Non-Debye Behavior of the Néel and Brown Relaxation in Interacting Magnetic Nanoparticle Ensembles

We used ac-susceptibility measurements to study the superspin relaxation in Fe(3)O(4)/Isopar M nanomagnetic fluids of different concentrations. Temperature-resolved data collected at different frequencies, χ″ vs. T|(f), reveal magnetic events both below and above the freezing point of the carrier fluid (T(F) = 197 K): χ″ shows peaks at temperatures T(p1) and T(p2) around 75 K and 225 K, respectively. Below T(F), the Néel mechanism is entirely responsible for the superspin relaxation (as the carrier fluid is frozen), and we found that the temperature dependence of the relaxation time, τ(N)(T(p1)), is well described by the Dorman-Bessais-Fiorani (DBF) model: τNT=τrexp⁡EB+EadkB T. Above T(F), both the internal (Néel) and the Brownian superspin relaxation mechanisms are active. Yet, we found evidence that the effective relaxation times, τ(eff), corresponding to the T(p2) peaks observed in the denser samples do not follow the typical Debye behavior described by the Rosensweig formula 1τeff=1τN+1τB. First, τ(eff) is 5 × 10(-5) s at 225 K, almost three orders of magnitude more that its Néel counterpart, τ(N)~8 × 10(-8) s, estimated by extrapolating the above-mentioned DBF analysis. Thus, 1τN≫1τeff, which is clearly not consistent with the Rosensweig formula. Second, the observed temperature dependence of the effective relaxation time, τ(eff)(T(p2)), is excellently described by τB-1T=Tγ0exp⁡-E'kBT-T0', a model solely based on the hydrodynamic Brown relaxation, τB(T)=3ηTVHkBT, combined with an activation law for the temperature variation of the viscosity, ηT=η0exp⁡E'/kB(T-T0'. The best fit yields γ0=3ηVHkB = 1.6 × 10(-5) s·K, E'/k(B) = 312 K, and T(0)' = 178 K. Finally, the higher temperature T(p2) peaks vanish in the more diluted samples (δ ≤ 0.02). This indicates that the formation of larger hydrodynamic particles via aggregation, which is responsible for the observed Brownian relaxation in dense samples, is inhibited by dilution. Our findings, corroborating previous results from Monte Carlo calculations, are important because they might lead to new strategies to synthesize functional magnetic ferrofluids for biomedical applications.