  We report a simple, efficient manner to assess magnetic interactions, more
specifically the exchange interaction, in systems as blocked magnetic
nanoparticles. Specifically, we investigate what is the theoretical limit for
the external magnetic susceptibility in a system described by the plain old
Stoner-Wohlfarth model. We go beyond and introduce a general mean field theory
for interacting systems, thus estimating how the magnetic susceptibility is
affected due to the dipolar and exchange interactions inside the system. We
disclose a fundamental inequality for the magnetic susceptibility and show its
violation is an unambiguous signature of the existence of exchange interactions
between nanoparticles in a collective system. To test the robustness of our
theoretical achievements, we examine magnetization measurements and Henkel
plots for blocked magnetic nanopowders. The agreement between experiment and
theory provides evidence to confirm the validity of our findings.
