# Tailored Magnetic Linear Birefringence in Wedge-Shaped Co Nanocluster Assemblies
## 3 Results
### Magneto-Optical Effect in Reflection Configuration  
Considering the existence of a strong thickness gradient along AB direction in our Co nanocluster assemblies, we proceeded with the study of their MOKE. Previously, that wedged sample was cut in six small squares, with an appropriate size for the electromagnet gap. Hereafter, these pieces are labeled as P1 to P6 from A to B points (see density plot in  
Figure 3: Panel of figures concerning AFM topographic characterization of our Co-cluster assemblies: (**a**,**b**) surface image and height distribution at \(t\)\(\sim\)2 nm, (**c**,**d**) reduced AFM scans at \(t\)\(\sim\)2 and 5 nm, respectively. Figure 4). The thickness of the Co nanocluster assembly at the center of each small piece is listed in Table 1.  
The corresponding vectorial MOKE was measured in P1-P6 pieces of that wedge sample to investigate, on one hand, the dependence of M on the relative orientation between \(H\) and the gradient direction, \(\Phi\) (see axes and angle diagram in Figure 4), and on the other hand, on \(t\) along AB direction. All magneto-optic Kerr effect loops are consistent with a collective magnetic behavior associated with the cluster assemblies which are large enough to have a ferromagnet-like magnetization. Concerning the M\({}_{L}\) component, resulting hysteresis loops and the angular dependence of Kerr rotation angle, \(\delta_{K}\) have been found to be practically identical for P6 and P5, and very similar between P3 and P2. In the case of P1 (ultrathin Co nanocluster assembly), the required external field for magnetic saturation exceeded \(H_{max}\), pointing to an M\({}_{out}\) component ruled by a strong perpendicular magnetic anisotropy (PMA). Thus, and for the sake of brevity, we have selected \(\delta_{K}\) cycles for \(\Phi=0,40\) and \(90^{\circ}\) for P6, P4, and P3. However, summarized results for P5 and P2 can be found in the Supplementary Material. It is readily seen in Figure 5 how the \(\delta_{K}(H)\) loop evolves from open to closed shape as \(H\) direction changes from perpendicular to parallel to the gradient direction, respectively. As \(H\) is applied perpendicular to that TGD, i.e., constant thickness at \(\Phi=90^{\circ}\), Co nanoclusters are progressive and magnetically coupled along the substrate plane, yielding a square \(\delta_{K}(H)\) loop. Contrarily, a closed hysteresis cycle is found at \(\Phi=0^{\circ}\), suggesting the thickness gradient to play a dominant role as a new magnetic anisotropy source in our Co nanocluster assemblies. In the case of P6 and P4, that dominance is gradual with decreasing \(t\), yielding a partially closed \(\delta_{K}(H)\) loop. However, as the bulk contribution to M is strongly decreased in P3, the hysteresis cycle is completely closed, evidencing the appearance of a different mechanism for magnetization reversal as \(H\) is parallel to TGD, in comparison with open cycles. In addition, for P3 piece, M\({}_{T}\) cycles have been measured for \(H\) orientation in the angular interval of \(\pm 20^{\circ}\) around that gradient direction. The corresponding results shown in Figure 6 evidence a reversing M under a coherent rotation process, pointing to the thickness gradient as responsible for an eventual out-of-plane magnetization in our samples. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Square** & P1 & P2 & P3 & P4 & P5 & P6 \\ \hline
**Thickness (nm)** & 1.58 & 2.32 & 5.41 & 11.5 & 18.26 & 24.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Table indicates \(t\) values in respective square pieces used in the following characterization of magneto-optic effects. These values have been extrapolated from the measured thickness profile of the Co nanocluster assembly (see Figure 2). Figure 4: (**a**) Red squares in the density plot correspond to the small pieces of the sample where their magneto-optical effects were measured in this work. Those pieces are numbered in the text as P1 to P6 from A to B position, respectively.