From vanishing interaction to superferromagnetic dimerization: Experimental determination of interaction lengths for embedded Co clusters

We report on the magnetic properties of Co clusters (around 2.5 nm diameter) embedded in different matrices (C, Au, and Cu). Firstly, we accurately determine the intrinsic magnetic properties of the particles, using highly diluted samples where no interactions are detected, and a procedure relying on the theoretical description of various magnetometry measurements, and we show how both the magnetic size and anisotropy can be impacted by the nature of the matrix. Then, by considering nanoparticle assemblies of increasing concentrations, we investigate the effects of interactions between particles. In order to account for the observed evolution of the measurements, we propose a simple model where magnetic dimers are formed for distances lower than a given interaction length (of the order of one nanometer). This superferromagnetic correlation, which can be consistently inferred for each matrix, modifies the magnetic size distribution, which has a drastic effect as soon as particles are close enough to each other.