2 Interparticle Interactions: Theory and Mesoscopic Modeling
41
along the interface called “exchange bias” [20]. In these structures, the interplay
between internal nanoparticle structural characteristics and interparticle interaction
leads to enhanced or novel magnetic properties [21, 22]. MC simulations have shown
that in random assemblies of ferromagnetic (FM)/antiferromagnetic (AFM) nanoparticles, the exchange interparticle interactions play a major role causing the experimentally observed increase in the H C and the exchange bias field H ex with the concentration of the nanoparticles [21]. Therefore, the modification of the coercive and
the exchange bias field in assemblies of nanoparticles with core/shell morphology,
which results from the competition between the intra-particle exchange anisotropy
and interparticle interactions, is a challenging issue. It is evident that the basic understanding of the magnetic properties of random assemblies of bi-magnetic nanoparticles is of crucial importance for the next generation of high performance magnetic
nanomaterials.
Importantly, the improved production techniques enable the production of ultrasmall nanoparticles below 5 nm in size. For these sizes, it has been demonstrated
experimentally and numerically that the particle surface plays the dominant role in
their magnetic behavior. Therefore, surface effects have to be taken explicitly into
account in the calculations, in order to understand the magnetic properties of the
assemblies [7].
Another factor that influences the magnetic behavior of the nanoparticles is the
assembly’s structure. For instance, clustering of nanoparticles in an assembly can be
achieved by bringing magnetic nanoparticles at distances where they can strongly
interact. In this case, either colloidal assemblies are produced and capping with
molecules prevents the exchange coupling between them [23–25], or nanoparticles
(NPs) are created by deposition techniques that they do not allow them to coalesce
but retain a distinct boundary with a significant free volume among aggregates
of exchange coupled particles [26]. Their observed magnetic behavior has been
analyzed through numerical modeling, revealing interesting effects like stepwise
behavior in the hysteresis loops and the virgin magnetization curves [27, 28].
Finally, there is experimental evidence that diluted assemblies of magnetic
nanoparticles in a magnetic matrix exhibit exchange bias behavior and dynamical effects. Indeed, a diluted assembly of Co nanoparticles randomly embedded
in magnetically and structurally disordered Mn matrix [29–31] shows enhanced
exchange bias field and SSG state. These characteristics are attributed to the intraparticle characteristics, namely the Co/Mn alloying at the surface of Co nanoparticles,
that create strong exchange interaction at the Co/Mn interface, and to the granularity
of the matrix in mediating interparticle interactions, through exchange and dipole–
dipole coupling between the uncompensated moments of Mn grains, as they are
confirmed by Monte Carlo simulations [32].
Atomic scale modeling of assemblies of magnetic nanoparticles including interparticle interactions, especially for dense samples, demands a very big amount of
CPU memory and time. For this reason, the single-spin treatment of the Stoner Wohlfarth (SW) coherent rotation model [33, 34] was usually implemented in the study of
assemblies of magnetic nanoparties. However, in the recent years, modeling assemblies of ultra-small nanoparticles where core/shell or core/surface morphology affects
41
along the interface called “exchange bias” [20]. In these structures, the interplay
between internal nanoparticle structural characteristics and interparticle interaction
leads to enhanced or novel magnetic properties [21, 22]. MC simulations have shown
that in random assemblies of ferromagnetic (FM)/antiferromagnetic (AFM) nanoparticles, the exchange interparticle interactions play a major role causing the experimentally observed increase in the H C and the exchange bias field H ex with the concentration of the nanoparticles [21]. Therefore, the modification of the coercive and
the exchange bias field in assemblies of nanoparticles with core/shell morphology,
which results from the competition between the intra-particle exchange anisotropy
and interparticle interactions, is a challenging issue. It is evident that the basic understanding of the magnetic properties of random assemblies of bi-magnetic nanoparticles is of crucial importance for the next generation of high performance magnetic
nanomaterials.
Importantly, the improved production techniques enable the production of ultrasmall nanoparticles below 5 nm in size. For these sizes, it has been demonstrated
experimentally and numerically that the particle surface plays the dominant role in
their magnetic behavior. Therefore, surface effects have to be taken explicitly into
account in the calculations, in order to understand the magnetic properties of the
assemblies [7].
Another factor that influences the magnetic behavior of the nanoparticles is the
assembly’s structure. For instance, clustering of nanoparticles in an assembly can be
achieved by bringing magnetic nanoparticles at distances where they can strongly
interact. In this case, either colloidal assemblies are produced and capping with
molecules prevents the exchange coupling between them [23–25], or nanoparticles
(NPs) are created by deposition techniques that they do not allow them to coalesce
but retain a distinct boundary with a significant free volume among aggregates
of exchange coupled particles [26]. Their observed magnetic behavior has been
analyzed through numerical modeling, revealing interesting effects like stepwise
behavior in the hysteresis loops and the virgin magnetization curves [27, 28].
Finally, there is experimental evidence that diluted assemblies of magnetic
nanoparticles in a magnetic matrix exhibit exchange bias behavior and dynamical effects. Indeed, a diluted assembly of Co nanoparticles randomly embedded
in magnetically and structurally disordered Mn matrix [29–31] shows enhanced
exchange bias field and SSG state. These characteristics are attributed to the intraparticle characteristics, namely the Co/Mn alloying at the surface of Co nanoparticles,
that create strong exchange interaction at the Co/Mn interface, and to the granularity
of the matrix in mediating interparticle interactions, through exchange and dipole–
dipole coupling between the uncompensated moments of Mn grains, as they are
confirmed by Monte Carlo simulations [32].
Atomic scale modeling of assemblies of magnetic nanoparticles including interparticle interactions, especially for dense samples, demands a very big amount of
CPU memory and time. For this reason, the single-spin treatment of the Stoner Wohlfarth (SW) coherent rotation model [33, 34] was usually implemented in the study of
assemblies of magnetic nanoparties. However, in the recent years, modeling assemblies of ultra-small nanoparticles where core/shell or core/surface morphology affects