Tailoring Heat Dissipation in Ordered Arrays of Dipolar Coupled Magnetic Nanoparticles

The main aim of the present work is to analyse the effect of dipolar interaction strength $\lambda$, particle size $D$ and temperature $T$ on the hysteresis mechanism in ordered arrays of magnetic nanoparticles (MNPs) using computer simulations. The anisotropy axes of the MNPs are assumed to have random orientation to mimic the real system. In the absence of thermal fluctuations and dipolar interaction, the hysteresis follows the Stoner and Wohlfarth model irrespective of $D$, as expected. The hysteresis loop area is minimal for particle sizes $D \approx8-16$ nm at $T=300$ K and $\lambda=0.0$, indicating the dominance of superparamagnetic character. Switching magnetic interaction on is able to move the MNPs from superparamagnetic to a ferromagnetic state even at room temperature; therefore, magnetic interaction of enough strength enhances the hysteresis loop area. Interestingly, the hysteresis loop area is significant and is the same as that of Stoner and Wohlfarth particle even $T=300$ K and negligible dipolar interaction for ferromagnetic MNPs ($D>16$ nm). The coercive field $\mu^{}_oH^{}_c$ and blocking temperature $T^{}_B$ also get enhanced with an increase in $\lambda$ and $D$. The rigorous analysis of the coercive field $\mu^{}_oH^{}_c$ vs temperature data also reveals significant deviation from $T^{3/4}$ dependence of $\mu^{}_oH^{}_c$ because of dipolar interaction. The amount of heat dissipated $E^{}_H$ and $\mu_oH^{}_c$ decrease rapidly with $T$ for $D\approx 8-16$ nm and $\lambda\leq0.6$. On the other hand, $E^{}_H$ and $\mu^{}_oH^{}_c$ depend weakly on $T$ with $D>16$ nm, even in the weak dipolar limit. The present work should provide a better understanding of magnetic hyperthermia to researchers working on this subject. For physicists, it would be interesting to test experimentally the results described in this article.