Crossover From Individual to Collective Magnetism in Dense Nanoparticle Systems: Local Anisotropy Versus Dipolar Interactions

Dense systems of magnetic nanoparticles may exhibit dipolar collective behavior. However, two fundamental questions remain unsolved: i) whether the transition temperature may be affected by the particle anisotropy or it is essentially determined by the intensity of the interparticle dipolar interactions, and ii) what is the minimum ratio of dipole-dipole interaction ($E_\text{dd}$) to nanoparticle anisotropy ($K_{\text{ef}}V$, anisotropy $\times$ volume) energies necessary to crossover from individual to collective behavior. A series of particle assemblies with similarly intense dipolar interactions but widely varying anisotropy is studied. The $K_\text{ef}$ is tuned through different degrees of cobalt-doping in maghemite nanoparticles, resulting in a variation of nearly an order of magnitude. All the bare particle compacts display collective behavior, except the one made with the highest anisotropy particles, which presents ``marginal'' features. Thus, a threshold of $K_{\text{ef}} V/E_{\text{dd}} \approx 130$ to suppress collective behavior is derived, in good agreement with Monte Carlo simulations. This translates into a crossover value of $\approx 1.7$ for the easily accessible parameter $T_\text{MAX}$(interacting)$/T_\text{MAX}$(non-interacting) (ratio of the peak temperatures of the zero-field-cooled magnetization curves of interacting and dilute particle systems), which is successfully tested against the literature to predict the individual-like$/$collective behavior of any given interacting particle assembly comprising relatively uniform particles.