Frequency dependence of magnetic susceptibility for populations of single-domain grains

A recent paper (Dearing et al. 1996) on the use of frequency dependence of magnetic susceptibility (X(fd)) in magnetic grain-size investigations of environmental materials has proposed a fundamentally new model for the magnetic susceptibility of single-domain (SD) grains measured at different frequencies, and is divergent from the now well-established theory of SD behaviour. This new model appears to be founded on a confusion about the behaviour of SD grains, as predicted by theory, and magnetic measurements of real materials, which naturally have a distribution of magnetic grain sizes. Here I try to clear up this confusion by showing how different log-normal distributions of magnetic grain sizes affect the frequency dependence of magnetic susceptibility measurement. This analysis highlights that the limiting maximum X(fd) value of similar to 15 per cent obtained for environmental materials can be explained simply as a constraint imposed by the magnetic grain-size distribution having a finite minimum width (similar to 1.0 on a natural log scale). There is no reason to suppose that if the grain-size dispersion was narrower higher X(fd) values could not be observed. Furthermore, the X(fd) value is non-unique and so cannot be used quantitatively to determine the amount or grain-size distribution of SD grains in a sample.