Magnetization Dynamics in the Lanthanide Metal Gadolinium

In this thesis we investigate the rare-earth metal Gd aiming to gain more insight into the complex interplay of physical processes leading to optically induced ultrafast magnetization dynamics. Using X-ray magnetic circular dichroism (XMCD) we study the magnetization dynamics in Gd over a wide range of time scales and pump laser fluences, while using photoemission spectroscopy (PES) we focus on the first 100 fs of the dynamics showing an increase in exchange splitting of the 5d6s bulk bands. Moreover, we analyze oscillations in the kinetic energy of the photoemitted electrons for negative pump-probe delays in our PES data. Using XMCD in reflection we find a two-step demagnetization on sub-ps and tens of ps time scales with a remagnetization on a hundred ps time scale for various pump laser fluences. An extended version of the microscopic three-temperature model (M3TM) captures the dynamics of the whole data set and suggests Elliott-Yafet-type spin-flip scattering to play a dominant role in the 100 fs to ns magnetization dynamics in Gd. On the fast time scale the demagnetization magnitude depends exponentially on the pump laser fluence implying that a complete demagnetization on that time scale in pure Gd is not physically possible. Results for varying pump photon energies indicate an influence of the initial hot electron distribution on the following dynamics, where lower pump photon energies cause a weaker demagnetization in the early sub-ps dynamics. Our PES study reveals new results particularly in the first 100 fs, where the majority-spin bulk band reacts directly to laser excitation and is not delayed as found in literature. Shifts in the minority- and majority-spin bulk band binding energies lead to a surprising increase in exchange splitting of the 5d6s valence bands in Gd for a few dozen fs after laser excitation indicating an increase in magnetization. Concurrently, the majority-spin bulk and surface states shift in opposing directions despite the same spin polarization. We find optically induced spin transfer (OISTR) between the surface and bulk states in Gd likely to account for this phenomenon. At negative pump-probe delays we observe oscillations in the kinetic energy of photoemitted electrons, a phenomenon explained in literature by ponderomotive acceleration by a transient grating formed by the interference of the incoming and reflected pump laser pulse. We observe a strong enhancement of the oscillation amplitudes on Gd in accordance with the model. We find similar oscillations on W and model parameters show the expected pump photon energy dependence. However, we see different amplitudes for electrons emitted out of different states in W with only slightly different kinetic energy, an unexpected result since photoemitted, free electrons subject to the same potential should experience the same force

A remark on the weak ω\omega-limit set for micromagnetism equation

International audienc

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described