Chapter 2
Interparticle Interactions: Theory
and Mesoscopic Modeling
Marianna Vasilakaki, George Margaris, and Kalliopi Trohidou
Abstract In this chapter, we discuss the interparticle interaction effects in assemblies of magnetic nanoparticles. For our study, we have developed a mesoscopic scale
model that takes into account: (a) the morphology of the assemblies and (b) the interplay between the interparticle and intra-particle characteristics of the nanoparticles.
The hysteresis loops, the virgin magnetization curves and the temperature-dependent
(Field Cooled (FC)/zero-field cooled (ZFC)) magnetization curves have been calculated with our model. Results are presented for three case studies of different nanoparticles’ morphologies assemblies and they show that our mesoscopic model reproduces well the experimentally studied systems and reveals the origin of the observed
magnetic behavior.
2.1 Introduction
Magnetic nanoparticles are commonly formed in random or ordered assemblies.
Ferrofluids [1] and granular magnetic solids are usually characterized as random
nanoparticle assemblies while patterned media and self-assembled arrays [2] are
described as ordered ensembles. The crucial role in determining the magnetic
behavior of both types of assemblies is played by the interparticle interactions,
namely the long-range dipolar interactions and the short-range exchange interactions for nanoparticles in contact which are usually meet in the random assemblies.
It has been demonstrated that the presence of interparticle exchange interactions
changes the physical properties of a nanoparticles system [3]. If the strength of the
interparticle interactions is relatively weak, namely the interparticle energy is much
lower than the individual particle anisotropy energy, the interparticle interactions
are considered just a perturbation to the superparamagnetic state; this leads to the
so-called interacting superparamagnet model [4], where the static and dynamical
M. Vasilakaki · G. Margaris · K. Trohidou (B)
Institute of Nanoscience and Nanotechnology, NCSR Demokritos, 15310, Aghia Paraskevi,
Attiki, Greece
e-mail: k.trohidou@inn.demokritos.gr
© Springer Nature Switzerland AG 2021
D. Peddis et al. (eds.), New Trends in Nanoparticle Magnetism,
Springer Series in Materials Science 308,
https://doi.org/10.1007/978-3-030-60473-8_2
39
Interparticle Interactions: Theory
and Mesoscopic Modeling
Marianna Vasilakaki, George Margaris, and Kalliopi Trohidou
Abstract In this chapter, we discuss the interparticle interaction effects in assemblies of magnetic nanoparticles. For our study, we have developed a mesoscopic scale
model that takes into account: (a) the morphology of the assemblies and (b) the interplay between the interparticle and intra-particle characteristics of the nanoparticles.
The hysteresis loops, the virgin magnetization curves and the temperature-dependent
(Field Cooled (FC)/zero-field cooled (ZFC)) magnetization curves have been calculated with our model. Results are presented for three case studies of different nanoparticles’ morphologies assemblies and they show that our mesoscopic model reproduces well the experimentally studied systems and reveals the origin of the observed
magnetic behavior.
2.1 Introduction
Magnetic nanoparticles are commonly formed in random or ordered assemblies.
Ferrofluids [1] and granular magnetic solids are usually characterized as random
nanoparticle assemblies while patterned media and self-assembled arrays [2] are
described as ordered ensembles. The crucial role in determining the magnetic
behavior of both types of assemblies is played by the interparticle interactions,
namely the long-range dipolar interactions and the short-range exchange interactions for nanoparticles in contact which are usually meet in the random assemblies.
It has been demonstrated that the presence of interparticle exchange interactions
changes the physical properties of a nanoparticles system [3]. If the strength of the
interparticle interactions is relatively weak, namely the interparticle energy is much
lower than the individual particle anisotropy energy, the interparticle interactions
are considered just a perturbation to the superparamagnetic state; this leads to the
so-called interacting superparamagnet model [4], where the static and dynamical
M. Vasilakaki · G. Margaris · K. Trohidou (B)
Institute of Nanoscience and Nanotechnology, NCSR Demokritos, 15310, Aghia Paraskevi,
Attiki, Greece
e-mail: k.trohidou@inn.demokritos.gr
© Springer Nature Switzerland AG 2021
D. Peddis et al. (eds.), New Trends in Nanoparticle Magnetism,
Springer Series in Materials Science 308,
https://doi.org/10.1007/978-3-030-60473-8_2
39