Theoretical Limit for the Initial Magnetic Susceptibility in Collective Systems of Noninteracting Macrospins

We address the inequality for the initial magnetic susceptibility χ0 recently proposed by our group in the context of the Stoner–Wohlfarth model and show it is not restricted for noninteracting single-domain (macrospin) blocked systems, but is valid for any collective system consisting of noninteracting macrospins. We derive the theoretical limit for the initial magnetic susceptibility following an approach constructed having as basis assumptions that do not take into account strictly the Stoner–Wohlfarth model, thus achieving a generalized version of the fundamental inequality for χ0. From experimental results of the magnetization response in different blocked magnetic nanopowders and superparamagnetic nanoparticles, we evaluate such generalization for dissimilar macrospin systems. By invoking a mean-field approximation for interacting macrospin systems, we show how the magnetic susceptibility is affected by interparticle dipolar and exchange interactions, and provide evidence for the validity of our findings. Hence, we demonstrate that the violation of the inequality for the initial magnetic susceptibility is a signature of the existence of ferromagnetic exchange interactions between single-domain nanoparticles in a collective system.