Magnetic relaxation and correlating effective magnetic moment with particle size distribution in maghemite nanoparticles

•Magnetic properties of γ-Fe2O3 nanoparticles, size=7.04(0.78)nm, are reported.•Attempt frequency fo=2.6×1010 Hz and no interparticle interactions are inferred.•M vs. H above TB analyzed using modified Langevin yields µp≈7300 µB per particle.•M vs. H above TB fit to distribution of moments yields results consistent with µp.•Modified Langevin fit is meaningful if width of moment distribution is <0.83.

The role of particle size distribution inherently present in magnetic nanoparticles (NPs) is examined in considerable detail in relation to the measured magnetic properties of oleic acid-coated maghemite (γ-Fe2O3) NPs. Transmission electron microscopy (TEM) of the sol–gel synthesized γ-Fe2O3 NPs showed a log-normal distribution of sizes with average diameter 〈D〉=7.04 nm and standard deviation σ=0.78 nm. Magnetization, M, vs. temperature (2–350 K) of the NPs was measured in an applied magnetic field H up to 90 kOe along with the temperature dependence of the ac susceptibilities, χ′ and χ″, at various frequencies, fm, from 10 Hz to 10 kHz. From the shift of the blocking temperature from TB=35 K at 10 Hz to TB=48 K at 10 kHz, the absence of any significant interparticle interaction is inferred and the relaxation frequency fo=2.6×1010 Hz and anisotropy constant Ka=5.48×105 erg/cm3 are determined. For TTB, the data of M vs. H up to 90 kOe at several temperatures are analyzed two different ways: (i) in terms of the modified Langevin function yielding an average magnetic moment per particle μp=7300(500) μB; and (ii) in terms of log-normal distribution of moments yielding 〈μ〉=6670 µB at 150 K decreasing to 〈μ〉=6100 µB at 300 K with standard deviations σ≃〈μ〉/2. It is argued that the above two approaches yield consistent and physically meaningful results as long as the width parameter, s, of the log-normal distribution is less than 0.83.