52
M. Vasilakaki et al.
Fig. 2.6 Assembly of NPs interacting with two different dipolar interaction strengths g (assembly
concentration p = 0.5). a Initial magnetization versus H curves (VC) at temperature T = 0.005 and
b ZFC/FC magnetization versus T curves with H cool = 0.05 [28]
We have to note that the strong effective interparticle exchange coupling (j inter ≥
1) in an area and the uniaxial anisotropy result in a nonzero initial magnetization
in each area even in the absence of a field, after a few steps. This fact and the
small number of areas may result to an initial average value of the magnetization
different from zero. This deviation is of the order of 1
2
√ n a (= 0.176 for n a = 8),
under the condition that the interaction strength between the areas is weak. When the
exchange interaction between particles in the different clusters is strong, the initial
magnetization raises and specific initial configurations have to be chosen to reduce
the problem [45].
The role of the dipolar strength in the magnetization behavior of the assembly
is examined next, in the case of a dense non-uniform assembly (p = 0.5). Dipolar
interactions give rise to collective effects [18]. As the dipolar coupling increases,
dipolar interactions start playing a more important role, start competing initially and
gradually dominating over the exchange interactions and the anisotropy. In this case,
we have a slower increase of the magnetization at low fields and a slower approach
to saturation in the virgin curve (Fig. 2.6a). The local dipolar field is the sum of the
fields of all the randomly oriented dipoles and oscillates randomly on every node.
As a result, in some cases, reversals of clusters may create locally large dipolar
fields, helping other spins or clusters to overcome their energy barrier and triggering
their reversal more easily. These local fluctuations are larger as the dipolar strength
increases. Consequently, smaller steps are present, at different positions as the value
of g increases (Fig. 2.6a and b). It is expected that with the increase of the dipolar
strength, we have an increase in the maximum of the ZFC magnetization versus
temperature curve [28].
We compare our results with those of the uniform morphology for the nanoparticles’ assembly. In this case, we distribute the particles at random on the nodes of
the lattice with occupation probability p = 0.5. All particles interact via exchange
interaction of the same strength and dipolar interactions. In the case that the exchange
coupling constant is equal to the anisotropy constant (j inter = k = 1), there is a strong
M. Vasilakaki et al.
Fig. 2.6 Assembly of NPs interacting with two different dipolar interaction strengths g (assembly
concentration p = 0.5). a Initial magnetization versus H curves (VC) at temperature T = 0.005 and
b ZFC/FC magnetization versus T curves with H cool = 0.05 [28]
We have to note that the strong effective interparticle exchange coupling (j inter ≥
1) in an area and the uniaxial anisotropy result in a nonzero initial magnetization
in each area even in the absence of a field, after a few steps. This fact and the
small number of areas may result to an initial average value of the magnetization
different from zero. This deviation is of the order of 1
2
√ n a (= 0.176 for n a = 8),
under the condition that the interaction strength between the areas is weak. When the
exchange interaction between particles in the different clusters is strong, the initial
magnetization raises and specific initial configurations have to be chosen to reduce
the problem [45].
The role of the dipolar strength in the magnetization behavior of the assembly
is examined next, in the case of a dense non-uniform assembly (p = 0.5). Dipolar
interactions give rise to collective effects [18]. As the dipolar coupling increases,
dipolar interactions start playing a more important role, start competing initially and
gradually dominating over the exchange interactions and the anisotropy. In this case,
we have a slower increase of the magnetization at low fields and a slower approach
to saturation in the virgin curve (Fig. 2.6a). The local dipolar field is the sum of the
fields of all the randomly oriented dipoles and oscillates randomly on every node.
As a result, in some cases, reversals of clusters may create locally large dipolar
fields, helping other spins or clusters to overcome their energy barrier and triggering
their reversal more easily. These local fluctuations are larger as the dipolar strength
increases. Consequently, smaller steps are present, at different positions as the value
of g increases (Fig. 2.6a and b). It is expected that with the increase of the dipolar
strength, we have an increase in the maximum of the ZFC magnetization versus
temperature curve [28].
We compare our results with those of the uniform morphology for the nanoparticles’ assembly. In this case, we distribute the particles at random on the nodes of
the lattice with occupation probability p = 0.5. All particles interact via exchange
interaction of the same strength and dipolar interactions. In the case that the exchange
coupling constant is equal to the anisotropy constant (j inter = k = 1), there is a strong