Anisotropic Effect of Dipolar Interaction in Ordered Ensembles of Nanoparticles

We implement extensive computer simulations to investigate the hysteresis characteristics in the ordered arrays ($l^{}_x\times l^{}_y$) of magnetic nanoparticles as a function of aspect ratio $A^{}_r=l^{}_y/l^{}_x$, dipolar interaction strength $h^{}_d$, and external magnetic field directions. We have considered the aligned anisotropy case, $\alpha$ is the orientational angle. It provides an elegant en route to unearth the explicit role of anisotropy and dipolar interaction on the hysteresis response in such a versatile system. The superparamagnetic character is dominant with weak dipolar interaction ($h^{}_d\leq0.2$), resulting in the minimal hysteresis loop area. Remarkably, the double-loop hysteresis emerges even with moderate interaction strength ($h^{}_d\approx0.4$), reminiscent of antiferromagnetic coupling. These features are strongly dependent on $\alpha$ and $A^{}_r$. Interestingly, the hysteresis loop area increases with $h^{}_d$, provided $A^{}_r$ is enormous, and the external magnetic field is along the $y$-direction. The coercive field $\mu^{}_oH^{}_c$, remanent magnetization $M^{}_r$, and the heat dissipation $E^{}_H$ also depend strongly on these parameters. Irrespective of the external field direction and weak dipolar interaction ($h^{}_d\leq0.4$), there is an increase in $\mu^{}_oH^{}_c$ with $h^{}_d$ for a fixed $\alpha$ and $A^{}_r\leq4.0$. The dipolar interaction also elevates $M^{}_r$ as long as $A^{}_r$ is huge and the field is along the $y$-direction. $E^{}_H$ is minimal for negligible and weak dipolar interaction, irrespective of $A^{}_r$, $\alpha$, and the field directions. Notably, the magnetic interaction enhances $E^{}_H$ if $A^{}_r$ is enormous and the magnetic field is along the long axis of the system. These results are beneficial in various applications of interest such as digital data storage, spintronics, etc.