Evidence of Individual Superspin Relaxation in Diluted Fe[sub.3]O[sub.4]/Hexane Ferrofluids

We used dc magnetization and ac susceptibility to investigate the magnetic relaxation of ferrofluids made of 8 nm average-diameter Fe[sub.3]O[sub.4] nanoparticles dispersed in hexane. Samples of different concentrations (δ) spanning two orders of magnitude ranging from 0.66 to 0.005 mg (Fe[sub.3]O[sub.4])/mL (hexane) were used to vary the interparticle interaction strength. Our data reveal a critical concentration, δ[sub.c] = 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)=τ[sub.0]exp(EB/kBT) with a characteristic time τ[sub.o] ~10[sup.−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 < δ[sub.c]. At higher concentrations, between 0.02 and 0.66 mg/mL, we found that Δ exhibits a monotonic increase with the inverse concentration, 1/δ, and the collective superspin dynamics is described by a Vogel–Fulcher law, τ(T)=τ[sub.0]exp[EB/kBT−T0]. Within this regime, the dipolar interaction strength parameter T[sub.0] increases from T[sub.0] = 0 K at δ[sub.c] = 0.02 mg/mL to T[sub.0] = 14.7 K at δ = 0.66 mg/mL.