Relaxation in Ordered Assembly of Magnetic Nanoparticles

We study the relaxation characteristics in the two-dimensional ($l^{}_x \times l^{}_y$) array of magnetic nanoparticles (MNPs) as a function of aspect ratio $A^{}_r=l^{}_y/l^{}_x$, dipolar interaction strength $h^{}_d$ and anisotropy axis orientation using computer simulation. The anisotropy axes of all the MNPs are assumed to have the same direction, $\alpha$ being the orientational angle. Irrespective of $\alpha$ and $A^{}_r$, the functional form of the magnetization-decay curve is perfectly exponentially decaying with $h^{}_d\leq0.2$. There exists a transition in relaxation behaviour at $h^{}_d\approx0.4$; magnetization relaxes slowly for $\alpha\leq45^\circ$; it relaxes rapildy with $\alpha>45^\circ$. Interestingly, it decays rapidly for $h^{}_d>0.6$, irrespective of $\alpha$. It is because the dipolar interaction promotes antiferromagnetic coupling in such cases. There is a strong effect of $\alpha$ on the magnetic relaxation in the highly anisotropic system ($A^{}_r\geq25$). Interesting physics unfolds in the case of a huge aspect ratio $A^{}_r=400$. There is a rapid decay of magnetization with $\alpha$, even for weakly interacting MNPs. Remarkably, magnetization does not relax even with a moderate value of $h^{}_d=0.4$ and $\alpha=0^\circ$ because of ferromagnetic coupling dominance. Surprisingly, there is a complete magnetization reversal from saturation (+1) to $-1$ state with $\alpha>60^\circ$. The dipolar field and anisotropy axis tend to get aligned antiparallel to each other in such a case. The effective N\'eel relaxation time $\tau^{}_N$ depends weakly on $\alpha$ for small $h^{}_d$ and $A^{}_r\leq25.0$. For large $A^{}_r$, there is a rapid fall in $\tau^{}_N$ as $\alpha$ is incremented from 0 to $90^\circ$. These results benefit applications in data and energy storages where such controlled magnetization alignment and desired structural anisotropy are desirable.