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The collective organization of magnetic nanoparticles (MNPs) influences significantly their hyperthermic properties, relevant for their in vitro and in vivo applications. We report a systematic investigation of the effects of the concentration and the static bias direct current (DC) magnetic field superposed over the alternating magnetic field (AMF), both in a parallel and perpendicular configuration, on the specific absorption rate (SAR) by using zinc ferrite MNPs. The nonmonotonic dependence of the SAR on the concentration, with a maximum at very small concentrations (c ≤ 0.1 mgFe/mL), followed by a minimum at 0.25 mgFe/mL, and the second maximum of 3.3 kW/gFe at around 1 mgFe/mL, was explained by the passage of the MNPs from a single particle behavior to a collective one and the role of the dipolar interactions. By superposing a static 10 kA/m bias DC field on the AMF we obtained an increase in the SAR for both parallel and perpendicular orientations, up to 4285 W/g_Fe and 4070 W/g_Fe, respectively. To the best of our knowledge, this is the first experimental proof of a significant enhancement of the SAR produced by a perpendicular DC field. The effect of the DC field to increase the SAR is accompanied by an increase in the hyperthermia coercive field (H_cHyp) for both configurations. No enhancement of the DC fields was noticed for the MNPs immobilized in a solid matrix but the DC field increases the H_cHyp only in the parallel configuration. This translates into a higher SAR value for the perpendicular configuration as compared to the parallel configuration. These results have practical applications for magnetic hyperthermia.