# Measurement of the Resonant Magneto-Optical Kerr Effect Using a Free Electron Laser
## 3 Techniques for Magnetization Dynamics Capture
Furthermore, through its enhancement of the energy resolution, RIXS has an advantage in that it can be used to detect collective magnetic excitations. Unlike similar techniques, RIXS can also detect momentum-resolved information. Small-angle X-ray scattering (SAXS) is similar to resonant X-ray scattering and can be used to determine magnetic structures on the nanometer scale [33; 34]. Recently, this method has been used to investigate the topological spin textures of the skyrmion. Fourier transform holography (FTH) in the EUV and soft X-ray ranges has been measured using coherent light sources such as HHG lasers and FELs [35; 36]. Conventional magnetic imaging has been performed by magnetictransmission X-ray microscopy using zone plates. The FTH scheme of holography measurements can be achieved without a lens, such as zone plate. In SAXS, the average correlation length can be extracted, while the FTH reveals the element-selective real-space magnetic distribution. The resonant soft X-ray diffraction (RSXD) technique has been used to investigate the charge, spin, orbital order and structural information of specific elements, particularly in strongly-correlated systems, such as transition metal oxides. This technique can determine the magnetic structures of antiferromagnets and helimagnets. Resonant X-ray diffraction is also measured in the hard X-ray range for detection of charges and orbital orders; however, the magnetic scattering cross-section is extremely small in the hard X-ray range when compared with that in the soft X-ray range [30; 37]. Additionally, because the 3\(d\) states can be accessed directly in the soft X-ray range, resonant magnetic scattering is mainly used in the soft X-ray range. The following must be kept in mind for RSXD measurements: (1) the target ordering structure is limited, with a typically long periodic length of \(>\)10 A, because the wavelength of the soft X-ray is longer than that in the hard X-ray range; (2) the attenuation length is smaller (\(\sim\)100-200 nm) than that in the hard X-ray and neutron scattering ranges. When transient magnetization measurements have been performed above the EUV range, HHG lasers, FELs and laser slicing light sources have been combined with the experimental methods described above. Transverse RMOKE (T-RMOKE) has recently been combined with an HHG laser to reveal in-plane magnetization dynamics on a femtosecond timescale [8; 38; 39]. When a grating is used, the time-resolved T-RMOKE spectrum can be measured using an HHG laser that covers the energy range around the \(M\)-edge of the 3\(d\) transition metals. Only recently, a time-resolved T-RMOKE technique has been combined with FEL at FERMI@Elettra [40]. Time-resolved XMCD (TR-XMCD) measurements have mainly been performed in the soft X-ray range, particularly for the \(L\)-edges of 3\(d\) transition metals when using a laser slicing light source [3; 41]. Recently, TR-XMCD measurements of the \(M\)-edge of a 3\(d\) transition metal have been demonstrated using an HHG laser [42] and an FEL [43]. These time-resolved reflectivity measurements using circular (XMCD) and linear polarization (T-RMOKE) have had an importance in tracing in-plane magnetization dynamics in the previous studies. A time-resolved RIXS (TR-RIXS) method with a femtosecond timescale has also been demonstrated using an FEL [9]. This enables tracing of the magnetic correlation with nanometer-scale momentum resolution, which provides information with regard to magnetic melting on various length scales. A time-resolved SAXS (TR-SAXS) method has been used to reveal the magnetic spatial response on a nanometer scale during demagnetization or magnetization reversal processes using FELs or HHG lasers [44; 45; 46]. Time-resolved FTH (TR-FTH) has been performed using both SR sources [47; 48] and an FEL [49]. Because of the higher brilliance and shorter pulse durations of FELs when compared with those of SR sources, holographic images can be obtained in much shorter times when the FEL is used.