Scaling behavior of the dipole coupling energy in two-dimensional disordered magnetic nanostructures

TL;DR

This study investigates how the average dipole-coupling energy in two-dimensional disordered magnetic nanostructures scales with particle coverage, revealing a transition from a disorder-sensitive small exponent to a classical 3/2 power law at higher coverages.

Contribution

It demonstrates the scaling behavior of dipole energy in disordered nanostructures and links the scaling exponent to the degree of disorder and magnetic arrangement, providing a new criterion for interaction strength.

Findings

At low coverage, the dipole energy scales with an exponent around 0.8-1.0.

At high coverage, the scaling exponent reaches 1.5, consistent with periodic structures.

The scaling exponent can distinguish between weakly and strongly interacting particle ensembles.

Abstract

Numerical calculations of the average dipole-coupling energy $\bar E_\mathrm{dip}$ in two-dimensional disordered magnetic nanostructures are performed as function of the particle coverage $C$. We observe that $\bar E_\mathrm{dip}$ scales as $\bar E_\mathrm{dip}\propto C^{\alpha^*}$ with an unusually small exponent $\alpha^*\simeq 0.8$--1.0 for coverages $C\lesssim20%$. This behavior is shown to be primarly given by the contributions of particle pairs at short distances, which is intrinsically related to the presence of an appreciable degree of disorder. The value of $\alpha^*$ is found to be sensitive to the magnetic arrangement within the nanostructure and to the degree of disorder. For large coverages $C\gtrsim20%$ we obtain $\bar E_\mathrm{dip}\propto C^\alpha$ with $\alpha=3/2$, in agreement with the straighforward scaling of the dipole coupling as in a periodic particle setup. Taking into account the effect of single-particle anisotropies, we show that the scaling exponent can be used as a criterion to distinguish between weakly interacting ($\alpha^* \simeq 1.0$) and strongly interacting ($\alpha^* \simeq 0.8$) particle ensembles as function of coverage.