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Abstract
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The exchange integral in the magnetic response of a spherical metallic iron (Fe) and nickel (Ni)
nanoparticle is theoretically studied by using Monte Carlo simulations. To this end, using the
nanoparticles model in spherical coordinates, we compute magnetization, magnetic susceptibility,
specific heat, internal energy, and hysteresis loop over a wide range of temperatures for an Fe and Ni
nanoparticle with a size of about 2 nm. The phase transition temperatures are interpolated versus the
exchange parameters, and it is observed that the dependence on the coupling parameter is
completely linear. Moreover, from the susceptibility results of the samples, the sharpest peak with the
least fluctuation gives us the most appropriate Curie temperature and exchange integral for this
system. However, the peak related to the heat capacity is also in the Curie temperature range. From
the internal energy results, it can be understood that with the increase in phase transition and
interaction, the system reaches equilibrium. The magnetic coercive field and remanent magnetization
caused by nanoparticles indicate superparamagnetic properties at room temperature. At the end, the
obtained results allow us to theoretically determine the magnetic properties of spherical nanoparticles
and pave the way for the development of nanoparticles for many applications.
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