Enhancing magneto-optic effects in two-dimensional magnets by thin-film interference

The magneto-optic Kerr effect is a powerful tool for measuring magnetism in thin films at microscopic scales, as was recently demonstrated by the major role it played in the discovery of two-dimensional (2D) ferromagnetism in monolayer CrI$_3$ and Cr$_2$Ge$_2$Te$_6$. These 2D magnets are often stacked with other 2D materials in van der Waals heterostructures on a SiO$_2$/Si substrate, giving rise to thin-film interference. This can strongly affect magneto-optical measurements, but is often not taken into account in experiments. Here, we show that thin-film interference can be used to engineer the magneto-optical signals of 2D magnetic materials and optimize them for a given experiment or setup. Using the transfer matrix method, we analyze the magneto-optical signals from realistic systems composed of van der Waals heterostructures on SiO$_2$/Si substrates, using CrI$_3$ as a prototypical 2D magnet, and hexagonal boron nitride (hBN) to encapsulate this air-sensitive layer. We observe a strong modulation of the Kerr rotation and ellipticity, reaching several tens to hundreds of milliradians, as a function of the illumination wavelength, and the thickness of the SiO$_2$ and layers composing the van der Waals heterostructure. Similar results are obtained in heterostructures composed by other 2D magnets, such as CrCl$_3$, CrBr$_3$ and Cr$_2$Ge$_2$Te$_6$. Designing samples for the optimal trade-off between magnitude of the magneto-optical signals and intensity of the reflected light should result in a higher sensitivity and shorter measurement times. Therefore, we expect that careful sample engineering, taking into account thin-film interference effects, will further the knowledge of magnetization in low-dimensional structures.