[1] Although most paleomagnetic and environmental magnetic papers incorporate a Day plot of the hysteresis parameters Mrs/Ms versus Hcr/Hc, a comprehensive theory covering superparamagnetic (SP), single-domain (SD), pseudo-single-domain (PSD), and multidomain (MD) (titano)magnetites is lacking. There is no consensus on how to quantify grain-size trends within the Day plot, how to distinguish MD from SP trends/mixtures, or whether magnetite, titanomagnetites, and other minerals have distinctive trends by which they might be identified. This paper develops the theory of the Day plot parameters for MD, MD + SD, PSD, and SP + SD grains of titanomagnetite (Fe 3– xTixO4) with compositions x = 0 (TM0 or magnetite) and x = 0.6 (TM60). MD grains have a separate trend that intersects the curve for SD + MD mixtures. SP + SD mixtures generate a variety of trends, depending on the SP grain size. All SP + SD curves lie much above those for MD or SD + MD trends, as has been proposed, but not demonstrated, previously. Data for PSD-size magnetites of many different origins fall along a single trend, but different levels of internal stress shift points for similar grain sizes along the ‘‘master curve.’’ In order to use the Day plot to determine grain size, one must have independent information about the state of internal stress. Theoretical model curves for SD + MD mixtures match the PSD magnetite and TM60 data quite well, although the SD!MD transition region in grain size is much narrower for TM60 than for magnetite. The agreement between PSD data and SD + MD mixing curves implies that PSD behavior is due to superimposed independent SD and MD moments, either in individual or separate grains, and not to exotic micromagnetic structures such as vortices. The theory also matches Mrs and Hc values in mechanical mixtures of very fine and very coarse grains, although nonlinear mixing theory is required to explain some Hcr and Hcr/Hc data. INDEX TERMS: 1540 Geomagnetism and Paleomagnetism: Rock and mineral magnetism; 1594 Geomagnetism and Paleomagnetism: Instruments and techniques; 1533 Geomagnetism and Paleomagnetism: Remagnetization; 1512 Geomagnetism and Paleomagnetism: Environmental magnetism;

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2001JB000486

Theory and application of the Day plot (Mrs/Ms versus Hcr/Hc) 1. Theoretical curves and tests using titanomagnetite data

Paleomagnetic and environmental magnetic studies are commonly conducted on samples containing mixtures of magnetic minerals and/or grain sizes. Major hysteresis loops are routinely used to provide information about variations in magnetic mineralogy and grain size. Standard hysteresis parameters, however, provide a measure of the bulk magnetic properties, rather than enabling discrimination between the magnetic components that contribute to the magnetization of a sample. By contrast, first-order reversal curve (FORC) diagrams, which we describe here, can be used to identify and discriminate between the different components in a mixed magnetic mineral assemblage. We use magnetization data from a class of partial hysteresis curves known as first-order reversal curves (FORCs) and transform the data into contour plots (FORC diagrams) of a two-dimensional distribution function. The FORC distribution provides information about particle switching fields and local interaction fields for the assemblage of magnetic particles within a sample. Superparamagnetic, single-domain, and multidomain grains, as well as magnetostatic interactions, all produce characteristic and distinct manifestations on a FORC diagram. Our results indicate that FORC diagrams can be used to characterize a wide range of natural samples and that they provide more detailed information about the magnetic particles in a sample than standard interpretational schemes which employ hysteresis data. It will be necessary to further develop the technique to enable a more quantitative interpretation of magnetic assemblages; however, even qualitative interpretation of FORC diagrams removes many of the ambiguities that are inherent to hysteresis data.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000JB900326

First-order reversal curve diagrams: A new tool for characterizing the magnetic properties of natural samples

The conventional rules, derived from empirical and theoretical considerations, for the interpretation of anisotropy of magnetic susceptibility (AMS) in terms of microstructure and deformation are subject to numerous exceptions as a result of particular rock magnetic effects. Unusual relationships between structural and magnetic axes (so-called inverse or intermediate magnetic fabrics) can occur because of the presence of certain magnetic minerals, either single domain magnetite or various paramagnetic minerals. When more than one mineral is responsible for magnetic susceptibility, various problems appear, in particular the impossibility of using anisotropy to make quantitative inferences on the intensity of the preferred orientation and consequently on strain. In ferromagnetic grains, AMS may also be influenced by the magnetic memory of the grains (including natural remanence). The effect of alternating field or thermal demagnetization on AMS is briefly discussed. As discussed in this article, various rock magnetic techniques, specific to AMS interpretation, have to be developed for a better assessment of the geological significance of AMS data. These techniques mainly rely on measurements of susceptibility versus magnetic field and temperature, together with anisotropy of remanence. 93 refs., 11 figs., 1 tab.

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Rock magnetism and the interpretation of anisotropy of magnetic susceptibility

A comparison of different magnetic methods for determining the relative grain size of magnetite in natural materials: Some results from lake sediments

Because the response of a magnetic substance to an applied field depends strongly on the physical properties of the material, much can be learned by monitoring that response through what is known as a “magnetic hysteresis loop”. The measurements are rapid and quickly becoming part of the standard set of tools supporting paleomagnetic research. Yet the interpretation of hysteresis loops is not simple. It has become apparent that although classic “single-domain”, “pseudo-single-domain”, and “multidomain” loops described in textbooks occur in natural samples, loops are frequently distorted, having constricted middles (wasp-waisted loops) or spreading middles and slouching shoulders (potbellies). Such complicated loops are often interpreted in oversimplified ways leading to erroneous conclusions. The physics of the problem have been understood for nearly half a century, yet numerical simulations appropriate to geological materials are almost unavailable. In this paper we discuss results of numerical simulations using the simplest of systems, the single-domain/superparamagnetic (SD/SP) system. Examination of the synthetic hysteresis loops leads to the following observations: (1) Wasp-waisting and potbellies can easily be generated from populations of SD and SP grains. (2) Wasp-waisting requires an SP contribution that saturates quickly, resulting in a steep initial slope, and potbellies require low initial slopes (the SP contribution approaching saturation at higher fields). The approach to saturation is dependent on volume, hence the cube of grain diameter. Therefore there is a very strong dependence of hysteresis loop shape on the assumed threshold size. (3) We were unable to generate potbellies using an SP/SD threshold size as large as 30 nm, and wasp waists cannot be generated using a threshold size as small as 8 nm. The occurrence of both potbellies and wasp waists in natural samples is consistent with a room temperature threshold size of some 15 nm (±5). (4) Simulations using a threshold size of 15–20 nm with populations dominated by SP grain sizes, that is with a small number of SD grains, produce synthetic hysteresis loops consistent with measured hysteresis loops and transmission electron microscopic observations from submarine basaltic glass. (5) Simulations and measurements using two populations with distinct coercivity spectra can also generate wasp-waisted loops. A relatively straightforward analysis of the resulting loops can distinguish the latter case from wasp-waisting resulting from SP/SD behavior.

Potbellies, wasp-waists, and superparamagnetism in magnetic hysteresis

Hysteresis properties of titanomagnetites: Grain-size and compositional dependence

The effect os cooling rate on the intensity of low-field thermoremanent magnetization (TRM) in uniaxial, single-domain magnetite is calculated, using both numerical and analytical techniques. These calculations indicate that when a single-domain assemblage is cooled much more slowly than in a typical laboratory experiment, it can remain magnetically unblocked and in thermal equilibrium with an external field at temperatures significantly lower than the 'laboratory' blocking temperature. Owing to the rapid rise of spontaneous magnetization just below the Curie temperature the TRM can consequently be elevated by several tens of percent over that acquired in the laboratory. The paleointensity obtained from rocks that have cooled in nature over geologic time may therefore be erroneously high, if single-domain particles are the primary carriers of NRM. These calculations indicate that when the ratio of 'natural' to laboratory cooling rates approximately equals 10/sup -11/, as in the case of orogenic bodies that have cooled over several million years, the paleointensity obtained by the Thellier method can be more than 50% too igh, unless the role of cooling rate is taken into account.

The effect of cooling rate on the intensity of weak‐field trm in single‐domain magnetite

Synthetic titanomagnetites ((1−x)Fe3O4, - xFe2TiO4, 0 ≤ × ≤ 0.6) were prepared by the ceramic oxide method and the equilibrium atmosphere method, and two size fractions were separated out. The first contained particles of size >150 μm, while the second, which was ground in a water slurry, had a mean particle size of about 0.1μm. The magnetic hysteresis properties, i.e., coercive force HC, remanent coercive force ERC, saturation remanence JRS, JRS/JS, and initial susceptibility x0, were measured at room temperature. The coarse grain samples were found to be magnetically soft (HC ∼ 30 Oe) and the hysteretic properties independent of composition. In contrast, the fine grain samples were extremely hard (HC ∼ 400–2000 Oe) and their magnetic characteristics strongly dependent on composition. When compared with the Stoner-Wohlfarth model for single-domain magnetization, the agreement was good, indicating that these latter samples contain mainly single-domain grains. Samples containing both hard and soft fractions exhibited hysteretic properties that depended on the relative proportions of each size fraction.

Magnetic hysteresis properties of synthetic titanomagnetites

An ac bridge method has been used to study the effect of uniaxial compression on the initial magnetic susceptibility of rocks and separated titanomagnetites. The samples used were basalts containing titanomagnetite with varying grain size and morphology and dispersions of magnetite and titanomagnetite powders in epoxy. The results indicate that, (l) the effect of pressure on susceptibility decreases with decreasing grain size, not in a continuous manner but rather depending upon whether the dominant magnetic grain size is multidomain, pseudo single-domain or single-domain, (2) the pressure response increases with the composition parameter x of the titanomagnetite in the solid solution series xFe2TiO4 (1−x)Fe2O4, and (3) the morphology of the grains influences the pressure response. The results are interpreted in terms of the behavior of the multidomain, pseudo single-domain and single-domain material. Changes in thermoremanent magnetization and the acquisition of pressure remanent magnetization under uniaxial compression, which were observed in conjunction with the susceptibility studies, suggest that rocks containing coarse grain titanomagnetites as the dominant magnetic mineral phase are the most efficient stress transducers. Hence a definitive seismomagnetic experiment would be easiest in a seismically active region in which such rocks are prominent.

The effect of uniaxial compression on the initial susceptibility of rocks as a function of grain size and composition of their constituent titanomagnetites

R. Day

Papers

Hysteresis properties of titanomagnetites: Grain-size and compositional dependence

The effect of cooling rate on the intensity of weak‐field trm in single‐domain magnetite

Magnetic hysteresis properties of synthetic titanomagnetites

The effect of uniaxial compression on the initial susceptibility of rocks as a function of grain size and composition of their constituent titanomagnetites

Intensity determination by continuous thermal cycling