Micromagnetic modelling allows the systematic study of the effects of particle size and shape on the first-order reversal curve (FORC) magnetic hysteresis response for magnetite particles in the single-domain (SD) and pseudo-single domain (PSD) particle size range. The interpretation of FORCs, though widely used, has been highly subjective.  Here, we use micromagnetics to model randomly oriented distributions of particles to allow more physically meaningful interpretations.  We show that one commonly found type of PSD particle - namely single vortex (SV) particles - has far more complex signals than SD particles, with multiple peaks and troughs in the FORC distribution, where the peaks have higher switching fields for larger SV particles. Particles in the SD to SV transition zone have the lowest switching fields. Symmetrical and prolate particles display similar behavior, with distinctive peaks forming near the vertical axis of the FORC diagram. In contrast, highly oblate particles produce `butterfly' structures, suggesting that these are potentially diagnostic of particle morphology. We also consider FORC diagrams for distributions of particle sizes and shapes and produce an online application that users can use to build their own FORC distributions.  There is good agreement between the model predictions for distributions of particle sizes and shapes, and the published experimental literature.

Magnetic hysteresis measurements are routinely made in the Earth and planetary sciences to identify geologically meaningful  magnetic recorders, and to study variations in present and past environments. Interpreting magnetic hysteresis data in terms of domain state (particle size)  and paleomagnetic stability are major motivations behind undertaking these measurements, but the interpretations remain  fraught with challenges and ambiguities.To shed new light on these ambiguities, we have undertaken a systematic micromagnetic study to quantify the magnetic hysteresis behavior of room-temperature magnetite as a function of particle size (50-195 nm; equivalent spherical volume diameter) and shape (oblate, prolate and equant);our models span uniformly magnetized single domain (SD) to non-uniformly magnetized single vortex (SV) states.Within our models the reduced magnetization  marks a clear boundary between SD (≥0.5) and SV (<0.5) magnetite.We further identify particle sizes and shapes with unexpectedly low coercivity and coercivity of remanence. These low coercivity regions correspond to magnetite particles that typically have multiple possible magnetic domain states, which has been previously linked to a zone of unstable magnetic recorders.Of all hysteresis parameters investigated, transient hysteresis is most sensitive to particles that exhibit such domain state multiplicity, leading us to suggest that transient behavior be more routinely measured during rock magnetic investigations.

First-order reversal curve (FORC) diagrams are a standard rock magnetic tool for analyzing bulk magnetic hysteresis behaviors, which are used to estimate the magnetic mineralogies and magnetic domain states of grains within natural materials. However, the interpretation of FORC distributions is challenging due to complex domain-state responses, which introduce well-documented uncertainties and subjectivity. Here, we propose a neural network algorithm (FORCINN) to invert the size and aspect ratio distribution from measured FORC data. We trained and tested the FORCINN model using a dataset of synthetic numerical FORCs for single magnetite grains with various grain-sizes (45-400 nm) and aspect ratios (oblate and prolate grains). In addition to successfully testing FORCINN against synthetic datasets, we also tested FORCINN against FORC data measured on natural samples with accurately determined grain-size and aspect ratio distributions. FORCINN was found to provide good estimates of the grain-size distributions for basalt samples and marine sediments.

The ability of rocks to hold a reliable record of the ancient geomagnetic field depends on the structure and stability of magnetic domain-states contained within the rock’s magnetic particles. In paleomagnetic studies, the Day plot is an easily constructed graph of magnetic hysteresis parameters that is frequently used (and mis-used) to estimate the likely magnetic recording stability of samples. Often samples plot in the region of the Day plot attributed to so-called pseudo-single-domain (PSD) particles with little under standing of the implications for domain-states or recording fidelity. Here we use micromagnetic models to explore the hysteresis parameters of magnetite particles with idealized prolate and oblate truncated-octahedral geometries containing single domain (SD), single-vortex (SV) and occasionally multi-vortex (MV) states. We show that these do main states exhibit a well-defined trend in the Day plot that extends from the SD region well into the multi-domain (MD) region, all of which are likely to be stable remanence carriers. We suggest that although the interpretation of the Day plot and its vari33 ants might be subject to ambiguities, if the magnetic mineralogy is known, it can still provide some useful insights about paleomagnetic specimens’ dominant domain state, average particle sizes and, consequently, their paleomagnetic stability.