Static Measurements
4.3.1 Fe M -edge Resonance
In Fig. 4.20, we show the spectrum of the relative transmission and phase shift in the energy range from 40 eV to 70 eV for the Gd25Fe75 sample for both magnetic saturation fields. The Fe M-edge begins at about 52 eV. Compared to the values from [67], this is shifted by 0.7 eV to lower energies. The spectral shift is comparable to the one between the measured spectrum of Gd25Co75 and pure Co. The same argumentation for the origin of the spectral shift as for Gd25Co75 applies to Gd25Fe75, too (see Ch. 4.2.1). The lower electronegativity of Gd compared to Fe is expected to cause a shift of the Gd25Fe75
spectrum toward lower energies compared to the spectrum for pure Fe. Nevertheless, we cannot exclude a small energy offset due to a miscalibrated beamline.
Beside the M-edge resonance, the Ta signature below 47 eV is visible. The slope of the whole spectrum can be explained by the Ta present in the sample. The relative transmission and phase shift of a Ta layer is given in the appendix B.1.
In Fig. 4.21 (right panel), we show the normalized difference of the spectrum for both saturation fields. In Fig. 4.21 (left panel), the magneto-optical constants are calculated.
In the off-resonant regions, where the asymmetry is nearly constant (40–51 eV and 61–70 eV), two adjacent data points were binned to one point located at the photon energy average. The maximum standard deviation for those regions is σ(a(φ)) = 3·10−5 for the phase asymmetry and σ(trel) = 6.5·10−4 for the asymmetry of the relative transmission.
The overall shape of the magneto-optical constants for Fe are similar to the one of Co (see Fig. 4.7, left panel).
As for the Co data, we have a sizeable magnetic asymmetry in the pre-edge region.
For the dispersive part ∆δ of the Co and Fe data, the asymmetry changes sign at around 44 eV. In Ch. 4.2.1, we explained this sign change with the presence of Ta in the sample.
This explanation applies to the measurement with the Gd25Fe75 sample as well. In the post-edge region at 57.6 eV, ∆β overshoots to positive values and falls to zero at 63.4 eV.
This overshoot is stronger than in the Co data. The maximum of ∆β can be found at 54.6 eV.
In Fig. 4.22, we compare the magneto-optical constants from our triple-slit measurement
Figure 4.21: Spectroscopic response of the complex dichroic part of the optical constants for the Fe content of the Gd25Fe75 alloy at the Fe M-edge with circularly polarized light.
Magnetic asymmetry a is shown on the left side, the magneto-optical constants are shown on the right side.
to the ones published by Willems et al. [3]. Their work determined the absorptive and dispersive part of the magneto-optical indices by independently measuring XMCD and the Farady rotation on pure Fe. Even though the data is in qualitative good agreement, the pre-edge and on-resonance values of our ∆δ and ∆β are only 70 % in size compared to the values from Willems et al. For the Gd25Co75 alloy, the deviation from the literature values could be explained by the in-plane magnetization of the sample and corrected by an appropriate scaling factor. In the case of our Gd25Fe75data, the sample magnetic easy axis was out-of-plane and saturated (hysteresis is shown in Fig. 3.4). It is possible that an error during the sample fabrication process caused an error in the Gd25Fe75 layer thickness or the Gd25Fe75 composition. Both uncertainties would manifest themselves as scaling errors in the reconstruction of the magneto-optical indices, as the layer thickness of the magnetic material is included in the calculation as a linear scaling factor. For example, if the exact effective layer thickness of Fe would be 12.5 nm instead of 15.5 nm (corresponding to 67 atomic % of the alloy instead of 75 atomic %), both the data of Willems et al. and our data would match within the measurement error.
To investigate the parameters of the sample layer, we analysed slices of the sample with transmission electron microscopy (TEM) and the sample composition with energy dispersive x-ray analysis (EDX). The TEM analysis showed that the Gd25Fe75 layer thickness was 27.5–32.0 nm ±1.00 nm (Fig. 4.23), i.e., within the measuring error the Gd25Fe75 layer thickness was as intended. Due to the low SNR of the EDX analysis, we cannot clearly deduce the correct fraction of the Fe content. Within the measuring error of the EDX analysis, it is possible that our sample Fe content was too low. An overestimation of the layer thickness would explain the underestimation of the magneto-optical indices.
We note that usually the error in stoichiometry is below 1 % due to the precise deposition rate (0.2 A s−1) in the magnetron sputtering process. Taking into account the results of the TEM and EDX analysis, we are convinced that the values we determined for the
Figure 4.22: Comparison of the magneto-optical constants for the Fe content in Gd25Fe75
alloy with data measured by Willems et al. measured on a pure Fe sample [3] at the Fe M-edge.
Figure 4.23: TEM slice of Gd25Fe75 alloy.
complex magneto-optical index are most likely accurate.
Besides the mismatch in the pre-edge and on-resonance values, it is noticeable that the post-edge ∆β becomes slightly more positive at around 59 eV. If our values of ∆β are scaled to match the on-resonant amplitude of ∆β from Willems et al., the post-edge peak is larger by 160 % in our measurement compared to the findings by Willems et al.
This deviation from our data to the data of Willems et al. was also slightly visible in the comparison between our Gd25Co75 spectrum and the spectrum for pure Co from Willems et al. (Fig. 4.9). According to Willems et al., this difference can be attributed to a different magnitude of the exchange splitting of the semicore states.
4.3.2 Gd N -edge Resonance
The spectrum for the Gd25Fe75sample at the GdN-edge for both saturation field directions is shown in Fig. 4.24. The transition minimum can be found at 148.0 eV for positive
Figure 4.24: Spectroscopic response of relative transmission trel and phase shift φ at the Gd N-edge with circularly polarized light for the Si3N4(150 nm)/Ta(2 nm)/Gd25Fe75(30 nm)/Ta(2 nm) sample layer.
magnetization direction and at 148.8 eV for negative direction. Contrary to the energy shift of the N-edge resonance, the pre-edge features from 138 eV to 143.5 eV only change in amplitude for different magnetization directions. This observation is similar to the results from the results from the Gd25Co75 alloy in Ch. 4.2.2: The energy shift of the transmission for different magnetization orientations originates from the 4d104f7[8S] → 4d94f8[8P] transitions and stems from a different allowed intermediate state. For parallel orientation of photon spin and sample magnetization, the 8P5/2 state (148 eV) is populated, for anti-parallel orientation, the 8P9/2 state (150 eV) [60].
In Fig. 4.25 (left panel), we show the normalized difference of the spectrum of both magnetization directions. On the right panel of Fig. 4.25, the magneto-optical constants of the Gd content in the Gd25Fe75 alloy are shown and compared to the ones from the Gd25Co75 measurements. The overall appearance of the spectrum of both alloys, from the pre-edge features to the resonance, and the off-resonant convergence to zero, matches very well. The only deviation is a small difference in the on-resonance values. That the deviation of both spectra is small is to be expected, since the electron configuration of Fe and Co are similar. However, we cannot exclude the possibility that an uncertainty in the composition of the Gd25Fe75 alloy leads to the small deviation of both spectra (see EDX discussion in Ch. 4.3.1). Other than that, the good agreement of the magneto-optical values for the GdN-edge for both independently measured alloys increases the confidence in our new method.