# Measurement of the Resonant Magneto-Optical Kerr Effect Using a Free Electron Laser
## 5 Static RMOKE Measurement
In [97; 98; 99; 91], depth profile measurements using Fe, Co and Ni \(L\)-edge L-RMOKE were demonstrated by selecting appropriate angles of incidence and energies. The \(L_{2,3}\) spectra of the rotation angles and the ellipticities were measured for the Fe, Co and Ni metal samples [12; 100]. The L-RMOKE Kerr rotation angle was related to the T-RMOKE signals, while the L-MOKE ellipticities corresponded to the XMCD spectra of the reflected beam. The researchers also discovered notable interference effects from the light reflected from the surface and the interfaces in the L-RMOKE spectra. Recently, \(M\)-edge L-RMOKE measurements of Co and Ni were reported in [83; 101]. A P-RMOKE experiment has recently been the subject of intense attention from researchers because it has the only measurement geometry that can detect perpendicular magnetization (Figure 2), which is significant for the development of modern storage devices. The P-RMOKE was predicted in 1975 when Ni metal showed a \(\theta_{k}\) value at the \(M_{2,3}\)-edge that was 10-times larger than that in the visible region [102]. Then, P-RMOKE measurements were carried out at a synchrotron radiation bending-magnet beamline and confirmed that \(\theta_{k}\) was 50-times larger at the Ni \(M_{2,3}\) edges [56]. Basically, there is no apparent physical difference in the RMOKE signals between the longitudinal and polar MOKE geometries. Either technique can be used, depending on whether the magnetization direction is parallel or perpendicular. We now provide an example of RMOKE for a thin-film structure of Ta (2 nm)/Gd\({}_{21}\)(Fe\({}_{90}\)Co\({}_{10}\))\({}_{79}\) (20 nm)/Ta (10 nm) that was fabricated on thermally-oxidized silicon wafers using a radio-frequency(RF) magnetron sputtering process. The Gd\({}_{21}\)(Fe\({}_{90}\)Co\({}_{10}\))\({}_{79}\) alloy is ferrimagnetic. The magnetic moment of the transition metal (Fe) sublattice at room temperature is higher than that of the rare earth (Gd) metal, and the direction of the magnetic moment of the Fe atom is parallel to that of the external magnetic field. The Ta (2 nm) capping layer prevents oxidation of the Gd\({}_{21}\)(Fe\({}_{90}\)Co\({}_{10}\))\({}_{79}\), and the Ta (10 nm) underlayer helps with adhesion to the Si substrate. Figure 9a shows a set of soft X-ray absorption spectra for the Gd\({}_{21}\)(Fe\({}_{90}\)Co\({}_{10}\))\({}_{79}\) sample that were measured under saturated magnetization conditions (Figure 5), where the external field of \(\pm\)0.47 T was applied perpendicularly to the sample surface. The measurements were performed at bending-magnet beamline BL5B at the Ultraviolet Synchrotron Orbital Radiation facility (UVSOR, Okazaki, Japan). The degree of linear polarization is at least 0.98 [101]. The spectra were obtained using the total electron yield mode. The vertical axis in Figure 9a was normalized by incident intensity measured by a gold mesh. The peaks at 33 eV, 42 eV, 53 eV and 66 eV were assigned to the Ta 5\(p_{3/2}\), 5\(p_{1/2}\), Fe and Co 3\(p\) absorptions, respectively. Figure 9b shows the experimental RMOKE spectra obtained around the Fe \(M\)-absorption edge. The RMOKE measurements were conducted in a polar geometry (P-RMOKE), and the Kerr rotation angle values were obtained by the RAE method, which was shown in Figure 7. At the Fe 3\(p\) absorption, \(\theta_{K}\) was approximately 3\({}^{\circ}\), while at the Co 3\(p\) absorption, \(\theta_{K}\) was approximately 5\({}^{\circ}\), and these values were approximately 10-times larger than those obtained from the visible MOKE, as shown in Figure 5. From a set of the absorption and RMOKE spectra, the photon energy of 53 eV is found to have sufficiently large values for both the absorption peak and \(\theta_{K}\), and the Fe atom is thus the most suitable candidate for tracing of the magnetization dynamics in Gd\({}_{21}\)(Fe\({}_{90}\)Co\({}_{10}\))\({}_{79}\) during ultrafast switching for the time-resolved measurements.