Scaling behavior of the dipole coupling energy in two-dimensional disordered magnetic nanostructures
Abstract
Numerical calculations of the average dipole-coupling energy
E
¯
dip
in two-dimensional disordered magnetic nanostructures are performed as function of the particle coverage
C
. We observe that
E
¯
dip
scales as
E
¯
dip
∝
C
α
∗
with an unusually small exponent
α
∗
≃0.8
--1.0 for coverages
C≲20
. 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
α
∗
is found to be sensitive to the magnetic arrangement within the nanostructure and to the degree of disorder. For large coverages
C≳20
we obtain
E
¯
dip
∝
C
α
with
α=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 (
α
∗
≃1.0
) and strongly interacting (
α
∗
≃0.8
) particle ensembles as function of coverage.