[1] Plots of the first-order reversal curve (FORC) function are used to characterize ferromagnetic particles in rocks. The function is based on classical Preisach theory, which represents magnetic hysteresis by elementary loops with displacement H u and half width H c . Using analytical and numerical integration of single-particle magnetization curves, a high-precision FORC function is calculated for a sample with randomly oriented, noninteracting, elongated single-domain (SD) particles. Some properties of the FORC function are independent of the distribution of particle orientations and shapes. There is a negative peak near the H u axis, and the FORC function is identically zero for H u > 0. The negative peak, previously attributed to particle interactions, is due to the increasing slope of a reversible magnetization curve near a jump. This peak is seen in experimental FORC functions of SD samples but not of samples with larger particles, probably because of Barkhausen jumps. The second feature is not seen in any experimental FORC function. A spread of the function to H u > 0 can be caused by particle interactions or nonuniform magnetization.

The demagnetizing tensor for ferromagnets is generalized to include interactions between uniformly magnetized bodies. This “mutual” demagnetizing tensor is symmetric, has a trace of zero, and has other simple geometric properties. The tensor is then used to develop an expression for the macroscopic magnetic field in non‐uniformly magnetized bodies of arbitrary shape. Finally, the theory is applied to a block model of magnetization and explicit formulae for the tensor components are given.

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, so in this size range the SD state is less stable. To calculate the critical sizes, we use rigorous nucleation theory and obtain analytical expressions. The analytical form allows us to explore the effect of grain shape, stress, crystallographic orientation and titanium content in titanomagnetites. We adapt the theory to cubic anisotropy with K1 < 0, which allows us to apply the expressions to titanomagnetites. We find that the size range for SD coercivity is always small. The size range for SD remanence can vary enormously depending on the anisotropy. If the easy axes are oriented favorably, the SD state can occur in large x = 0.6 titanomagnetite grains. Ensembles of magnetite grains with aspect ratios greater than 5 have SD-like remanence but low coercivity. However, most synthetic magnetite grains are nearly equant, and the predicted size range for SD remanence is small to nonexistent. This, rather than grain interactions, may be the reason they have properties such as saturation remanence that do not agree well with standard SD theory.

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