  Magnetic nanoflowers are densely packed aggregates of superferromagnetically
coupled iron oxide nanocrystallites, which excel during magnetic hyperthermia
experiments. Here, we investigate the nature of the moment coupling within a
powder of such nanoflowers using spin-resolved small-angle neutron scattering.
Within the powder the nanoparticles are agglomerated to clusters, and we can
show that the moments of neighboring nanoflowers tend to align parallel to each
other. Thus, the whole system resembles a hierarchical magnetic nanostructure
consisting of three distinct levels, i.e. (i) the ferrimagnetic
nanocrystallites as building blocks, (ii) the superferromagnetic nanoflowers,
and (iii) the \textit{supra}ferromagnetic clusters of nanoflowers. We surmise
that such a supraferromagnetic coupling explains the enhanced magnetic
hyperthermia performance in case of interacting nanoflowers.
