Optical contrast-based determination of number of layers for two-dimensional van der Waals magnet Fe$_3$GeTe$_2$

Abstract

Recent advances in revealing intrinsic magnetism in two-dimensional (2D) materials have highlighted their potential for future spintronic applications, driven by their novel physical properties, promising for future spintronic devices. In order to explore layer dependent magnetic behavior, in general, mechanically exfoliated flakes from high-quality single crystals are used. It is crucial to determine the number of layers of these materials accurately. In the absence of an efficient and quick method, researchers often rely on atomic force microscopy (AFM) imaging to identify their number of layers. In this work, we report an optical contrast study as a quick and cost-effective technique to determine the number of layers of Fe$_3$GeTe$_2$ (FGT). Here, we observed a linear relationship between the optical contrast (derived from optical microscopic images) observed for mechanically exfoliated FGT nano-flakes and their thickness, as measured by the AFM imaging method. This technique requires no additional equipment; it relies solely on a conventional optical microscope. Additionally, our results reveal a thickness-dependent evolution of the intensity; in contrast, the Raman frequency demonstrates no significant dependence on layer thickness. Also, our studies reveal two additional Raman modes of FGT, at the frequency of 129\,cm$^-1$ \& 190\,cm$^-1$. Both modes show the intensity dependence on the thickness of FGT, same as out-of-plane (A$_{1g}$) Raman modes.