# Measurement of the Resonant Magneto-Optical Kerr Effect Using a Free Electron Laser
## 3 Techniques for Magnetization Dynamics Capture  
Figure 3 presents the various experimental methods that have been used to trace magnetization dynamics in previous studies, including MOKE. Each method is shown with respect to the energy required and the timescale of the operation, together with the relevant optical transitions and magnetization dynamics phenomena. The optical transitions are classified into two regimes: one from the perspective of the valence bands for energies of a few eV and the other from the perspective of the core levels for energies higher than those of the EUV range. Three light sources with sub-picosecond pulses, comprising the FEL, the HHG laser and the laser slicing source, are shown based on the energy ranges in which each source can emit. In the microwave and millimeter-wave range, magnetic resonance, such as ferromagnetic resonance (FMR) [18] and antiferromagnetic resonance (AFMR) [19], has been used to investigate the precession frequency and the magnetic collective excitation or magnon. Inelastic light scattering, for example Brillouin (BLS) and Raman light scattering methods, is also employed for exploring the nature of collective spin excitation modes. These occur on a timescale of hundreds of picoseconds. Terahertz time-domain spectroscopy (THz-TDS) can directly visualize the electric field waveforms of ultrashort pulses [20]. Additionally, in time-resolved measurements, THz pulses can excite the system without being absorbed by the target materials, which means that heating effects can be avoided during the analysis of the magnetization dynamics [21]. In the energy range from the infrared to the ultraviolet, the magneto-optical effects in both reflection (Kerr) and transmission (Faraday) regimes have been used. In some magnetic compounds composed of rare-earths and transition-metals, element-specific measurements were reported by probing different wavelength for each magnetic element [22]. Furthermore, a nonlinear magneto-optical effect, magnetization-induced second harmonic generation (MSHG), has also been used to detect magnetic systems without inversion symmetry, such as systems involving surface and interface magnetism [23; 24]. While these methods can be used easily with laboratory-based lasers, most of them lack elemental selectivity because they are involved with the optical transitions that occur between delocalized states. Above the EUV range, magnetic probe measurements are generally performed by tuning the photon energy to a specific absorption edge, which then enables element-specific measurements. In static measurements, the Kerr and Faraday effects in the EUV and soft X-ray ranges were particularly investigated from the late 1990s until the mid-2000s. Magneto-optical effects that are sensitive to <M\({}^{2}\)> are also used, including the Voigt effect [25] and X-ray magnetic linear dichroism (XMLD) [26]. These methods can probe both the ferromagnetic and antiferromagnetic orders. However, these magneto-optical effects, which are proportional to <M\({}^{2}\)> are much smaller than those proportional to <M\(>\)[25; 27]. Additionally, in XMLD measurements, it is difficult to separate the magnetic and nonmagnetic contributions [28]. XMCD is the most commonly-used technique for probing of ferro-/ferri-magnets, particularly in the soft X-ray range, and uses circularly-polarized light. This method can extract the spin and the orbital magnetic moment separately using magneto-optical sum-rules. While the XMCD signals in the EUV range are quite small when compared with the signal in the soft X-ray range, \(M\)-edge XMCD for \(3d\) transition metals has also been demonstrated using a circularly-polarized HHG laser. The resonant inelastic X-ray scattering (RIXS) method is relatively new when compared with the other magnetic probing techniques and is complementary to the inelastic neutron scattering method [29; 30; 31; 32]. This method could become more easily available as a result of the increasing brilliance of third generation SR sources and the advent of the FEL.