2 Interparticle Interactions: Theory and Mesoscopic Modeling
47
and we have calculated the hysteresis loop and the ZFC/FC magnetization curves
together with the fully interacting system.
As we can see from Fig. 2.1, when the dipolar strength is zero, consequently only
the intra-particle exchange interactions and the anisotropy energy term contribute to
the total energy, the blocking temperature of the non-interacting particle system
decreases (Fig. 2.1b). The characteristics of the ZFC/FC magnetization curves
(Fig. 2.1b) also indicate the movement from the super spin glass nanoparticle system
to a non-interacting blocked assembly of nanoparticles. The coercive field does not
seem to be affected, probably due to the strong competition between the intra-particle
exchange coupling and the surface anisotropy.
On the other hand, in the absence of intra-particle interactions (j c1 = j c2 = j srf = 0)
(Fig. 2.2), the spins inside each nanoparticle do not interact with each other; thus, this
frustration does not exist and the coercivity is decreased. The blocking temperature
also is slightly decreased. Our results are in agreement with the experimental findings
[27].
(b) Core/shell nanoparticle dense assemblies interacting with dipolar and
exchange interparticle interactions
Next, we study the magnetic behavior of dense random assemblies of FM core/AFM
shell nanoparticles. In this case, we take into account the interparticle dipolar and
exchange interactions. The simulations are based on Co/CoO (FM/AFM) nanoparticles with 6 nm total diameter and a thin antiferromagnetic shell (~1 nm). Considering
a dense assembly of Co/CoO nanoparticles with very thin CoO layer, we develop a
three-spin model for the Co/CoO nanoparticle to simulate dense 2D and 3D assemblies [21, 41]. In each nanoparticle, the FM core was described by one spin and two
spins described the thin AFM shell with the appropriate anisotropy (k c = 0.1, k shell
= 8.0) and exchange parameters (j c1 = 0.32, j c2 = 0.3, j shell = −6). The anisotropy
axes of each nanoparticle were randomly oriented, one for the core and one common
for the shell. The interparticle dipolar strength was taken as g = 0.1. If the nanoparticles are in direct contact, the interparticle exchange interactions are considered also
between the core spins and the neighboring surface spins due to the very small shell
thickness. Thus, additionally to the exchange coupling of the neighboring surface
spins that is characterized by the strength parameter j inter = 2.5, we consider also
the exchange interaction of the core spin of the one nanoparticle with the surface
spins of the other nanoparticle with strengths j coreshell1 = 2.0, j coreshell2 = 0.5. The
interparticle exchange interactions in these systems are particularly strong.
We have demonstrated in Margaris et al. [21] the effectiveness of our mesoscopic
method based on a Monte Carlo approach to simulate 2D large ensembles of bimagnetic core/shell nanoparticles and their important role on the exchange bias
behavior of these system. Our MC simulation results of the effect of the exchange
interactions on the exchange bias are in excellent agreement with the experimental
results in the study of 2D random assemblies of Co/CoO core/shell nanoparticles
[21]. Here, we simulate disordered arrays of nanoparticles where N particles are
placed, randomly, on the nodes of a 3D cubic lattice inside a box of edge length L =
10a. We simulate the hysteresis loops (Fig. 2.3a, c) at T = 0.02 and the temperature
47
and we have calculated the hysteresis loop and the ZFC/FC magnetization curves
together with the fully interacting system.
As we can see from Fig. 2.1, when the dipolar strength is zero, consequently only
the intra-particle exchange interactions and the anisotropy energy term contribute to
the total energy, the blocking temperature of the non-interacting particle system
decreases (Fig. 2.1b). The characteristics of the ZFC/FC magnetization curves
(Fig. 2.1b) also indicate the movement from the super spin glass nanoparticle system
to a non-interacting blocked assembly of nanoparticles. The coercive field does not
seem to be affected, probably due to the strong competition between the intra-particle
exchange coupling and the surface anisotropy.
On the other hand, in the absence of intra-particle interactions (j c1 = j c2 = j srf = 0)
(Fig. 2.2), the spins inside each nanoparticle do not interact with each other; thus, this
frustration does not exist and the coercivity is decreased. The blocking temperature
also is slightly decreased. Our results are in agreement with the experimental findings
[27].
(b) Core/shell nanoparticle dense assemblies interacting with dipolar and
exchange interparticle interactions
Next, we study the magnetic behavior of dense random assemblies of FM core/AFM
shell nanoparticles. In this case, we take into account the interparticle dipolar and
exchange interactions. The simulations are based on Co/CoO (FM/AFM) nanoparticles with 6 nm total diameter and a thin antiferromagnetic shell (~1 nm). Considering
a dense assembly of Co/CoO nanoparticles with very thin CoO layer, we develop a
three-spin model for the Co/CoO nanoparticle to simulate dense 2D and 3D assemblies [21, 41]. In each nanoparticle, the FM core was described by one spin and two
spins described the thin AFM shell with the appropriate anisotropy (k c = 0.1, k shell
= 8.0) and exchange parameters (j c1 = 0.32, j c2 = 0.3, j shell = −6). The anisotropy
axes of each nanoparticle were randomly oriented, one for the core and one common
for the shell. The interparticle dipolar strength was taken as g = 0.1. If the nanoparticles are in direct contact, the interparticle exchange interactions are considered also
between the core spins and the neighboring surface spins due to the very small shell
thickness. Thus, additionally to the exchange coupling of the neighboring surface
spins that is characterized by the strength parameter j inter = 2.5, we consider also
the exchange interaction of the core spin of the one nanoparticle with the surface
spins of the other nanoparticle with strengths j coreshell1 = 2.0, j coreshell2 = 0.5. The
interparticle exchange interactions in these systems are particularly strong.
We have demonstrated in Margaris et al. [21] the effectiveness of our mesoscopic
method based on a Monte Carlo approach to simulate 2D large ensembles of bimagnetic core/shell nanoparticles and their important role on the exchange bias
behavior of these system. Our MC simulation results of the effect of the exchange
interactions on the exchange bias are in excellent agreement with the experimental
results in the study of 2D random assemblies of Co/CoO core/shell nanoparticles
[21]. Here, we simulate disordered arrays of nanoparticles where N particles are
placed, randomly, on the nodes of a 3D cubic lattice inside a box of edge length L =
10a. We simulate the hysteresis loops (Fig. 2.3a, c) at T = 0.02 and the temperature