  Using first-principle calculations and kinetic Monte Carlo simulation, we
study the local and averaged hysteresis in tiny clusters of k magnetic
nanoparticles (MNPs) or k-mers. We also analyze the variation of local dipolar
field acting on the constituent nanoparticles as a function of the external
magnetic field. The dipolar interaction is found to promote chain-like
arrangement in such a cluster. Irrespective of cluster size, the local
hysteresis response depends strongly on the corresponding dipolar field acted
on a nanoparticle. In a small k-mer, there is a wide variation in local
hysteresis as a function of nanoparticle position. On the other hand, the local
hysteresis is more uniform for larger k-mer, except for MNPs at the boundary.
In the case of superparamagnetic nanoparticle and weak dipolar interaction, the
local hysteresis loop area Ai is minimal and depends weakly on the k-mer size.
While for ferromagnetic counterpart, Ai is considerably large even for weakly
interacting MNPs. The value of Ai is found to be directly proportional to the
dipolar field acting on the nanoparticle. The dipolar interaction and k-mer
size also enhances the coercivity and remanence. There is always an increase in
Ai with clutser size and dipolar interaction strength. Similarly, the averaged
hysteresis loop area A also depends strongly on the k-mer size, particle size
and dipolar interaction strength. A and Ai always increase with k-mer size and
dipolar interaction strength. Interestingly, the value of A saturates for k>=20
and considerable dipolar interaction irrespective of particle size. We believe
that the present work would help understand the intricate role of dipolar
interaction on hysteresis and organizational structure of MNPs and their usage
in drug delivery and hyperthermia applications.
