Monte Carlo Studies of Magnetic Nanoparticles

Abstract

Magnetic nanoparticles are complex mesoscopic systems which have unique physical properties that clearly differ from those of atoms and bulk materials. They find numerous technological applications ranging from ultra-high-density recording media (Bader, 2006) to biomedicine (Pankhurst et al., 2003). The necessity to reduce the size of the nanoparticles for these applications have raised a key issue in their study which is their thermal stability. The Monte Carlo (MC) simulation technique with the implementation of the Metropolis Algorithm (Metropolis et al., 1953) has been proved a very powerful tool for the systematic study of the magnetic behaviour of nanoparticles and nanoparticle assemblies. The two major advantages of this technique are a) the possibility for atomic scale treatment of the nanoparticles, so the details of their microstructure can be studied and b) the implementation of finite temperature through the Metropolis algorithm. Although, the obtained dynamics in the Monte Carlo simulations is intrinsic and the time evolution of the system does not come from any deterministic equation for the magnetisation, the results of the Monte Carlo simulations reproduce qualitatively the trend of the experimental data (Binder 1987). Actually this good qualitative agreement between the simulation results and the experimental data enable us to have a better insight into the nanoscaled phenomena, though some of them stem from non-equilibrium processes (Landau & Binder, 2000). A microscopic treatment of the magnetisation of ferromagnetic nanoparticles, using Monte Carlo techniques, was first developed by Binder and co-workers (Binder et al., 1970; Wildpaner 1974). An important demonstration of the work was the reduction of the magnetisation near the surface of the particle. Clearly this was to be expected because a surface spin has a smaller number of neighbours than it would have in bulk and, hence, experiences a reduced mean field. For very small particles (less than say 5 nm) the proportion of surface spins is such that they will make a major contribution to the magnetisation. As a result, the magnetisation will decrease with temperature over a range where the bulk magnetisation is roughly constant and deviations from Curie-law behaviour in the susceptibility are to be expected. In the period following the Monte Carlo work cited above, interest has been developed in finite-size scaling, and it is in this context that subsequent advances (Landau, 1976) in the nanoparticle magnetism have occurred. In addition, over the last decade there is a continuous effort to reduce the nanoparticles size and at the same time to overcome the thermal instability at room temperature (Skumryev et