Disorder-Induced Complex Magnetization Dynamics in Planar Ensembles of Nanoparticles

The magnetic relaxation characteristics are investigated in the two-dimensional ($l^{}_x\times l^{}_y$) assembly of nanoparticles as a function of out-of-plane positional disorder strength $\Delta(\%)$ using numerical simulations. Such defects are redundantly observed in experimentally fabricated nanostructures, resulting in unusual magnetization dynamics. The magnetization decays exponentially for small and negligible dipolar interaction strength $h^{}_d\leq0.2$. In such a case, the magnetization relaxation does not depend on $\Delta$ and aspect ratio $A^{}_r=l^{}_y/l^{}_x$, as expected. In square-like MNPs ensembles and perfectly ordered system ($\Delta(\%)=0$), the magnetization relaxes rapidly with an increase in $h^{}_d$. Consequently, the effective N\'eel relaxation time $\tau^{}_N$ decreases with $h^{}_d$. The dipolar interaction of sufficient strength promotes antiferromagnetic coupling in such a system, resulting in rapid magnetization decay. Remarkably, the out-of-plane disorder instigates the magnetic moment to interact ferromagnetically in the presence of large $h^{}_d$, even in the square-like assembly of MNPs. As a result, magnetization relaxation slows down, resulting in a monotonous increase of $\tau^{}_N$ with an increase in $\Delta$ and $h^{}_d$ in such cases. Notably, there is a prolonged magnetization decay in the highly anisotropic system with large $h^{}_d$. The dipolar interaction induces ferromagnetic coupling along the long axis of the system in such cases. Therefore, the magnetization ceases to relax as a function of time for large $h^{}_d$, irrespective of disorder strength $\Delta(\%)$. The present work could provide a concrete theoretical basis to explain the unexpected relaxation behaviour observed in experiments. These results are also beneficial in digital data storage and spintronics based applications where such nanostructures are extensively used.