Abstract. Stable single-domain (SSD) grains were mixed separately with superparamagnetic, pseudosingle-domain, and multidomain (MD) magnetite/maghemite particles in order to test the linearity of various magnetic parameters as a function of mixing ratio. Hysteresis loops, isothermal remanent magnetization acquisition curves, DC demagnetization curves, and low-temperature thermal demagnetization curves were measured on the mixtures. The experiments demonstrate that magnetization parameters are linearly dependent on the mixing ratio, while more complex parameters, e.g., coercivities, do not behave linearly as a function of mixing ratio. Armed with linearity, we apply a mathematical technique which, given a database of type curves, uses singular value decomposition to solve for the various concentrations of the magnetic phases in the mixture and a Monte Carlo simulation to determine the error in the inversion. We then test the technique on numerical mixtures, on the physical mixtures, and on a small set of natural samples from Lake Pepin, Minnesota. Finally, the magnetic behavior of the mixture of MD and SSD grains is considered, and two more mixture strains of MD and SSD grains (numerically produced) are considered to facilitate this discussion.

[1] In 1965, D. J. Dunlop showed that the joint distribution of particle volumes and microcoercivities f(V, H k0 ) can be determined for magnetically monomineralic, thermally stable single-domain (SSD) ensembles by taking advantage of the joint temperature and field dependence of relaxation time. We have developed a procedure that follows Dunlop's strategy to obtain f(V, H k0 ) for ensembles containing both superparamagnetic and SSD grains, based on backfield remanence curves measured over a range of temperatures. Each point on the derivative curves represents the integrated contribution from grains that lie along a corresponding blocking contour on the Néel plot. A suitable set of such line integral samples can be used to reconstruct the f(V, H k0 ) distribution using the methods of tomographic imaging. Samples of the basal Tiva Canyon Tuff have narrow size distributions of elongate Ti-poor titanomagnetite. Tomographic inversion of the low-temperature backfield spectra yield sharply peaked f(V, H k0 ) distributions, from which we calculate modal grain dimensions in good agreement with those observed by transmission electron microscopy. Analysis of synthetic samples containing bimodal populations clearly distinguishes the two modes. Because our simplified forward calculations incompletely account for the effects of orientation distribution, the width of the coercivity distribution at each temperature is underestimated, and consequently, the inverse calculations yield grain distributions that are overly broad. Frequency-and temperature-dependent susceptibilities calculated for the inverted f(V, H k0 ) distributions accord fairly well with measured susceptibilities for the weakly interacting Tiva Canyon samples, less well for a moderately interacting paleosol specimen, and poorly for a strongly interacting ferrofluid.Citation: Jackson, M., B. Carter-Stiglitz, R. Egli, and P. Solheid (2006), Characterizing the superparamagnetic grain distribution f(V, H k ) by thermal fluctuation tomography,

[1] We test how well a few hysteresis parameters (saturation remanence M rs , coercive force H c and remanent coercivity H cr ) serve to determine the proportions of end-members in binary mixtures. Our end-members are six magnetites whose grain sizes are within the superparamagnetic (SP), stable single-domain (SD, three samples), pseudo-SD (PSD), and multidomain (MD) ranges (Carter-Stiglitz et al., 2001). The three SD magnetites have contrasting origins and properties: (1) bacterial magnetite crystals of a single size and coercivity, arranged in chains; (2) natural volcanic magnetites with a narrow distribution of coercivities; and (3) synthetic magnetites precipitated in glass, with a broader coercivity distribution. Our parameter mixing theory assumes linear magnetization curves of the endmembers between zero field and the largest coercive force H c (that of the SD phase, if present). Similarly remanent hysteresis curves should be linear up to the maximum remanent coercive force H cr . Three of our mixtures (SP plus bacterial SD, PSD plus bacterial SD, MD plus volcanic SD) had acceptable agreement between predicted and measured dependences of H c , H cr and the curve of M rs /M s versus. H cr /H c (Day plot) on end-member concentrations. A nonlinear approximation to remanent hysteresis curves gave a reasonable fit to MD plus glass SD results. In this case, H cr /H c for the most MDrich mixture is larger than H cr /H c of either end-member. Such behavior is characteristic of bimodal mixtures in which H cr is largely determined by the hard (SD) phase and H c by the soft (MD) phase. The only mixture that could not be modeled by linear or nonlinear parameter theory was MD plus bacterial SD. The bacterial SD hysteresis loop descends almost vertically at ÀH c because of the extremely narrow range of particle sizes and coercivities. In general, linear and nonlinear parameter mixing models are adequate if only an approximate fit to real data is needed. An inversion method using complete magnetization curves as end-member basis functions is preferable as an unmixing technique. However, comparison of measured data to type curves, for example, on a Day plot, gives a quick indication of what end-member phases might be involved in the mix and provides additional insight before beginning an inversion.

Magnetic exchange bias is a phenomenon whereby the hysteresis loop of a 'soft' magnetic phase is shifted by an amount H(E) along the applied field axis owing to its interaction with a 'hard' magnetic phase. Since the discovery of exchange bias fifty years ago, the development of a general theory has been hampered by the uncertain nature of the interfaces between the hard and soft phases, commonly between an antiferromagnetic phase and a ferro- or ferrimagnetic phase. Exchange bias continues to be the subject of investigation because of its technological applications and because it is now possible to manipulate magnetic materials at the nanoscale. Here we present the first documented example of exchange bias of significant magnitude (>1 T) in a natural mineral. We demonstrate that exchange bias in this system is due to the interaction between coherently intergrown magnetic phases formed through a natural process of phase separation during slow cooling over millions of years. Transmission electron microscopy studies show that these intergrowths have a known crystallographic orientation with a known crystallographic structure and that the interfaces are coherent.

[1] A numerical model is developed in order to simulate the loss of low-temperature remanence while warming through the Verwey transition. We concentrate on the amount of remanence lost (d fc and d zfc ) during field cooled and zero field cooled low temperature demagnetization curves for stable single domain (SSD) particles of (1) inorganic magnetite and (2) biogenic magnetite in the form of magnetosome chains. The model predicts that delta ratios (d fc /d zfc ) for inorganic SSD magnetite increase from 1 to 1.6 with increasing aspect ratio and that magnetosome chains have elevated delta ratios of at least 2.0. Disaggregated magnetosomes are predicted to behave similarly to inorganic acicular SSD magnetite. The numerical results agree with experimental results.

[1] An unpredicted effect of the Verwey transition in magnetite is that a field-cooled (FC) remanent magnetization can be less intense than a zero-field cooled (ZFC) isothermal remanence. The effect, only documented in a handful of multidomain (MD) samples, is thought to be unique to MD material. Data for new MD samples all show an elevation of ZFC over FC remanences. Current theory suggests that the FC easy axis bias alone produces the effect. We measured hysteresis loops after three cooling pretreatments; the results are inconsistent with the aforementioned theory. They are, however, consistent with a previous hypothesis which cites the absence of transformational twins in FC samples as an important factor. Our initial low-temperature domain observations in FC and ZFC magnetite further support this theory. We also present data for MD titanomagnetites (x = 0.16, 0.35). These samples also show elevated ZFC remanences below a critical temperature (T crit ). The titanomagnetites' frequency dependence of susceptibility around T crit , the suppression of the amplitude dependence of susceptibility below T crit , and Mössbauer data suggest that the change in magnetic anisotropy at T crit is related to a suppression of B site electron hopping at low temperature, at least on the timescale of the magnetic measurements. Given our remanence data, field cooling must affect the orientation of the new low-temperature magnetic easy axis. We appeal to the same process as we did for magnetite to explain the elevation of ZFC moments, noting that the exact nature of the transition across T crit is not completely understood.Citation: Carter-Stiglitz, B., B. Moskowitz, P. Solheid, T. S. Berquó, M. Jackson, and A. Kosterov (2006), Low-temperature magnetic behavior of multidomain titanomagnetites: TM0, TM16, and TM35,

The loss in remanence at the Verwey transition (TV) was modeled for elongate stable single domain magnetite for two experiments: 1) thermal cycling of room temperature saturation isothermal remanent magnetization (RTSIRM), 300 → 10 → 300 K, and 2) warming of zero‐field cooled and field‐cooled remanences from 10 K to 300 K. The RTSIRM simulations used magnetocrystalline anisotropy constants for stoichiometric magnetite and aspect ratios (AR) from 1 to ∞, for assemblages of inorganic particles and 10‐magnetosome chains. The results match the experimentally observed behavior of reversibility. The second set of simulations was conducted with low‐temperature magnetocrystalline anisotropy constants for varying degrees of non‐stoichiometry, and AR = 5. Minor non‐stoichiometry lowers the drop in remanence at TV and increases the “delta ratio” (δfc/δzfc) to values as high as ∼6. New experiments demonstrate that maghematization (non‐stoichiometry) can partly explain the low‐temperature magnetic behavior observed in magnetotactic magnetite to date.

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