## 2 Results and Discussions
### Time Resolved Faraday Rotation  
In this section, we present time resolved measurements based on the resonant Faraday Effect to demonstrate distinct ultrafast magnetization dynamics of the two magnetic sublattices of an FeGd ferrimagnetic alloy. The magnetic structure of the FeGd is schematically depicted in Figure 2c with Fe and Gd antiferromagnetically aligned in an out-of-plane direction. In panel (a) of Figure 2, we show the scheme of the experiment, as implemented at the beamline BL2 of the FEL facility FLASH, at DESY in Hamburg, Germany [41]. Linearly polarized pulses with a temporal duration between 50-80 fs are tuned to a photon energy resonant with either the Fe \(M_{2,3}\) at \(\approx 56\) eV or with the Gd \(N_{4,5}\) edge at \(\approx 149\) eV and impinge on the sample under normal incidence. The fluence of the XUV radiation is adjusted to remain below 1 mJ cm\({}^{-2}\) to avoid an influence of the probe pulses on the dynamics and to limit the risk of sample damage. The magnetization of Fe\({}_{26}\)Gd\({}_{74}\) (15 nm thickness) can be set with an external magnetic field to point parallel (\(B_{+}\)) or antiparallel (\(B_{-}\)) to the wave vector of the probe pulses. After transmission through the magnetic sample, the polarization of the XUV pulses is analyzed by a Rabinovitch polarimeter [42], consisting of a mirror aligned at the Brewster angle and an XUV sensitive photo diode. For Gd, the analyzer is a multilayer mirror (OptixFab GmbH, Jena) which has been optimized for a large contrast between the reflectance of s- and p-polarized light centered at 150 eV with a full width at half maximum of 10 eV. The reflectances, \(R_{s,p}\), of the multilayer mirror were determined by a calibration measurement at the light source of the German national metrology institute, PTB, Berlin, Germany, using 99.3% degree p-polarization. For Fe, we used a gold coated mirror. The polarizing power of the analyzer elements is defined as \(P=(R_{s}-R_{p})/(R_{s}+R_{p})\) and listed with the respective reflectances in Table 1. The mirror-detector assembly can be rotated around the beam axis by the azimuthal angle \(\alpha\). Pump pulses centered at a wavelength of 800 nm, with a pulse duration of \(<\)60 fs and with a fluence of \(\approx 5\) mJ cm\({}^{-2}\) excite the sample in a collinear geometry to induce an ultrafast demagnetization. The time resolution is estimated to remain below 100 fs in all experiments, taking into account the temporal jitter of arrival times between optical and XUV pulses. Measurements are performed in a repetitive pump-probe scheme by averaging 100 shots at a 10 Hz repetition rate for each rotation angle or time delay. All data are normalized shot-to-shot by the photon numbers recorded by the gas monitor detector of the FLASH photon diagnostics. The XUV intensity recorded with the XUV photo diode is a function of the azimuthal rotation angle, \(\alpha\), and is given by [36]:  
\[I_{\pm}=\frac{1}{2}I_{0}T(R_{s}+R_{p})\left[1+P_{\text{Lin}}P\cos(2\alpha\pm 2 \theta_{F})\right], \tag{4}\]  
where \(I_{0}\) is the incident intensity, \(T\) the transmittance of the sample and \(P_{\text{Lin}}\) takes into account the small effects due to an induced ellipticity of the beam after transmission through the magnetized sample. In Figure 3a, we show the measured intensity for photon energies resonant at the Gd \(N_{4,5}\) edge. The measurements before optical excitation at \(t=-10\) ps for two opposite magnetization directions of the sample are shifted by \(2\theta_{F}=4^{\circ}\). We note that the rotation angle is smaller than the maximum value that is predicted according to the measurement shown in Figure 1. We attribute this to the uncertainty in determining the absolute photon energy combined with the difficulty to scan the photon energy