Anisotropic Effect of Dipolar Interaction in Ordered Ensembles of Nanoparticles

TL;DR

This study uses computer simulations to explore how anisotropic dipolar interactions influence the magnetic hysteresis in ordered nanoparticle arrays, revealing complex dependencies on aspect ratio, interaction strength, and field orientation.

Contribution

It provides new insights into the anisotropic effects of dipolar interactions on hysteresis behavior in nanoparticle ensembles, highlighting the roles of aspect ratio and external field direction.

Findings

Weak dipolar interactions lead to superparamagnetic behavior with minimal hysteresis.

Double-loop hysteresis appears at moderate interaction strengths, similar to antiferromagnetic coupling.

Hysteresis loop area and coercivity increase with interaction strength for large aspect ratios and specific field directions.

Abstract

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.