Monte Carlo study of magnetic behaviour of single Fe and Ni nanoparticles

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.