[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

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

Rock magnetic studies of complex systems that contain mixtures of magnetic minerals or mixed grain size distributions have demonstrated the need for a better method of distinguishing between different magnetic components in geological materials. Hysteresis loops that are constricted in the middle section, but are wider above and below the middle section, are commonly observed in mixed magnetic assemblages. Such “wasp-waisted” hysteresis loops have been widely documented, particularly with respect to rare earth permanent magnets, basaltic lava flows, remagnetized Paleozoic carbonate rocks, and an increasingly wide range of other rocks. Our modelling, combined with a review of previous work, indicates that there are several conditions that give rise to, as well as magnetic properties that are characteristic of, wasp-waisted hysteresis loops. First, at least two magnetic components with strongly contrasting coercivities must coexist. This condition can arise from either mixtures of grain sizes of a single magnetic mineral, or a combination of magnetic minerals with contrasting cocrcivities, or a combination of these two situations. Second, materials that give rise to wasp-waisted hysteresis loops will have relatively high ratios of the coercivity of remanence to coercive force (B cr /B c ) because B0 is controlled by the soft (low coercivity) component, whereas Bcris controlled by the hard (high coercivity) component. Third, values of B cr /B c ? 10 usually only occur for strongly wasp-waisted loops when the low coercivity component comprises an overwhelmingly large fraction of the total volume of magnetic grains. Fourth, a given mixture of superparamagnetic and single-domain (SD) grains is more likely to give rise to wasp-waisted hysteresis loops than an equivalent mixture of SD and multidomain grains. Fifth, our results provide empirical confirmation that the total magnetization of a material is the sum of the weighted contributions of each component, in the absence of significant magnetic interaction between particles. Thus to contribute significantly to wasp-waisted behavior, a mineral magnetic component must give rise to a significant portion of the total magnetization of the rock. As a result, minerals with weak magnetic moments such as hematite need to occur in large concentrations to cause wasp-waistedness in materials that also contain ferrimagnetic minerals. We outline a method for determining the magnetic components that can give rise to wasp-waisted hysteresis loops. This method is based on high- and low-temperature magnetic measurements that are used to identify the dominant remanence-bearing mineral/s and on mineral magnetic techniques that are used to discriminate between different magnetic domain states. The method is illustrated with several examples from archaeological, geological, and synthetic materials.

Wasp-waisted hysteresis loops: Mineral magnetic characteristics and discrimination of components in mixed magnetic systems

This is an updated collation of magnetic parameters of rocks and minerals for geologists, geochemists, and geophysicists. Since the publication of the previous edition of Handbook of Physical Constants [74], two other collations have appeared [16, 18]. In addition, selected magnetic parameters have also been assembled [19, 22, 38, 41, 88]. Rather than produce a fully comprehensive collection, we have aimed for high-precision data obtained from wellcharacterized samples. Both tables and figures have been used for presenting the data, and best-fit equations have been provided for some of the displayed ata so that interpolations can be made easily. In an attempt to discourage the use of the outdated cgs system, all values are in the SI system (see Moskowitz, this volume). References have been cited for the sources used here. However, a more comprehensive bibliography has also been provided from which information can be extracted for samples which have not been included. The single-crystal constants and their variation with temperature and composition are for use by rock magnetists. Paleomagnetists and magnetic anomaly modelers have been provided with the magnetic properties of rocks and polycrystalline mineral samples. Lastly, we have made an effort to address the needs of environmental magnetism, a new group of researchers who require the values of sizeand

http://www.alaska-gold.com/RF003p0189.pdf

Magnetic Properties of Rocks and Minerals

At the Verwey transition (Tv≈110–120 K), magnetite transforms from monoclinic to cubic spinel structure. It has long been believed that magnetic remanence and susceptibility would change markedly at Tv in the case of coarse grains but only slightly or inappreciably in the case of fine (<1 µm) grains. We find on the contrary that remanence changes at Tv by 50–80% in both large and small crystals, if they are stoichiometric. However, minor surface oxidation suppresses the transition, and the fact that fine grains oxidize more readily leads to an apparent size dependence. Our experiments used submicron magnetite cubes with mean sizes of 0.037, 0.076, 0.10 and 0.22 µm which were initially non-stoichiometric (oxidation parameter z from 0.2–0.7). A saturation isothermal remanent magnetization (SIRM) given in a 2.5 T field at 5 K decreased steadily during zero-field warming to 300 K with little or no indication of the Verwey transition. After the oxidized surface of each crystal was reduced to stoichiometric magnetite, the SIRM decreased sharply during warming by 50–80% around 110 K. The change in SIRM for the 0.22 µm grains was almost identical to that measured for a 1.5 mm natural magnetite crystal. Thus a 1012 change in particle volume does not materially affect the remanence transition at Tv but oxidation to z=0.3 essentially suppresses the transition. The effect of the degree of oxidation on Tv provides a sensitive test for maghemitization in soils, sediments and rocks.

/pdf/the-effect-of-oxidation-on-the-verwey-transition-in-lpis99fhta.pdf

The effect of oxidation on the Verwey transition in magnetite

It has long been hypothesized that the pseudo-single-domain properties of submicron magnetites are a result of coexisting multidomain and single-domain-like remanences. We have separated these two types of remanence by low-temperature demagnetization (LTD), in which samples are cooled through the low-temperature magnetite isotropic point and rewarmed to room temperature, all in zero field. At the isotropic point, the first crystalline anisotropy constant vanishes, and multidomain remanence due to displaced domain walls will be unpinned. We measured stepwise alternating field (AF) and thermal demagnetization curves of weak-field thermoremanent magnetization (TRM) and anhysteretic remanent magnetization and of saturation isothermal remanent magnetization (IRMs), both with and without prior LTD, for magnetites with mean particle sizes of 215, 390, and 540 nm. The memory fraction of remanence recovered after LTD, which represents the single-domain-like component, decreased from 44% for 215-nm grains to 23% for 540-nm grains in the case of IRMs. Memory of TRM was approximately twice as large. AF decay curves were soft and multidomain-like before LTD but became harder and single-domain-like in shape after LTD. LTD removed most low unblocking temperature TRM and IRMs. Distributed low unblocking temperatures are therefore a multidomain phenomenon, probably resulting from successive adjustments of domain walls to changing internal fields and pinning strengths during heating.

Separating multidomain and single-domain-like remanences in pseudo-single-domain magnetites (215–540 nm) by low-temperature demagnetization

We have measured initial susceptibility χ0 and the dependence of anhysteretic remanent magnetization (ARM) and thermoremanent magnetization (TRM) on applied field for seven samples of magnetite, with mean grain sizes from 40 to 540 nm. TRM acquisition is nonlinear in geomagnetically relevant weak fields, contrary to the usual assumption made in paleointensity determination. Over the 40–540 nm range, χ0 varies with particle shape but only weakly with particle size d and can be used to correct for varying magnetite concentrations in sediment cores. ARM is strongly size dependent over the same range and is the best parameter for monitoring grain size variations in natural samples. ARM and TRM have similar variations, as d−1 for d≤1 μm, suggesting a common source for this pseudo-single-domain (PSD) dependence on grain size. However, TRM is 10–20 times more intense than ARM in grains around 0.2 μm in size. The TRM microstate seems to be a two-domain structure, whereas the ARM microstate may be a vortex structure, which has never before been convincingly demonstrated by magnetic measurements. Independent evidence comes from theoretical fits to TRM and ARM field dependence data. In moderate and strong fields, TRM in 215–540 nm magnetites is explained by two-domain theory, but ARM is not. In smaller grains (d≤0.1 μm), a PSD theory predicts that TRM is carried by single-domain (SD) moments of entire grains but ARM resides in moments (≈1 per grain) 20–40 times weaker. These remanence levels match those of (metastable) SD and vortex states, respectively. We therefore propose that magnetite grains in the 0.1–0.5 μm size range can remain in metastable SD or two-domain states following acquisition of TRM but revert to a vortex ground state when field-cycled, for example, in ARM acquisition or alternating field demagnetization.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/97JB00957

Thermoremanence, anhysteretic remanence and susceptibility of submicron magnetites: Nonlinear field dependence and variation with grain size

Approximately equidimensional magnetite crystals, with mean sizes of 215, 390, and 540 nm, respectively, have been produced by reducing hematite crystals. Isothermal magnetic hysteresis properties show a clear progression toward multidomain-like behavior as the mean grain size increases. Saturation remanences Mrs are only 5–10% of saturation magnetization Ms, coercive forces HC are low (5.5–8 mT), and both Mrs and HC have grain-size dependences compatible with those previously established for smaller and larger hydrothermally produced magnetites. Coercivities during remanence acquisition are greater than those measured during demagnetization. The difference between acquisition and destructive fields increases in the larger grains as a result of the increasing importance of the internal demagnetizing field. The low-temperature transition is well expressed in the Mrs and HC data of the 540-nm sample but is more subdued for smaller grains. Magnetostrictive, magnetocrystalline, and magnetostatic mechanisms in turn govern coercivity as the temperature rises. Remanence and coercivity ratios, Mrs/Ms and HR/HC, are almost temperature independent up to 500°C, indicating that domain wall configurations resulting from saturating fields are about the same at any temperature. A thermal fluctuation analysis of high-temperature coercive force data suggests that regions 200–250 nm in size are thermally activated as a unit in grains of all sizes; these are likely domain walls. Apparent demagnetizing factors calculated from both low- and high-temperature data are consistent with a mixture of two-domain (2D) and three-domain (3D) grains in all samples. However, theories of remanence in conventional 2D and 3D grains or in mixtures of 2D, 3D, and metastable single-domain grains do not explain the data in a satisfying way.

Low‐temperature and high‐temperature hysteresis of small multidomain magnetites (215–540 nm)

Domain state energy calculations have been made for submicron magnetite cubes, based on a model consisting of planar domains of uniform magnetization separated by 180° domain walls (DWs). The magnetization within a DW is assumed to rotate uniformly, resulting in the appearance of magnetic poles of average density ±(2/π)Js on the particle faces bounding the DWs. Equilibrium domain structure configurations have been determined by minimization of the sum of the demagnetizing and wall energies. Domain structure transition sizes and particle remanences are reported for two-domain and three-domain magnetite cubes.

Theoretical domain structure in multidomain magnetite particles

We describe three useful techniques for investigating magnetic microstructure and granulometry, high-temperature alternating-field (AF) demagnetization, thermal fluctuation analysis (TFA), and determination of the demagnetizing factor N, and give examples of their use For synthetic magnetite samples, thennoremanent magnetization and anhysteretic remanent magnetization are shown to differ in their AF demagnetization spectra at all temperatures up to the blocking range Moreover, various coercivity fractions of either spectrum evolve differently with temperature than does the bulk coercive force TFA of high-temperature coercive force data for dispersed magnetite crystals with mean sizes of 215, 390 and 540 run indicate that ≈200 nm regions are thermally activated in each case These regions may be responsible for pseudo-single-domain behaviour A crude estimate of N for multidomain grains at any temperature is the ratio between bulk coercive force and saturation remanence The 215–540 nm magnetites appear to contain two or three domains between −100°C and 400°C; new domains may nucleate at higher temperatures

Kenneth S. Argyle

Papers

Separating multidomain and single-domain-like remanences in pseudo-single-domain magnetites (215–540 nm) by low-temperature demagnetization

Thermoremanence, anhysteretic remanence and susceptibility of submicron magnetites: Nonlinear field dependence and variation with grain size

Low‐temperature and high‐temperature hysteresis of small multidomain magnetites (215–540 nm)

Theoretical domain structure in multidomain magnetite particles

High-temperature techniques for measuring microcoercivity, crystallite size, and domain state