of the LSDA. This fun...

In our contribution, we extend a P1 finite element scheme for the discretization of the Landau-LifshitzGilbert equation (LLG), which has originally been proposed by Alouges [1] for a simpler model problem. Unlike prior works [2], [5], we allow arbitrary contributions to the effective field and elaborate the circumstances under which weak subconvergence towards a weak solution can mathematically...

The Landau-Lifshitz-Gilbert equation describes magnetic behavior in ferromagnetic materials. Construction of numerical strategies to approximate weak solutions for this equation is made difficult by its top order nonlinearity and nonconvex constraint. In this paper, we discuss necessary scaling of numerical parameters and provide a refined convergence result for the scheme first proposed by Alo...

We propose and analyze a decoupled time-marching scheme for the coupling of the Landau-Lifshitz-Gilbert equation with a quasilinear diffusion equation for the spin accumulation. This model describes the interplay of magnetization and electron spin accumulation in magnetic and nonmagnetic multilayer structures. Despite the strong nonlinearity of the overall PDE system, the proposed integrator re...

We consider the numerical approximation of inertial Landau–Lifshitz–Gilbert equation (iLLG), which describes dynamics magnetisation in ferromagnetic materials at subpicosecond time scales. propose and analyse two fully discrete schemes: The first method is based on a reformulation problem as linear constrained variational formulation for velocity. second exploits order system angular momentum. ...