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We investigate the dependence of magnetic properties on the out-of-planedisorder strength $\Delta$, dipolar interaction strength $h^{}_d$ intwo-dimensional ($l^{}_x\times l^{}_y$) ensembles of nanoparticles usingnumerical simulations. Such positional defects are redundantly observed inexperiments. The superparamagnetic character is dominant with negligible andweak interaction strength $h^{}_d$, irrespective of $\Delta$ and aspect ratioof the system $A^{}_r=l^{}_y/l^{}_x$. The double-loop hysteresis curve,characteristics of antiferromagnetic coupling dominance, emerges with large$h^{}_d$ and $\Delta(\%)\leq5$ in the square-like nanoparticles' assays.Remarkably, the dipolar interaction of sufficient strength drives the magneticorder from antiferromagnetic to ferromagnetic with large $\Delta$ and$A^{}_r\leq4.0$, resulting in an enhancement in the hysteresis loop area. Onthe other hand, the ferromagnetic coupling gets increased with $h^{}_d$ insystems with huge $A^{}_r$. Consequently, the hysteresis loop is enormous, evenwith moderate $h^{}_d$. The variation of the coercive field $\mu^{}_oH^{}_c$,remanence $M^{}_r$, and amount of heat released $E^{}_H$ (due to thehysteresis) with these parameters also suggests the transformation of naturedipolar interaction. They are significant even with large $h^{}_d$ and smaller$A^{}_r$, indicating the antiferromagnetic coupling dominance. Interestingly,there is an enhancement in these with $\Delta$ and large $h^{}_d$ due toferromagnetic interaction. Notably, they are very significant even withmoderate $h^{}_d$ in the highly anisotropic system and external field along thelong axis of the sample. These results could help the experimentalist inexplaining the unusual hysteresis characteristics observed in such systems andshould also be beneficial in diverse applications such as data storage,magnetic hyperthermia, etc.

Controlling Dipolar Interaction Effect in Two-Dimensional Magnetic Nanostructures