Characterizing the superparamagnetic grain distribution f(V, H_k) by thermal fluctuation tomography

In 1965, D. J. Dunlop showed that the joint distribution of particle volumes and microcoercivities f(V, H_k0) can be determined for magnetically monomineralic, thermally stable single-domain (SSD) ensembles by taking advantage of the joint temperature and field dependence of relaxation time. We have developed a procedure that follows Dunlop's strategy to obtain f(V, H_k0) for ensembles containing both superparamagnetic and SSD grains, based on backfield remanence curves measured over a range of temperatures. Each point on the derivative curves represents the integrated contribution from grains that lie along a corresponding blocking contour on the Néel plot. A suitable set of such line integral samples can be used to reconstruct the f(V, H_k0) distribution using the methods of tomographic imaging. Samples of the basal Tiva Canyon Tuff have narrow size distributions of elongate Ti-poor titanomagnetite. Tomographic inversion of the low-temperature backfield spectra yield sharply peaked f(V, H_k0) distributions, from which we calculate modal grain dimensions in good agreement with those observed by transmission electron microscopy. Analysis of synthetic samples containing bimodal populations clearly distinguishes the two modes. Because our simplified forward calculations incompletely account for the effects of orientation distribution, the width of the coercivity distribution at each temperature is underestimated, and consequently, the inverse calculations yield grain distributions that are overly broad. Frequency- and temperature-dependent susceptibilities calculated for the inverted f(V, H_k0) distributions accord fairly well with measured susceptibilities for the weakly interacting Tiva Canyon samples, less well for a moderately interacting paleosol specimen, and poorly for a strongly interacting ferrofluid.