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M. Vasilakaki et al.
greatly their magnetic behavior becomes an excessively complicated computational
issue, since the single-spin treatment becomes insufficient to describe their magnetic
structure. We have developed a novel mesoscopic scale model for the study of these
nanoparticle systems that consider more than one macrospin for the description of
each nanoparticle together with the interparticle interactions [7, 21]. Our model
gives the possibility for explicit treatment of all the regions inside each nanoparticle,
namely the core, the shell, the core/shell interface and the surface [21, 35]. As we
will describe below, the number of the effective spins for each nanoparticle depends
on the characteristics of the studied system.
The Monte Carlo (MC) simulation technique with the implementation of the
Metropolis algorithm [36, 37] has been proven a very powerful and reliable tool
for the systematic study of the magnetic behavior of nanoparticle systems at
finite temperature. Especially in the case of NPs with core–shell or core–surface
morphology, the technique is advantageous because it gives the possibility to take
into account explicitly the regions of each nanoparticle, so the details of their internal
structure can be studied together with the interparticle interactions using the suitable
mesoscopic model. The appropriate choice of a model Hamiltonian is the starting
point of MC simulations, and then the random number generator is used to calculate
statistical fluctuations in order to generate the correct thermo-dynamical probability
distribution simulating a canonical ensemble [37].
In this chapter, we present for three cases our work on the magnetic behavior of
assemblies of nanoparticles using numerical modeling. We describe in our mesoscopic model that takes into account: (a) the morphology of the macroscopic assemblies and (b) the interplay between the interparticle interactions and the intraparticle characteristics of each nanoparticle. For the numerical modeling of these
systems, we use the Monte Carlo simulation technique with the implementation of
the Metropolis algorithm [3] that includes explicitly the temperature. The characteristics of the hysteresis loops, magnetization curves as a function of the applied field
and the temperature-dependent ZFC/FC magnetization are studied. A comparison
with experimental findings is given in all cases.
2.2 Case Studies
2.2.1 Case Study 1: Magnetic Behavior of Nanoparticle
Assemblies: Interplay of Nanoparticles Morphology
(Core/Surface and Core/Shell) with the Interparticle
Interactions
Here, we review our work on dense assemblies of nanoparticles where the nanoparticle’s morphology is taken into account. We present results on (a) ferrite nanoparticles with core/surface morphology, more specifically for spherical γ-Fe 2 O 3 nanoparticles covered with an organic surfactant in the case that only dipolar interparticle
M. Vasilakaki et al.
greatly their magnetic behavior becomes an excessively complicated computational
issue, since the single-spin treatment becomes insufficient to describe their magnetic
structure. We have developed a novel mesoscopic scale model for the study of these
nanoparticle systems that consider more than one macrospin for the description of
each nanoparticle together with the interparticle interactions [7, 21]. Our model
gives the possibility for explicit treatment of all the regions inside each nanoparticle,
namely the core, the shell, the core/shell interface and the surface [21, 35]. As we
will describe below, the number of the effective spins for each nanoparticle depends
on the characteristics of the studied system.
The Monte Carlo (MC) simulation technique with the implementation of the
Metropolis algorithm [36, 37] has been proven a very powerful and reliable tool
for the systematic study of the magnetic behavior of nanoparticle systems at
finite temperature. Especially in the case of NPs with core–shell or core–surface
morphology, the technique is advantageous because it gives the possibility to take
into account explicitly the regions of each nanoparticle, so the details of their internal
structure can be studied together with the interparticle interactions using the suitable
mesoscopic model. The appropriate choice of a model Hamiltonian is the starting
point of MC simulations, and then the random number generator is used to calculate
statistical fluctuations in order to generate the correct thermo-dynamical probability
distribution simulating a canonical ensemble [37].
In this chapter, we present for three cases our work on the magnetic behavior of
assemblies of nanoparticles using numerical modeling. We describe in our mesoscopic model that takes into account: (a) the morphology of the macroscopic assemblies and (b) the interplay between the interparticle interactions and the intraparticle characteristics of each nanoparticle. For the numerical modeling of these
systems, we use the Monte Carlo simulation technique with the implementation of
the Metropolis algorithm [3] that includes explicitly the temperature. The characteristics of the hysteresis loops, magnetization curves as a function of the applied field
and the temperature-dependent ZFC/FC magnetization are studied. A comparison
with experimental findings is given in all cases.
2.2 Case Studies
2.2.1 Case Study 1: Magnetic Behavior of Nanoparticle
Assemblies: Interplay of Nanoparticles Morphology
(Core/Surface and Core/Shell) with the Interparticle
Interactions
Here, we review our work on dense assemblies of nanoparticles where the nanoparticle’s morphology is taken into account. We present results on (a) ferrite nanoparticles with core/surface morphology, more specifically for spherical γ-Fe 2 O 3 nanoparticles covered with an organic surfactant in the case that only dipolar interparticle