  The magnetic relaxation characteristics are investigated in the
two-dimensional ($l^{}_x\times l^{}_y$) assembly of nanoparticles as a function
of out-of-plane positional disorder strength $\Delta(\%)$ using numerical
simulations. Such defects are redundantly observed in experimentally fabricated
nanostructures, resulting in unusual magnetization dynamics. The magnetization
decays exponentially for small and negligible dipolar interaction strength
$h^{}_d\leq0.2$. In such a case, the magnetization relaxation does not depend
on $\Delta$ and aspect ratio $A^{}_r=l^{}_y/l^{}_x$, as expected. In
square-like MNPs ensembles and perfectly ordered system ($\Delta(\%)=0$), the
magnetization relaxes rapidly with an increase in $h^{}_d$. Consequently, the
effective N\'eel relaxation time $\tau^{}_N$ decreases with $h^{}_d$. The
dipolar interaction of sufficient strength promotes antiferromagnetic coupling
in such a system, resulting in rapid magnetization decay. Remarkably, the
out-of-plane disorder instigates the magnetic moment to interact
ferromagnetically in the presence of large $h^{}_d$, even in the square-like
assembly of MNPs. As a result, magnetization relaxation slows down, resulting
in a monotonous increase of $\tau^{}_N$ with an increase in $\Delta$ and
$h^{}_d$ in such cases. Notably, there is a prolonged magnetization decay in
the highly anisotropic system with large $h^{}_d$. The dipolar interaction
induces ferromagnetic coupling along the long axis of the system in such cases.
Therefore, the magnetization ceases to relax as a function of time for large
$h^{}_d$, irrespective of disorder strength $\Delta(\%)$. The present work
could provide a concrete theoretical basis to explain the unexpected relaxation
behaviour observed in experiments. These results are also beneficial in digital
data storage and spintronics based applications where such nanostructures are
extensively used.

Materials Science;Mesoscale and Nanoscale Physics