Dynamic magnetic phenomena in fine-particle goethite

The distinctive M\"ossbauer spectra of fine-particle goethite ({α}-FeOOH) have been attributed by many authors to superparamagnetism. However, measurements of the magnetic anisotropy energy and particle volume show that the superparamagnetic blocking temperature for most samples is much greater than the N\'eel temperature. A model involving magnetic ordering of clusters created by high concentrations of vacancy defects is proposed, in which the cluster moments slowly relax, thus producing a Boltzmann distribution in the z component of the magnetization. The model provides excellent fits to the temperature-dependent hyperfine-field distributions observed in the M\"ossbauer spectra, and may have wider applicability to other diamagnetically substituted iron oxide materials. A linear relation is observed between TN and the inverse mean crystallite dimension in the [111] direction of -1060(130) K nm, and it is shown that goethite particles must have a volume of less than 1000 nm³ in order to show superparamagnetic M\"ossbauer spectra at room temperature.