Presently we explored nanosandwich structures with graphite (Gt) and graphene (Gn) nanolayers. We found that in Pt-SiO2-Gt, Pt-BN-Gt and Pt-SiO2-Ni-Gn structures the spectra may be decomposed into several components, each corresponding to a different value of the total spin angular momentum S. Only one component was required to describe the Pt-SiO 2-Ni-Gn spectra at 5.3 K, with additional components appearing at higher temperatures. On the other hand, a single component described the Pt-BN-Ni-Gn spectra at all temperatures. Temperature dependence of the spectra of the Pt-SiO2-Ni-Gn system was studied in the 5.3-75.3 K range. Presently we obtained experimental results for novel sandwich systems, with the Gn layer only two monoatomic layers thick. Thus, we compared experimental spectra of a three-nanolayer sandwich system containing a Gt nanolayer with those of a four-nanolayer system containing a diatomic Gn layer. The experimental results were discussed using a theoretical model of the respective physical mechanisms. We propose an exchange anticrossing mechanism, whereby the spin-state polarization of the given Zeeman×.