We have numerically solved the Landau-Lifshitz-Gilbert (LLG) equation in its standard and inertial forms to study the magnetization switching dynamics in a 3d thin film ferromagnet. The dynamics is triggered by ultrashort magnetic field pulses of varying width and amplitude in the picosecond and Tesla range. We have compared the solutions of the two equations in terms of switching characteristic, speed, and energy analysis. Both equations return qualitatively similar switching dynamics, characterized by regions of slower precessional behavior and faster ballistic motion. In the case of inertial dynamics, ballistic switching is found in a 25% wider region in the parameter space given by the magnetic field amplitude and width. The energy analysis of the dynamics is qualitatively different for the standard and inertial LLG equations. In the latter case, an extra energy channel, interpreted as the kinetic energy of the system, is available. Such an extra channel is responsible for a resonant energy absorption at THz frequencies, consistent with the occurrence of spin nutation.

The advent of X-ray free-electron lasers (XFELs) has revolutionized fundamental science, from atomic to condensed matter physics, from chemistry to biology, giving researchers access to X-rays with unprecedented brightness, coherence and pulse duration. All XFEL facilities built until recently provided X-ray pulses at a relatively low repetition rate, with limited data statistics. Here, results from the first megahertz-repetition-rate X-ray scattering experiments at the Spectroscopy and Coherent Scattering (SCS) instrument of the European XFEL are presented. The experimental capabilities that the SCS instrument offers, resulting from the operation at megahertz repetition rates and the availability of the novel DSSC 2D imaging detector, are illustrated. Time-resolved magnetic X-ray scattering and holographic imaging experiments in solid state samples were chosen as representative, providing an ideal test-bed for operation at megahertz rates. Our results are relevant and applicable to any other non-destructive XFEL experiments in the soft X-ray range.

We study the charge and spin dependent scattering in a set of CoFeB thin films whose crystalline order is systematically enhanced and controlled by annealing at increasingly higher temperatures. Terahertz conductivity measurements reveal that charge transport closely follows the development of the crystalline phase, with the increasing structural order leading to higher conductivity. The terahertz-induced ultrafast demagnetization, driven by spin-flip scattering mediated by the spin–orbit interaction, is measurable in the pristine amorphous sample and much reduced in the sample with the highest crystalline order. Surprisingly, the largest demagnetization is observed at intermediate annealing temperatures, where the enhancement in spin-flip probability is not associated with an increased charge scattering. We are able to correlate the demagnetization amplitude with the magnitude of the in-plane magnetic anisotropy, which we characterize independently, suggesting a magnetoresistance-like description of the phenomenon. 

Demagnetization in a thin film due to a terahertz pulse of magnetic field is investigated. Linearized Landau-Lifshitz-Gilbert (LLG) equation in the Fourier space to describe the magnetization dynamics is derived, and spin wave time evolution is studied. Finally, the demagnetization due to spin wave dynamics and recent experimental observations on similar magnetic system is compared. As a result, the marginal role of spin wave dynamics in loss of magnetization is established.

The understanding of how spins move and can be manipulated at pico- and femtosecond timescales has implications for ultrafast and energy-efficient data-processing and storage applications. However, the possibility of realizing commercial technologies based on ultrafast spin dynamics has been hampered by our limited knowledge of the physics behind processes on this timescale. Recently, it has been suggested that inertial effects should be considered in the full description of the spin dynamics at these ultrafast timescales, but a clear observation of such effects in ferromagnets is still lacking. Here, we report direct experimental evidence of intrinsic inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetization at a frequency of ~0.5 THz. This allows us to reveal that the angular momentum relaxation time in ferromagnets is on the order of 10 ps.

The past two decades have witnessed an increasing interest in understanding and controlling materials at the pico- and femtosecond time scales, the so-called ultrafast regime. Among the broad field of condensed matter physics, magnetism and magnetic materials have attracted much interest both from a fundamental and an applied perspective. The field of ultrafast magnetism is at the frontier of current physics research, with fundamental questions that are still unanswered but which have the potential of impacting the data storage technology upon which our digitalized world relies on. Ultrafast lasers in the visible range (i.e., with energies in the eV range) have been widely used to study ultrafast magnetization dynamics, but due to the relatively large photon energy, they create highly non equilibrium states which tend to mask the fundamental coupling processes leading to ultrafast demagnetization. However, the relatively recent appearance of intense coherent terahertz (THz) radiation (with photon energies in the meV range) offers a new way to understand and manipulate the magnetic order, and is receiving much attention in the research community. As a major part of this thesis, a table-top experimental setup for generating intense THz radiation has been developed for the purpose of carrying out pump-probe studies of thin ferromagnetic metallic films. The setup is capable of delivering state-of-the-art THz electric fields as large as 1 MV/cm, corresponding to 0.3 T magnetic fields which can directly couple to the magnetization to trigger ultrafast dynamics. The ultrafast magnetization dynamics is probed with the time resolved magneto-optical Kerr effect with a resolution of approximately 40 fs. Three main scientific results have been obtained with this thesis work. First, the experimental evidence, in the form of a spin nutation in the THz range, of inertial magnetization dynamics in thin film ferromagnets, which we could describe with a modified version of the textbook Landau Lifshitz-Gilbert (LLG) equation to include a realistic inertial tensor. Second, with this modified LLG equation, we performed simulations to study the role of inertia in the switching of the magnetization with picosecond magnetic field pulses. We found that inertia leads to a so-called ballistic switching which is more robust to the details of the magnetic field pulse. Third, we studied the influence of crystalline order on the charge and spin transport at terahertz rates. We found that while the charge scattering follows the degree of crystalline order in the film, the spin scattering is enhanced at intermediate crystalline phases which have not fully ordered, but where the magnetic anisotropy is largest.

It is known that the use of conventional optical lasers for the study of ultrafast magnetization dynamics imparts heat to the materials under study, which creates a highly non equilibrium state and masks the fundamental coupling processes leading to ultrafast demagnetization. In order to understand, control and manipulate the dynamics of spins in magnetic systems a new kind of radiation called terahertz (THz) is starting to be used in recent years. Due to low photon energy (4 meV) as compared to near infrared radiation (1 eV), THz radiation can directly couple to spins. In the work shown in this thesis, a table-top experimental setup for generating intense THz radiation using organic crystals has been developed for the purpose of carrying out pump probe studies of metallic ferromagnets. With the set up being capable of delivering intense THz fields as high as 1 MV/cm (300 mT) it is possible to initiate magnetization dynamics by directly coupling to the spins. We probe the magnetization change using the femtosecond magneto-optical Kerr effect (MOKE).

In our quest to explore and understand the fast magnetization dynamics on the picosecond timescale we present in this thesis a direct experimental evidence of inertial spin dynamics in ferromagnetic thin films in the THz frequency regime based on the recent modification of the Landau-Lifshitz Gilbert equation (LLG). According to this equation spin nutations should appear at high frequencies which is orders of magnitude higher than the spin precession as observed from the conventional LLG equation. By using the femtosecond MOKE as a probe for the magnetization dynamics we observe a broad resonance in the MOKE response when the films were excited with intense narrowband THz magnetic field pulses of tunable center frequency. The behavior of the spin motion is similar to a forced Lorentz oscillator in the THz magnetic field. From the analysis of our experimental results we could extract the value of momentum relaxation time which is of the order of 10 ps. This quantifies the duration for spin nutation. Our experimental results were consistent with simulations based on the modified LLG equation (also called the inertial LLG equation). The experimental work presented here may be crucial for our current understanding of ultrafast spin dynamics. We believe that the exploitation of the inertial motion of spins may open up a new way of controlling dynamics in magnetism.