Magnetic Correlations in Co/CoO Core/Shell Nanoparticles Decorated on Graphene: Insights from a Modified 2D Law of Approaching Magnetic Saturation

Abstract

Graphene-based hybrid magnetic systems are promising platforms for spintronic appli- cations, yet the mechanisms governing magnetic correlations in these two-dimensional (2D) architectures remain incompletely understood. Here, we investigate the magnetic behavior of Co/CoO core–shell nanoparticles electrochemically deposited on graphene, focusing on the 25–50 K range, where the coercivity and exchange bias field reach their maximum values. Using a modified 2D integral-law framework for approaching magnetic saturation, adapted for 2D systems via the Meyer integral transform, we reconstruct the real-space correlation functions (CFs) of the magnetic anisotropy axes and extract the main micromagnetic parameters. The analysis reveals three distinct types of CFs, monotonic, non- monotonic, and jump-like, which we tentatively associate with different microstructural configurations, including isolated nanoparticles, dense clusters, and sparse conglomerates separated by graphene domain boundaries. The monotonic CFs exhibit long-range coher- ence of the magnetic anisotropy axes extending over nearly one micrometer. We propose that this long-range behavior may arise from a dual-scale mechanism: indirect RKKY-type exchange through the graphene layer, combined with strong local anisotropy from the CoO shells, which pins the magnetization of individual Co cores via exchange bias. These interpretations are presented as plausible hypotheses, and further experimental verification is required.