A wide variety of Earth and planetary materials are very good recorders of paleomagnetic information. However, most magnetic grains in these materials are not in the stable single domain grain size range but are larger and in nonuniform vortex magnetization states. We provide a detailed account of vortex phenomena in geologic materials by simulating first‐order reversal curves (FORCs) via finite‐element micromagnetic modeling of magnetite nanoparticles with realistic morphologies. The particles have been reconstructed from focused ion beam nanotomography of magnetite‐bearing obsidian and accommodate single and multiple vortex structures. Single vortex (SV) grains have fingerprints with contributions to both the transient and transient‐free zones of FORC diagrams. A fundamental feature of the SV fingerprint is a central ridge, representing a distribution of negative saturation vortex annihilation fields. SV irreversible events at multiple field values along different FORC branches determine the asymmetry in the upper and lower lobes of generic bulk FORC diagrams of natural materials with grains predominantly in the vortex state. Multivortex (MV) FORC signatures are modeled here for the first time. MV grains contribute mostly to the transient‐free zone of a FORC diagram, averaging out to create a broad central peak. The intensity of the central peak is higher than that of the lobes, implying that MV particles are more abundant than SV particles in geologic materials with vortex state fingerprints. The abundance of MV particles, as well as their single domain‐like properties point to MV grains being the main natural remanent magnetization carriers in geologic materials.

First‐order reversal curve (FORC) diagrams of synthetic binary mixtures with single‐domain, vortex state, and multidomain end‐members (EMs) were analyzed using principal component analysis (FORC‐PCA). Mixing proportions derived from FORC‐PCA are shown to deviate systematically from the known weight percent of EMs, which is caused by the lack of reversible magnetization contributions to the FORC distribution. The error in the mixing proportions can be corrected by applying PCA to the raw FORCs, rather than to the processed FORC diagram, thereby capturing both reversible and irreversible contributions to the signal. Here we develop a new practical implementation of the FORC‐PCA method that enables quantitative unmixing to be performed routinely on suites of FORC diagrams with up to four distinct EMs. The method provides access not only to the processed FORC diagram of each EM, but also to reconstructed FORCs, which enables objective criteria to be defined that aid identification of physically realistic EMs. We illustrate FORC‐PCA with examples of quantitative unmixing of magnetic components that will have widespread applicability in paleomagnetism and environmental magnetism.

This is the author accepted manuscript. The final version is available from the Geological Society of America via http://dx.doi.org/10.1130/G37490.

We describe a method for simulating first‐order reversal curve (FORC) diagrams of interacting single‐domain particles. Magnetostatic interactions are calculated in real space, allowing simulations to be performed for particle ensembles with arbitrary geometry. For weakly interacting uniaxial particles, the equilibrium magnetization at each field step is obtained by direct solution of the Stoner‐Wohlfarth model, assuming a quasi‐static distribution of interaction fields. For all other cases, the equilibrium magnetization is calculated using an approximate iterated solution to the Landau‐Lifshitz‐Gilbert equation. Multithreading is employed to allow multiple curves to be computed simultaneously, enabling FORC diagrams to be simulated in reasonable time using a standard desktop computer. Statistical averaging and post processing lead to simulated FORC diagrams that are comparable to their experimental counterparts. The method is applied to several geometries of relevance to rock and environmental magnetism, including densely packed random clusters and partially collapsed chains. The method forms the basis of FORCulator, a freely available software tool with graphical user interface that will enable FORC simulations to become a routine part of rock magnetic studies.

We describe a quantitative magnetic unmixing method based on principal component analysis (PCA) of first‐order reversal curve (FORC) diagrams. For PCA, we resample FORC distributions on grids that capture diagnostic signatures of single‐domain (SD), pseudosingle‐domain (PSD), and multidomain (MD) magnetite, as well as of minerals such as hematite. Individual FORC diagrams are recast as linear combinations of end‐member (EM) FORC diagrams, located at user‐defined positions in PCA space. The EM selection is guided by constraints derived from physical modeling and imposed by data scatter. We investigate temporal variations of two EMs in bulk North Atlantic sediment cores collected from the Rockall Trough and the Iberian Continental Margin. Sediments from each site contain a mixture of magnetosomes and granulometrically distinct detrital magnetite. We also quantify the spatial variation of three EM components (a coarse silt‐sized MD component, a fine silt‐sized PSD component, and a mixed clay‐sized component containing both SD magnetite and hematite) in surficial sediments along the flow path of the North Atlantic Deep Water (NADW). These samples were separated into granulometric fractions, which helped constrain EM definition. PCA‐based unmixing reveals systematic variations in EM relative abundance as a function of distance along NADW flow. Finally, we apply PCA to the combined data set of Rockall Trough and NADW sediments, which can be recast as a four‐EM mixture, providing enhanced discrimination between components. Our method forms the foundation of a general solution to the problem of unmixing multicomponent magnetic mixtures, a fundamental task of rock magnetic studies.