  We study relaxation behaviour in the two-dimensional assembly of magnetic
nanoparticles (MNPs) with aligned anisotropy axes and positional defects. The
anisotropy axes orientation and disorder strength is changed by varying
$\alpha$ and $\Delta$, respectively. The magnetization decay does not depend on
the aspect ratio $A^{}_r$ of the system and $\Delta$ for small dipolar
interaction strength $h^{}_d=0.2$. Remarkably, the magnetization decays rapidly
for considerable $h^{}_d$ with negligible $\Delta$ and $A_r=1.0$. The dipolar
interaction of enough strength promotes antiferromagnetic coupling in square
ensembles of MNPs. There is a prolonged magnetization decay for large $\Delta$
because of enhancement in ferromagnetic coupling. Notably, magnetization
relaxes slowly for $\alpha<\alpha^\star$ even with moderate $h^{}_d$ and a
significant $A^{}_r$. Interestingly, the slowing down of the magnetic
relaxation shifts to a lower $\alpha^{\star}$ with $h^{}_d=1.0$. The
magnetization ceases to relax for $\alpha\leq60^\circ$ and $h^{}_d\leq0.6$ due
to large shape anisotropy with $A^{}_r=400.0$. Remarkably, a majority of the
magnetic moment reverses its direction by $180^\circ$ for $\alpha>60^\circ$ and
large $h^{}_d$, resulting in the negative magnetization. The effective N\'eel
relaxation time $\tau^{}_N$ also depends strongly on these parameters.
$\tau^{}_N$ depends weakly on $\alpha$ and $\Delta$ for $h^{}_d\leq0.2$,
irrespective of $A^{}_r$. On the other hand, $\tau^{}_N$ decreases with
$\alpha$ for significant $h^{}_d$ provided $\alpha$ is greater than $45^\circ$
because of antiferromagnetic coupling dominance. In a highly anisotropic
system, there is an enhancement in $\tau^{}_N$ with $\alpha$ ($\leq30^\circ$)
even with moderate $h^{}_d$. While for $\alpha>30^\circ$, $\tau^{}_N$ decreases
with $\alpha$. These observations are useful in novel materials, spintronics
based applications, etc.
