54
M. Vasilakaki et al.
exchange, involving surface spins among different particles) and even increased
surface anisotropy [39].
We have studied controlled assemblies of single-crystal, colloidal maghemite
nanoparticles which is facilitated via a high temperature polyol-based pathway.
Structural characterization shows that size-tunable nanoclusters of 50 and 86 nm
diameters, with high dispersibility in aqueous media, are composed of 13 nm crystallographically oriented nanoparticles. The interaction effects are examined against
the increasing volume fraction, p, of the inorganic magnetic phase that goes from
individual colloidal nanoparticles (p = 0.47) to clusters (p = 0.60, 0.72) [27]. In
such nanoparticle assembled systems, with increased p, the role of the interparticle
dipolar interactions and that of the constituent nanoparticles’ surface spin disorder
in the emerging spin glass dynamics is expected to be significant.
In order to model the clusters morphology of the assembly of nanoparticles,
we consider N identical spherical ferrimagnetic NPs of diameter d being located
randomly on the nodes of a simple cubic lattice with lattice constant, a, inside a
box of edge length 10α measured in units α. The clusters have been produced by
dividing the lattice into eight areas with size 5a × 5a × 5a each and a variable
particle concentration per area, but under the constraint that the total concentration
is the same as the experimental one. The total number of NPs is N = p × (10 a × 10
a × 10 a), where p is the concentration of the particles in the model. In such a model,
the total concentration p = 0.60 for small clusters and p = 0.72 for large clusters is
spread into eight partial concentrations, namely [0.6, 0.7, 0.5, 0.6, 0.5, 0.7, 0.7, 0.5]
and [0.72, 0.82, 0.52, 0.72, 0.82, 0.72, 0.82, 0.62], respectively. In all cases, due to
the existence of the surfactant polymeric layer, it was assumed that there were no
direct exchange interactions (j inter = 0) between the nanoparticles, but instead they
interacted only via dipolar forces with dipolar strength g.
In this case, we go beyond the classical model of coherent rotation of the particle’s
Stoner–Wohlfarth magnetization, in which each nanoparticle is described by a classical spin vector as in the case of Fe nanoparticles. Our mesoscopic model involves
a set of three classical unit spin vectors, one for the core s 1i and two for the surface
layer s 2i , s 3i with magnetic moments m n = M n V n /M s V n = 1 stands for the core
and n = 2, 3 for the “up” and “down” shell or surface sublattices of the nanoparticle,
respectively, as it is described in Sect. 2.1.1. In this way, surface effects were included
for each i nanoparticle in the assembly.
The energy parameters in (2.1) are based on the bulk values of maghemite (M s =
4.2 × 10
5 A/m and K = 5 × 10
3 J/m
3 ), and their modifications are established
considering the nanoparticles morphology (e.g., reduced symmetry and reduced size)
using a mean field approach. Accordingly, the values of the intra-particle exchange
energy among the core spin and the surface spins were taken as j c1 = −7.77, j c2 = −
1.35, j srf = −0.091 and the anisotropy energy of the core as k C = 0.1, while that of
the surface as k srf = 2.5, since it is expected to be more than one order of magnitude
larger than that of the core.
The dipolar strength energies (g) and magnetic moments (m) have been calculated
taking into account the experimental values of the particle concentration (p) and
the saturation magnetization (M s ) of the nano-architectures for the three different
M. Vasilakaki et al.
exchange, involving surface spins among different particles) and even increased
surface anisotropy [39].
We have studied controlled assemblies of single-crystal, colloidal maghemite
nanoparticles which is facilitated via a high temperature polyol-based pathway.
Structural characterization shows that size-tunable nanoclusters of 50 and 86 nm
diameters, with high dispersibility in aqueous media, are composed of 13 nm crystallographically oriented nanoparticles. The interaction effects are examined against
the increasing volume fraction, p, of the inorganic magnetic phase that goes from
individual colloidal nanoparticles (p = 0.47) to clusters (p = 0.60, 0.72) [27]. In
such nanoparticle assembled systems, with increased p, the role of the interparticle
dipolar interactions and that of the constituent nanoparticles’ surface spin disorder
in the emerging spin glass dynamics is expected to be significant.
In order to model the clusters morphology of the assembly of nanoparticles,
we consider N identical spherical ferrimagnetic NPs of diameter d being located
randomly on the nodes of a simple cubic lattice with lattice constant, a, inside a
box of edge length 10α measured in units α. The clusters have been produced by
dividing the lattice into eight areas with size 5a × 5a × 5a each and a variable
particle concentration per area, but under the constraint that the total concentration
is the same as the experimental one. The total number of NPs is N = p × (10 a × 10
a × 10 a), where p is the concentration of the particles in the model. In such a model,
the total concentration p = 0.60 for small clusters and p = 0.72 for large clusters is
spread into eight partial concentrations, namely [0.6, 0.7, 0.5, 0.6, 0.5, 0.7, 0.7, 0.5]
and [0.72, 0.82, 0.52, 0.72, 0.82, 0.72, 0.82, 0.62], respectively. In all cases, due to
the existence of the surfactant polymeric layer, it was assumed that there were no
direct exchange interactions (j inter = 0) between the nanoparticles, but instead they
interacted only via dipolar forces with dipolar strength g.
In this case, we go beyond the classical model of coherent rotation of the particle’s
Stoner–Wohlfarth magnetization, in which each nanoparticle is described by a classical spin vector as in the case of Fe nanoparticles. Our mesoscopic model involves
a set of three classical unit spin vectors, one for the core s 1i and two for the surface
layer s 2i , s 3i with magnetic moments m n = M n V n /M s V n = 1 stands for the core
and n = 2, 3 for the “up” and “down” shell or surface sublattices of the nanoparticle,
respectively, as it is described in Sect. 2.1.1. In this way, surface effects were included
for each i nanoparticle in the assembly.
The energy parameters in (2.1) are based on the bulk values of maghemite (M s =
4.2 × 10
5 A/m and K = 5 × 10
3 J/m
3 ), and their modifications are established
considering the nanoparticles morphology (e.g., reduced symmetry and reduced size)
using a mean field approach. Accordingly, the values of the intra-particle exchange
energy among the core spin and the surface spins were taken as j c1 = −7.77, j c2 = −
1.35, j srf = −0.091 and the anisotropy energy of the core as k C = 0.1, while that of
the surface as k srf = 2.5, since it is expected to be more than one order of magnitude
larger than that of the core.
The dipolar strength energies (g) and magnetic moments (m) have been calculated
taking into account the experimental values of the particle concentration (p) and
the saturation magnetization (M s ) of the nano-architectures for the three different