Dynamic effects of dipolar interactions on the magnetic behavior of magnetite nanoparticles

Isothermal magnetization and initial dc susceptibility of spheroidal, nearly monodisperse magnetite nanoparticles (typical diameter: 8 nm) prepared by a standard thermo-chemical route have been measured between 10 and 300 K. The samples contained magnetite nanoparticles in the form of either a dried powder (each nanoparticle being surrounded by a stable oleic acid shell as a result of the preparation procedure) or a solid dispersion in PEGDA-600 polymer; different nanoparticle (NP) concentrations in the polymer were studied. In all samples the NPs were not tightly agglomerated nor their ferromagnetic cores were directly touching. The high-temperature inverse magnetic susceptibility is always found to follow a linear law as a function of T, crossing the horizontal axis at negative temperatures ranging from 175 to about 1,000 K. The deviation from the standard superparamagnetic behavior is related to dipolar interaction among NPs; however, a careful analysis makes it hard to conclude that such a behavior originates from a dominant antiferromagnetic character of the interaction. The results are well explained considering that the studied samples are in the interacting superparamagnetic (ISP) regime. The ISP model is basically a mean field theory which allows one to straightforwardly account for the role of magnetic dipolar interaction in a NP system. The model predicts the existence of specific scaling laws for the reduced magnetization which have been confirmed in all studied samples. The interaction of each magnetic dipole moment with the local, random dipolar field produced by the other dipoles results in the presence of a large fluctuating energy term whose magnitude is comparable to the static barrier for magnetization reversal/rotation related to magnetic anisotropy. On the basis of the existing theories on thermal crossing of a barrier whose height randomly fluctuates in time it is predicted that the rate of barrier crossing is substantially driven by the rate of barrier fluctuations, which is fast (10⁸–10⁹ Hz) and almost independent of temperature. As a consequence, the standard picture of superparamagnetic NPs which undergo single-particle blocking by a static barrier below the blocking temperature should be substantially revised, at least in the present materials. The ISP model is perfectly matching with the view of activated magnetization rotation whose kinetics is significantly modified by barrier height fluctuations.