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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., Comment: 24 pages (proof version), 6 figures

Applications based on aggregates of magnetic nanoparticles are becoming increasingly widespread, ranging from hyperthermia to magnetic recording. However, although some uses require a collective behavior, other need a more individual-like response, the conditions leading to either of these behaviors are still poorly understood. Here we use nanoscale-uniform binary random dense mixtures with different proportions of oxide magnetic nanoparticles with low$/$high anisotropy as a valuable tool to explore the crossover from individual to collective behavior. Two different anisotropy scenarios have been studied in two series of binary compacts: M1, comprising maghemite ($\gamma$-Fe$_2$O$_3$) nanoparticles of different sizes (9.0 nm $/$ 11.5 nm) with barely a factor of 2 between their anisotropy energies and M2, mixing equally-sized pure maghemite (low-anisotropy) and Co-doped maghemite (high-anisotropy) nanoparticles with a large difference in anisotropy energy (ratio $>$ 8). Interestingly, while the M1 series exhibits collective behavior typical of strongly-coupled dipolar systems, the M2 series presents a more complex scenario where different magnetic properties resemble either "individual-like" or "collective", crucially emphasizing that the collective character must be ascribed to specific properties and not to the system as a whole. The strong differences between the two series, offer new insight (systematically ratified by simulations) into the subtle interplay between dipolar interactions, local anisotropy and sample heterogeneity, to determine the behavior of dense assemblies of magnetic nanoparticles., Comment: 43 pages, 8 figures, 1 table; submitted to "Chemistry of Materials" on 14-Aug-2019 (Manuscript ID: cm-2019-032685); status on 30-Sept-2019: still under review