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

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 (gamma-Fe2O3) NPs. Transmission electron microscopy (TEM) of the sol-gel synthesized gamma-Fe2O3 NPs showed a log-normal distribution of sizes with average diameter < D >=7.04 rim and standard deviation sigma=0.78 nm. Magnetization, M, vs. temperature (2-350 K) of the NPs was measured in an applied magnetic field El up to 90 kOe along with the temperature dependence of the ac susceptibilities, chi' and chi, at various frequencies,fm, horn 10 Hz to 10 kHz. From the shift of the blocking temperature horn T-B=35 K at 10 Hz to T-B=48 K at 10 kHz, the absence of any significant interparticle interaction is inferred and the relaxation frequency f(o) =2.6 x 10(10) Hz and anisotropy constant K-a=5.48 x 10(5) erg/cm(3) are determined. For T < TB, the coercivity tic is practically negligible. For T > TB, 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 mu(p)=7300(500) mu(B); and (ii) in terms of log-normal distribution of moments yielding =6670 M-B at 150 K decreasing to =6100 mu(B) at 300 K with standard deviations sigma similar or equal to /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. (C) 2015 Elsevier B.V. All rights reserved