Monte Carlo simulations of ${rm Ni Fe_2O_4}$ Nanoparticles

We use Monte Carlo simulations to study ${rm Ni Fe_2O_4}$ nanoparticles. Finite size and surface effects differentiate them from their bulk counterparts. A continuous version of the Wang-Landau algorithm is used to calculate the joint density of states $g(M_z, E)$ efficiently. From $g(M_z, E)$, we obtain the Bragg-Williams free energy of the particle, and other physical quantities. The hysteresis is observed when the nanoparticles have both surface disorder and surface anisotropy. We found that the finite coercivity is the result of interplay between surface disorder and surface anisotropy. If the surface disorder is absent or the surface anisotropy is relatively weak, the nanoparticles often exhibit superparamagnetism.