# Tailored Magnetic Linear Birefringence in Wedge-Shaped Co Nanocluster Assemblies
## 4 Discussion
Too-thin pieces in the graded coating comprise isolated cluster assemblies randomly spread over the substrate, whereas the too-thick pieces must be formed from a continuous stack of clusters. Thus, it seems that a film morphology of interconnected cluster assemblies--as an intermediate case once coalesce occurs--can be appropriate for the appearance of magnetic effects, leading to a minor but detectable out-of-plane magnetization. The physical origin of the minor M\({}_{z}\) could arise from magnetic coupling of nanoclusters along terrace edges in this scenario. To speculate with the origin of out-of-plane component, we should recall similar magnetic phenomena: patterned planar arrays of interconnected dots/antidots have shown composite in-plane and out-of-plane magnetizations under in-plane applied fields due to the effect of geometric frustration of moments at the network nodes [33]. Our assembly system develops a minor out-of-plane magnetization and a dominant in-plane magnetization, under in-plane fields along TGD, the former one probably developed at a few nodes where the neighboring (in-plane) assembly moments point oppositely to each other. As these are expected to be scarce, this speculative explanation is difficult to microscopically confirm. For the intermediate thickness range, e.g., P3 of our Co nanocluster assembly, the maximum magnitude of Faraday rotation and, consequently, the MLB is reached at \(\Phi=0^{\circ}\), as seen in Figure 10, where a comparative study of \(\delta_{F}\) has been accomplished for P3, P4, and P6. Despite everything, the measurement of magneto-optical effects in transmission configuration has evidenced its capability to detect and monitor subtle thickness irregularities in our wedge assemblies, helping us to map the magnetization vector over the surface sample. Accordingly, this effect enables this 2D system to finely alter the polarization plane of the transmitted light, behaving as a polarization filter or rotator (sketched in Figure 11). Either for fundamental or applied applications, the improvement of the magnitude and accuracy of both magnetic linear birefringence and Faraday rotation, i.e., M\({}_{out}\), needs further research on tailoring the profile and sharpness of thickness gradient in these 2D nanocluster assemblies. Figure 10: Angular dependence of \(\delta_{F,max}\) for P3, P4, and P6. \(\delta_{F,max}\) refers to Faraday rotation at saturation magnetic field. **Supplementary Materials:** The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app12010100/s1](https://www.mdpi.com/article/10.3390/app12010100/s1)]([https://www.mdpi.com/article/10.3390/app12010100/s1](https://www.mdpi.com/article/10.3390/app12010100/s1)). **Author Contributions:** Conceptualization, M.A.A. ; methodology, M.A.A., E.H.S. and J.M.C. ; formal analysis, M.A.A., E.H.S., J.M.C. and V.R.-D.; investigation, M.A.A. and V.R.-D.; resources, M.A.A., J.L.S.-R. and J.M.C. ; data curation, M.A.A., E.H.S. and J.M.C. ; writing--original draft preparation, M.A.A., E.H.S. and J.M.C. ; writing--review and editing, all authors; acquisition, M.A.A. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by Spanish Ministry of Economy and Competitiveness, (MINECO, grant number UNCM08-1E-024), Spanish Ministry of Science and Innovation (MCIN, grant number MCIN/AEI/ 10.13039/501100011033) and FEDER \"ERDF A way of making Europe\" (grant number RTI18-094960-B-100). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request. **Conflicts of Interest:** The authors declare no conflicts of interest.