40
M. Vasilakaki et al.
properties of the individual particles are only partially modified by the interaction
with the neighboring particles. On the other hand, if the interparticle interactions are
strong and randomness in the distribution of particle positions and in the anisotropy
axes orientation exists, then a collective super spin glass state (SSG) is formed. This
SSG state is observed in concentrated frozen ferrofluids [5] and in concentrated granular systems where single-domain particles are dispersed in a non-magnetic matrix
[6, 7].
Various experiments demonstrated that the presence of dipolar interactions results
to: (a) a reduction of remanence at low temperature and of the coercive field [8],
(b) an increase of the blocking temperature (T B ) defined as the temperature that
corresponds to the maximum of ZFC magnetization curve [9], (c) an increase of
the energy barrier distribution width [9], (d) deviations of the ZFC magnetization
curves from the Curie behavior [10], (e) differences between in-plane and out-ofplane remanence, and (f) an increase of the blocking temperature with the frequency
of the applied field [11]. The first model that studied the magnetic interaction effects
on the coercivity was presented by Néel [12] and it was generalized by Wohlfarth [13]
taking into account the orientations and the geometrical arrangement of the particles.
According to this model, the coercive field decreases with the increase of the particle
concentration. Later, a detailed study on the effect of interparticle interactions was
reported by Dormann et al. [14] where it was demonstrated that the total energy
barrier increases with the dipolar interactions Monte Carlo simulations studies [15]
confirmed the increase of the blocking temperature of a dipolarly interacting system
with the increase of the concentration and that the magnetic properties of randomly
located and oriented nanoparticle systems are determined by the interplay between
the single-particle anisotropy energy and the dipolar interaction energy. Indeed, it
has been demonstrated that the dense face-centered cubic (FCC) packing of the
particles leads to more pronounced ferromagnetic (FM) behavior than the simple
cubic (SC) packing; this behavior is characterized by FM domains of supermoments
of particles, the so-called superferromagnetism [16]. The sample free boundaries and
the corresponding demagnetizing field have also a strong effect on the remanence
of the assembly while they produce a minor reduction to the coercivity [15]. Later,
Lu et al. by performing MC simulations found that the coercive field (H C ) can be
increased or decreased with dipole–dipole interactions, depending on the bonding
angle between the easy axes of the nanoparticles [17]. On the other hand, Vargas et al.
claimed that demagnetization role of dipole–dipole interactions reduces the H C of
the system [8]. However, Nadeem et al. observed an enhancement in H C and blocking
temperature of compacted Fe 3 O 4 nanoparticles compared with the powder sample
[18]. They attributed this result to the highlighting effect of interparticle interactions
on the energy barrier between equilibrium states.
Overall, it becomes evident that the magnetic characteristics (hysteresis loops,
blocking temperatures) of an assembly of magnetic nanoparticles depend not only
on the strength of the interactions but also on the morphology of the samples [19].
In the recent years, the effort to reduce the nanoparticle size and at the same time to
achieve high magnetic anisotropy led to the production of bi-magnetic nanoparticles
with enhanced nanoparticle anisotropy due to the extra unidirectional anisotropy
M. Vasilakaki et al.
properties of the individual particles are only partially modified by the interaction
with the neighboring particles. On the other hand, if the interparticle interactions are
strong and randomness in the distribution of particle positions and in the anisotropy
axes orientation exists, then a collective super spin glass state (SSG) is formed. This
SSG state is observed in concentrated frozen ferrofluids [5] and in concentrated granular systems where single-domain particles are dispersed in a non-magnetic matrix
[6, 7].
Various experiments demonstrated that the presence of dipolar interactions results
to: (a) a reduction of remanence at low temperature and of the coercive field [8],
(b) an increase of the blocking temperature (T B ) defined as the temperature that
corresponds to the maximum of ZFC magnetization curve [9], (c) an increase of
the energy barrier distribution width [9], (d) deviations of the ZFC magnetization
curves from the Curie behavior [10], (e) differences between in-plane and out-ofplane remanence, and (f) an increase of the blocking temperature with the frequency
of the applied field [11]. The first model that studied the magnetic interaction effects
on the coercivity was presented by Néel [12] and it was generalized by Wohlfarth [13]
taking into account the orientations and the geometrical arrangement of the particles.
According to this model, the coercive field decreases with the increase of the particle
concentration. Later, a detailed study on the effect of interparticle interactions was
reported by Dormann et al. [14] where it was demonstrated that the total energy
barrier increases with the dipolar interactions Monte Carlo simulations studies [15]
confirmed the increase of the blocking temperature of a dipolarly interacting system
with the increase of the concentration and that the magnetic properties of randomly
located and oriented nanoparticle systems are determined by the interplay between
the single-particle anisotropy energy and the dipolar interaction energy. Indeed, it
has been demonstrated that the dense face-centered cubic (FCC) packing of the
particles leads to more pronounced ferromagnetic (FM) behavior than the simple
cubic (SC) packing; this behavior is characterized by FM domains of supermoments
of particles, the so-called superferromagnetism [16]. The sample free boundaries and
the corresponding demagnetizing field have also a strong effect on the remanence
of the assembly while they produce a minor reduction to the coercivity [15]. Later,
Lu et al. by performing MC simulations found that the coercive field (H C ) can be
increased or decreased with dipole–dipole interactions, depending on the bonding
angle between the easy axes of the nanoparticles [17]. On the other hand, Vargas et al.
claimed that demagnetization role of dipole–dipole interactions reduces the H C of
the system [8]. However, Nadeem et al. observed an enhancement in H C and blocking
temperature of compacted Fe 3 O 4 nanoparticles compared with the powder sample
[18]. They attributed this result to the highlighting effect of interparticle interactions
on the energy barrier between equilibrium states.
Overall, it becomes evident that the magnetic characteristics (hysteresis loops,
blocking temperatures) of an assembly of magnetic nanoparticles depend not only
on the strength of the interactions but also on the morphology of the samples [19].
In the recent years, the effort to reduce the nanoparticle size and at the same time to
achieve high magnetic anisotropy led to the production of bi-magnetic nanoparticles
with enhanced nanoparticle anisotropy due to the extra unidirectional anisotropy