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, δ_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 $\mathsf{\tau }(\mathrm{T})={\mathsf{\tau }}_0\exp \left(\frac{{\mathrm{E}}_{\mathrm{B}}}{{\mathrm{k}}_{\mathrm{B}}\mathrm{T}}\right)$ with a characteristic time τ_o ~10⁻⁹ s. That is further confirmed by the observed invariance of the relative peak temperature variation per frequency decade $∆=\frac{∆\mathrm{T}}{\mathrm{T}·∆\mathrm{l}\mathrm{o}\mathrm{g}\left(\mathrm{f}\right)}$, which stays constant at ~0.185 when δ < δ_c. At higher concentrations, between 0.02 and 0.66 mg/mL, we found that Δ exhibits a monotonic increase with the inverse concentration, $\frac{1}{\delta }$, and the collective superspin dynamics is described by a Vogel–Fulcher law, $\mathsf{\tau }(\mathrm{T})={\mathsf{\tau }}_0\exp \left[\frac{{\mathrm{E}}_{\mathrm{B}}}{{\mathrm{k}}_{\mathrm{B}}\left(\mathrm{T}-{\mathrm{T}}_0\right)}\right]$. Within this regime, the dipolar interaction strength parameter T₀ increases from T₀ = 0 K at δ_c = 0.02 mg/mL to T₀ = 14.7 K at δ = 0.66 mg/mL.