6 Hollow Magnetic Nanoparticles
149
Fig. 6.8 Depiction of the evolution of the interfaces playing a role in the exchange coupling of
the core/shell and hollow MNPs, which gives rises to the horizontally shifted (EB) hysteresis loops
after field-cooling down to low temperatures
6.5 Monte Carlo Simulations
In order to understand the peculiarities of the magnetic behavior of hollow magnetic
structures from a theoretical point of view, one has to revert to a simulation approach
that is able to take into account not only the characteristics of their geometry, but also
the peculiarities of their specific composition and interactions among the spins at the
atomistic level. Although micromagnetic calculations in the continuum approximation [33] have been conducted to study the possible equilibrium magnetic order of
ferromagnetic hollow MNPs, they can only give a first approximation to the real situation since they are neither suitable for antiferromagnets such as magnetic oxides,
nor can they take into account the disorder at the inner and outer surfaces. For this
purpose, simulations at the atomistic level are required, describing the magnetic ions
by Heisenberg spins placed at the nodes of real magnetic oxide structures like the
one for maghemite that has spins in two sublattices characterized by tetrahedral and
octahedral coordination and different values and signs of the exchange interactions.
Moreover, we have seen experimentally that MNPs might not be homogeneous from
the structural point of view, so an atomistic approach can easily model variations
149
Fig. 6.8 Depiction of the evolution of the interfaces playing a role in the exchange coupling of
the core/shell and hollow MNPs, which gives rises to the horizontally shifted (EB) hysteresis loops
after field-cooling down to low temperatures
6.5 Monte Carlo Simulations
In order to understand the peculiarities of the magnetic behavior of hollow magnetic
structures from a theoretical point of view, one has to revert to a simulation approach
that is able to take into account not only the characteristics of their geometry, but also
the peculiarities of their specific composition and interactions among the spins at the
atomistic level. Although micromagnetic calculations in the continuum approximation [33] have been conducted to study the possible equilibrium magnetic order of
ferromagnetic hollow MNPs, they can only give a first approximation to the real situation since they are neither suitable for antiferromagnets such as magnetic oxides,
nor can they take into account the disorder at the inner and outer surfaces. For this
purpose, simulations at the atomistic level are required, describing the magnetic ions
by Heisenberg spins placed at the nodes of real magnetic oxide structures like the
one for maghemite that has spins in two sublattices characterized by tetrahedral and
octahedral coordination and different values and signs of the exchange interactions.
Moreover, we have seen experimentally that MNPs might not be homogeneous from
the structural point of view, so an atomistic approach can easily model variations