Abstract:
Dipolar interactions in a system of superparamagnetic nanoparticles play an important role in the magnetic response of the system, where it is well known that for a randomly oriented 3D system of particles, they depress the magnetization. In this study, we simulate a system of about 5000 interacting nanoparticles using Metropolis Monte Carlo method. In such a system, it is known that the dipolar interactions follow Gaussian distribution with approximately zero mean and with varying standard deviation depending on the applied field and the packing density.

We investigate the relation between the packing density and the standard deviation of the interaction fields at different applied fields for 2D and 3D system with different particles arrangements and dispersity. The results indicate that standard deviation of the interaction fields 𝜎𝐵𝑖𝑛𝑡 for 3D system obeys a linear fit with the packing density, while for 2D system it obeys a square root fit. We found that the fitting parameters themselves show a Gaussian/Lorentzian dependence on the applied field. The behavior of the fitting parameters can give a quantitative overall picture of the effects of different factors on the magnetic response.

We have also shown that the magnetization curves for the 3D system decreases with increasing particles concentration, where the 𝑥, 𝑦 components fields have a larger overall effect in depressing the magnetization of the system compared to the 𝑧 component fields.

Moreover, the total reduction in magnetization does not equal the individual reductions due to the 𝑥, 𝑦 and 𝑧 components and we showed that the reduction due to the 𝑧 component can be neatly approximated to be directly proportional to the curvature of the magnetization of the noninteracting system. However, the reduction due to the 𝑥, 𝑦 component field does not show this simple behavior.

As for the dispersity, we found that it has only a small effect in general on the distribution of the dipolar field. The effect, however, is larger for the special case of a 3D arranged system. In comparison, particle arrangements show more effect on the interaction field distributions than dispersity, but they are also small in general. The two-dimensional systems, in particular, are more sensitive to particle arrangements than the three-dimensional ones.

Overall, our results demonstrate a strong effect of dimensionality on the magnetization curves. We see that the magnetization curves along the applied field for 2D system are enhanced compared to the non-interacting system. This is attributed to the fact that the distributions of the dipolar fields for the components parallel to the applied field have non-zero means, assisting the external field in magnetizing the system.