Magnetic Relaxation in Two Dimensional Assembly of Dipolar Interacting Nanoparticles

Using the two-level approximation of the energy barrier, we perform extensive kinetic Monte Carlo simulations to probe the relaxation characteristics in a two-dimensional ($L^{}_x\times L^{}_y$) array of magnetic nanoparticle as a function of dipolar interaction strength $h^{}_d$, aspect ratio $A^{}_r=L^{}_y/L^{}_x$, and temperature $T$. In the case of weak dipolar interaction ($h^{}_d\approx0$) and substantial temperature, the magnetic relaxation follows the N\'eel Brown model as expected. Interestingly, the dipolar interaction of enough strength is found to induce antiferromagnetic coupling in the square arrangement of MNPs ($A^{}_r=1.0$), resulting in the fastening of magnetic relaxation with $h^{}_d$. There is also a rapid increase in relaxation even with $A^{}_r<100$ above a particular dipolar interaction strength $h^{\star}_d$, which gets enhanced with $A^{}_r$. Remarkably, there is a slowing down of magnetic relaxation with $h^{}_d$ for the highly anisotropic system such as linear chain of MNPs. It is because the dipolar interaction induces ferromagnetic interaction in such a case. The thermal fluctuations also affect the relaxation properties drastically. In the case of weak dipolar limit, magnetization relaxes rapidly with $T$ because of enhancement in thermal fluctuations. The effect of dipolar interaction and aspect ratio on the magnetic relaxation is also clearly indicated in the variation of N\'eel relaxation time $\tau^{}_N$. In the presence of strong dipolar interaction ($h^{}_d>0.3$) and $A^{}_r=1.0$, $\tau^{}_N$ decreases with $h^{}_d$ for a given temperature. On the other hand, there is an increase in $\tau^{}_N$ with $h^{}_d$ for huge $A^{}_r$ $(>100)$. We believe that the concepts presented in this work are beneficial for the efficient use of self-assembled MNPs array in data storage and other related applications.