We study the ground-state and magnetic hysteresis properties of $2d$ arrays $(L_x \times L_y)$ of dipolar interacting magnetic nanoparticles (MNPs) by performing micromagnetic simulations. Our primary interest is to understand the effect of sample shape, $\Theta$, the ratio of the dipolar strength to the anisotropy strength and the direction of the applied field $\vec{H}=H_0\hat{e}_H$ on the ground state and the magnetic hysteresis in an array of MNPs. To study the effect of the shape of the sample, we have varied the aspect ratio $A_r=L_y/L_x$, which in turn, is found to induce shape anisotropy in the system. Our main observations are: (a) When the dipolar interaction is strong (${\Theta}$ > 1), the ground-state morphology has an in-plane ordering of magnetic moments, (b) the ground-state morphology has randomly oriented magnetic moments that are robust regarding system sizes and $A_r$ for weakly interacting MNPs ($\Theta$ < 1), (c) micromagnetic simulations suggest that the dipolar interaction decreases the coercive field $H_c$, (d) the remanence magnetisation $M_r$ is found to be strongly dependent not only on the strength of dipolar interaction but also on the shape of the sample and (e) due to the anisotropic nature of dipolar interaction, a strong shape anisotropy effect is observed when the field is applied along the long axis of the sample. In such a case, the dipolar interaction induces an effective ferromagnetic coupling when the aspect ratio is enormous. These results are of vital importance in high-density recording systems, magneto-impedance sensors, etc

We perform numerical simulations to analyse the effect of dipolar interaction, particle size D and thermal fluctuations on the magnetic hysteresis in the linear array of magnetic nanoparticles (MNPs). The shape of the hysteresis curve is that of Stoner and Wohlfarth particle for non-interacting MNPs and temperature T = 0K. The area under the magnetic hysteresis curve is minimal with D ≈ 8–16 nm and T = 300 K, indicating the predominance of superparamagnetic character. Interestingly, the dipolar interaction of sufficient strength moves the nanoparticles from superparamagnetic to a blocked state even at T = 300 K, resulting in an enhanced hysteresis loop area in such cases. Even with negligible dipolar interaction strength (λ ≈ 0.0) and T = 300 K, the hysteresis looparea is appreciable for ferromagnetic particles (D > 16 nm). The coercive field μ$_0$H$_c$ and the blocking temperature T$_B$ also depend strongly on the dipolar interaction. They are found to increase with dipolar interaction strength λ andparticle size. Our extensive simulations also reveal a significant deviation of μ$_0$H$_c$ from T$^{ 3/4}$ dependence because of dipolar interaction. There is a rapid fall in the amount of heat dissipated EH and coercive field with temperature forsuperparamagnetic nanoparticles (D ≈ 8–16 nm) and small dipolar interaction strength (λ ≤ 0.6). In contrast, they are significantly large and depend weakly on thermal fluctuations for D >16 nm. Therefore, observations made inthe presentwork can help experimentalists to choose precise values of system parameters to obtain desired hysteresis properties, essential for diverse technological applications such as magnetic hyperthermia, data storage, etc.