Evidence of Individual Superspin Relaxation in Diluted Fe3O4/Hexane Ferrofluids

We used dc magnetization and ac susceptibility to investigate the magnetic relaxation of ferrofluids made of 8 nm average-diameter Fe3O4 nanoparticles dispersed in hexane. Samples of different concentrations (δ) spanning two orders of magnitude ranging from 0.66 to 0.005 mg (Fe3O4)/mL (hexane) were used to vary the interparticle interaction strength. Our data reveal a critical concentration, δc = 0.02 mg/mL, below which the ferrofluid behaves like an ideal nanoparticle ensemble where the superspins relax individually according to a Néel–Brown activation law τ(T) = τ0exp (EB/kBT) with a characteristic time τo ~10^(−9) s. That is further confirmed by the observed invariance of the relative peak temperature variation per frequency decade ∆ = ∆T / [T·∆log(f)], which stays constant at ~0.185 when δ < δc. At higher concentrations, between 0.02 and 0.66 mg/mL, we found that ∆ exhibits a monotonic increase with the inverse concentration, 1/δ, and the collective superspin dynamics is described by a Vogel–Fulcher law, τ(T) = τ0exp(EB/[kB(T−T0)]). Within this regime, the dipolar interaction strength parameter T0 increases from T0 = 0 K at δc = 0.02 mg/mL to T0 = 14.7 K at δ = 0.66 mg/mL.