# Tailored Magnetic Linear Birefringence in Wedge-Shaped Co Nanocluster Assemblies
## 3 Results
### Magneto-Optical Effect in Transmission Configuration  
To obtain further insight into the reversal process of M as in-plane \(H\) is applied along the gradient direction, we investigated the magneto-optical effect in transmission configuration for our wedge sample. The so called Voigt effect (MOVE) is particularly sensitive to any source of magnetic anisotropy existing in the in-plane M, i.e., M\({}_{xy}\) component in the corresponding rays diagram of Figure 8.  
As the transmitted light travels across the sample, its refraction index, \(n\), depends on the relative orientation between its polarization plane and \(H\) direction. That yields a rotation angle of the electric field plane, \(\delta_{V}\propto\mathrm{Re}(n_{\parallel}-n_{\perp})\), as E field is parallel or perpendicular to \(H\)[8]. This magnetic linear birefringence arises in magnetic 2D systems showing different mechanisms to reverse their magnetization along easy and hard magnetic axes [8,10]. From the experimental point of view, MOVE appears as intensity changes proportional to \(\Delta\mathrm{T}=\mathrm{T}_{\parallel}-\mathrm{T}_{\perp}\) in the transmitted light. As the sample is driven along its easy axis, \(\Delta\mathrm{T}=0\)  
Figure 8: Panels (**a**,**b**) show respective rays and angle diagrams for MOVE and MOFE measurements in transmission configuration, where the light path is always along z-axis. Panels (**c**–**e**) show the recorded intensity of the transmitted light at the differential amplifier circuit for P6, P4, and P3, respectively. In all cases, legends indicate \(\Phi\) values.  
Figure 7: Angular dependence of the (**a**) normalized coercive field and (**b**) remanence for four locations on the Co nanocluster assembly (P3 to P6).  
because M is reversed due to nucleation and growth of 180\({}^{\circ}\) domains in the sample plane. On the contrary, as \(H\) is applied off the easy axis, a magnetization contribution to M arises in the hard axis, with a different reversal mechanism, i.e., coherent rotation. This would lead us to detect MOVE effect as two symmetric and identical intensity peaks located at \(\pm H_{\text{C}}\) values [8,10].  
In that transmission configuration, obtained results for P3, P4, and P6 pieces of our nanocluster 2D assembly are shown in Figure 8. First, no MLB is displayed as \(H\) is perpendicular to the gradient direction, pointing to a magnetization reversal process in the sample plane. Secondly, as \(H\) aligns progressively with the gradient direction, the recorded signals show two small anomalies near \(\pm H_{\text{C}}\) values, but superimposed to a background signal whose intensity increases noticeably as \(\Phi\) approaches zero. According to the above introduction, this last and unexpected contribution cannot arise from a pure Voigt effect, only sensitive to in-plane magnetization reversal, but from a gradual appearance of an out-of-plane contribution to M, M\({}_{z}\), in our Co nanocluster assemblies. In this transmission configuration, M\({}_{z}\) would orientate normal to the sample plane and parallel to the light path (see the corresponding rays diagram in Figure 8). Accordingly, M\({}_{z}\) should yield a Faraday rotation angle in the polarization plane of the emerging light, \(\delta_{F}\), well known as the magneto-optical Faraday effect (MOFE). Therefore, the magneto-optical effect measured here in transmission configuration with in-plane \(H\) really shows a superposition of MOVE and MOFE.