S U M M A R YThe theory, measurement and interpretation of frequency-dependent susceptibility ( xFD) are examined. A new model is proposed which explains xFD in terms of the behaviour of all superparamagnetic grains (SP) with diameters between 0 and ~0 . 0 3 pm. The model predicts maximum xFD percentage values of 14-17 per cent for spherical SP ferrimagnetic grains in the grain-size range 0.01-0.025 pm, and a maximum value of 10-12 per cent for grain assemblages spanning a wider range of grain sizes (0-0.03 pm). Synthetic and experimental data support the model predictions in terms of both maximum xFD percentage values and the relationship between xFD percentage and mass specific xFD, which exhibits an envelope of data points partly related to grain-size distributions within the SP range. When the xFD percentage is at a maximum, the mass specific xFD term can be used to estimate the concentration of SP grains in a sample.Lower values of xFD percentage in soils are caused by the presence of narrow distributions of ultrafine SP grains, frequency-independent stable single and multidomain ferrimagnetic grains. Some soils with low susceptibilities may have low xFD percentages because of an appreciable content of paramagnetic and canted antiferromagnetic minerals. A simple mixing model predicts proportions of SP grains in mixed grain assemblages, but model validation requiring further characterization of grain interaction and grain-size distributions is needed before it can be applied to environmental data.

A range of low-temperature and isothermal magnetic measurements are used to identify the secondary ferrimagnetic mineral (SFM) grain sizes in 10 representative soil samples from Wales. A comparison of percentage frequency-dependent susceptibility ( zFD percentage) and low-temperature remanence measurements shows that they are sensitive to different ranges of superparamagnetic (SP) grains. The relative distributions of SP grains and stable single domain (SSD) grains are similar in nine of the samples. Typical distributions for soils dominated by SFMs are %20-30 per cent SSD and 70-80 per cent SP. Multidomain (MD) grains were not detected in the samples studied. There is evidence that some soils contain significant numbers of ultrafine SP grains <0.010 pm that are not detected by low-temperature remanence measurements at 20 K and which will have the effect of depressing values of low-field susceptibility (xLF) and zFD percentage. A mixing model suggests that zFD percentage may be used semiquantitatively to estimate the proportion of SP grains in a sample. The positively skewed grain-size distributions strongly suggest a mechanism of SFM formation that is driven by processes at the m scale, thus supporting weathering and fermentation as controlling processes, rather than the degradation of SSD bacterial magnetosomes and primary minerals.