# Measurement of the Resonant Magneto-Optical Kerr Effect Using a Free Electron Laser
## 6 Demonstration of TR-RMOKE with a Soft X-ray FEL  
Figure 10 shows a schematic of the TR-RMOKE experiment that was carried out on the Diffraction and Projection Imaging (DiProI) beamline [103] at the seeded FERMI FEL at the Elettra laboratory in Italy. We used the FEL-I, which is normally operated at 60-20 nm (where hv = 12.4-62 eV) with an electron beam energy of 1.2 GeV [104; 105]. The optical pumping was performed using the infrared (IR) lasers that are used for seeding of the FEL, and the pump pulses were thus intrinsically synchronized with the FEL probe pulses with practically jitter-free time resolution [106]. It should be noted that the seeded FEL at FERMI has excellent longitudinal coherence and spectral purity when compared with  
Figure 9: (**a**) Absorption spectrum and (**b**) \(\theta_{K}\) variation with photon energy measured using a polar geometry. The sample is a thin-film structure of Ta (2 nm)/Gd\({}_{21}\)(Fe\({}_{90}\)Co\({}_{10}\))\({}_{79}\) (20 nm)/Ta (10 nm)/SiO\({}_{2}\). The measurements were taken at room temperature. the commonly-used self-amplified spontaneous emission (SASE) scheme, and it also offers a multiple polarized pulse capability [61]. Measurements were performed using 23.6-nm (52.5 eV) FEL pulses with widths of 80-100 fs and a 780-nm IR laser. The pump-probe method was used with a repetition rate of 10 Hz. The FEL and IR laser beam spot sizes on the sample were 420 \(\upmu\)m and 530 \(\upmu\)m in diameter, respectively. The time resolution was limited by the pulse width of the pump laser of 150 fs. The fluences of the pump beam and the probe pulses were tuned to 14 mJ/cm\({}^{2}\) and 3 mJ/cm\({}^{2}\), respectively. The temporal overlap of these pulses was determined with 250 fs resolution by monitoring the reflectivity changes of Si\({}_{3}\)N\({}_{4}\) in the FEL pump/IR laser probe experiment [106; 107]. The spatial overlap was checked using a YAG crystal. The measurement configuration was set such that a linear-horizontally-polarized IR beam and the linear-vertically polarized FEL beam were coaxially incident on the sample. The degree of linear polarization of the FEL, which was nominally called vertical polarization, was \(\sim\)0.97 [108]. The FEL was used to irradiate the sample in the \(s\)-polarization configuration with an angle of incidence of 45\({}^{\circ}\) with respect to the surface normal. The ellipsometry was conducted by rotation of the RAE unit, in which the reflected FEL beam traveled through a rotary flange, which was then reflected at a Mo/Si multilayer mirror (10 periods of 19.1-nm layers) and was finally detected at the MCP. An Al filter was used to attenuate the reflected IR laser beam. The fluctuating pulse-to-pulse intensity of the FERMI pulses was monitored in a shot-by-shot manner using an intensity monitor composed of a gas cell. Figure 11 shows the results of time-resolved measurements of the Gd\({}_{21}\)(Fe\({}_{90}\)Co\({}_{10}\))\({}_{79}\) sample (using the Ta (2 nm)/Gd\({}_{21}\)(Fe\({}_{90}\)Co\({}_{10}\))\({}_{79}\) (20 nm)/Ta (10 nm)/SiO\({}_{2}\) structure) that has been known to enable ultrafast spin switching. Each panel shows the intensity variation when normalized with respect to the incident intensity, which was monitored in a shot-by-shot manner with \(\chi\) at each delay time. The vertical axis denotes the normalized intensity, i.e., the intensity that was detected at the MCP divided by the incident intensity. The intensity of the light that was reflected by the analyzer is monitored at the detector as a function of \(\chi\), as shown in the inset of Figure 10. The two curves (blue and red) correspond to measurements performed under applied magnetic fields in the up and down directions along the sample surface normal, respectively. The solid lines indicate cosine fitting (Equation (11)) to the experimental results.