  Magnetic nanoparticles (MNPs) have been proposed as an ultimate solution for
diverse applications including nanomedicine and logic devices over decades.
However, none has emerged revolutionary because realizing their magnetization
response in an assembly is, surprisingly, still elusive. We employ our fast and
universal magnetic characterization method, called the projection method, to
underlie the reversible (irreversible) magnetization response of several
assemblies. We then illustrate how the reversible (irreversible) magnetization
response is correlated to the intrinsic properties (the coercivity and
interaction fields) of the MNPs in an assembly. Our experimental observations
indicate that the reversible magnetization does not solely depend on the
interaction field, but it is indeed a function of the interaction field to
coercivity ratio. Furthermore, for large porosities, the interaction field
linearly changes with the porosity highlighting the predominant effects of
dipole-dipole interactions on the interaction fields. However, at low
porosities, the interaction field shows a nonlinear relationship with the
porosity indicating the dipole fluctuations effects dominantly determine the
interaction fields.
