The demagnetizing tensor for ferromagnets is generalized to include interactions between uniformly magnetized bodies. This “mutual” demagnetizing tensor is symmetric, has a trace of zero, and has other simple geometric properties. The tensor is then used to develop an expression for the macroscopic magnetic field in non‐uniformly magnetized bodies of arbitrary shape. Finally, the theory is applied to a block model of magnetization and explicit formulae for the tensor components are given.

The term “pseudo‐single domain” (PSD) has been used to describe the transitional state in rock magnetism that spans the particle size range between the single domain (SD) and multidomain (MD) states. The particle size range for the stable SD state in the most commonly occurring terrestrial magnetic mineral, magnetite, is so narrow (~20–75 nm) that it is widely considered that much of the paleomagnetic record of interest is carried by PSD rather than stable SD particles. The PSD concept has, thus, become the dominant explanation for the magnetization associated with a major fraction of particles that record paleomagnetic signals throughout geological time. In this paper, we argue that in contrast to the SD and MD states, the term PSD does not describe the relevant physical processes, which have been documented extensively using three‐dimensional micromagnetic modeling and by parallel research in material science and solid‐state physics. We also argue that features attributed to PSD behavior can be explained by nucleation of a single magnetic vortex immediately above the maximum stable SD transition size. With increasing particle size, multiple vortices, antivortices, and domain walls can nucleate, which produce variable cancellation of magnetic moments and a gradual transition into the MD state. Thus, while the term PSD describes a well‐known transitional state, it fails to describe adequately the physics of the relevant processes. We recommend that use of this term should be discontinued in favor of “vortex state,” which spans a range of behaviors associated with magnetic vortices.

Magnetotactic bacteria biomineralize iron into magnetite (Fe3O4) nanoparticles that are surrounded by lipid vesicles. These 'magnetosomes' have considerable potential for use in bio- and nanotechnological applications because of their narrow size and shape distribution and inherent biocompatibility. The ability to tailor the magnetic properties of magnetosomes by chemical doping would greatly expand these applications; however, the controlled doping of magnetosomes has so far not been achieved. Here, we report controlled in vivo cobalt doping of magnetosomes in three strains of the bacterium Magnetospirillum. The presence of cobalt increases the coercive field of the magnetosomes--that is, the field necessary to reverse their magnetization--by 36-45%, depending on the strain and the cobalt content. With elemental analysis, X-ray absorption and magnetic circular dichroism, we estimate the cobalt content to be between 0.2 and 1.4%. These findings provide an important advance in designing biologically synthesized nanoparticles with useful highly tuned magnetic properties.

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An unconstrained 3-D micromagnetic model for magnetite grains with resolutions up to 23 x 23 x 63 is presented. The model has been used to investigate the magnetic domain states of submicron parallelepipeds with various elongations. The method of fast Fourier transformation (FFT) has been implemented in three dimensions to accelerate the computation of the magnetostatic energy and its gradient, assuming constant magnetization for each subcube of the model. A 3-D implementation of the exchange energy and its gradient, using a five-point formula to approximate the Laplace operator, was chosen. Special attention has been paid to single-domain (SD) or flower states and pseudo-single-domain (PSD) configurations. A circular configuration, called vortex state, has been found to have the lowest energy of various PSD states. As a local energy minimum (LEM), the free energy of the vortex state is compared to that of a single-domain state. A comparison of these energies is used to determine a lower and an upper threshold size for the SD to PSD transition. In the interval between these two threshold sizes both configurations, SD and PSD, coexist. Above the upper threshold size we found metastable double-vortex configurations which seem to represent three-domain structures with closure domains.

Magnetotactic bacteria contain chains of magnetically interacting crystals (magnetosome crystals), which they use for navigation (magnetotaxis). To improve magnetotaxis efficiency, the magnetosome crystals (usually magnetite or greigite in composition) should be magnetically stable single-domain (SSD) particles. Smaller single-domain particles become magnetically unstable owing to thermal fluctuations and are termed superparamagnetic (SP). Previous calculations for the SSD/SP threshold size or blocking volume did not include the contribution of magnetic interactions. In this study, the blocking volume has been calculated as a function of grain elongation and separation for chains of identical magnetite grains. The inclusion of magnetic interactions was found to decrease the blocking volume, thereby increasing the range of SSD behaviour. Combining the results with previously published calculations for the SSD to multidomain threshold size in chains of magnetite reveals that interactions significantly increase the SSD range. We argue that chains of interacting magnetosome crystals found in magnetotactic bacteria have used this effect to improve magnetotaxis.

Accepted versio

Interpretations of palaeomagnetic observations assume that naturally occurring magnetic particles can retain their primary magnetic recording over billions of years. The ability to retain a magnetic recording is inferred from laboratory measurements, where heating causes demagnetization on the order of seconds. The theoretical basis for this inference comes from previous models that assume only the existence of small, uniformly magnetized particles, whereas the carriers of palaeomagnetic signals in rocks are usually larger, non-uniformly magnetized particles, for which there is no empirically complete, thermally-activated model. This study has developed a thermally-activated numerical micromagnetic model that can quantitatively determine the energy barriers between stable states in nonuniform magnetic particles on geological time scales. We examine in detail the thermal stability characteristics of equidimensional cuboctahedral magnetite and find that contrary to previously published theories, such non-uniformly magnetized particles provide greater magnetic stability than their uniformly magnetized counterparts. Hence, non-uniformly magnetized grains, which are commonly the main remanence carrier in meteorites and rocks, can record and retain highfidelity magnetic recordings over billions of years.micromagnetics | paleomagnetism | geomagnetism S ince the 1900s magnetic recordings observed in rocks and meteorites have been studied to understand the evolution of the Earth and the Solar System. The validity of the findings from these studies depends on a theoretical understanding of rock-magnetic recordings provided by Néel (1, 2) and numerous experimental studies, for example, Strangway et. al. (3) and Evans and Wayman (4). The overwhelming evidence from these authors was that stable natural magnetic remanence (NRM) in rocks resides within ultrafine, uniformly magnetized particles, called single domain (SD) particles. Néel's theory (1, 2) for the behavior of thermally-activated SD particles describes a unique relationship between thermal and temporal stability and gave confidence that palaeomagnetic recordings that become unstable (unblocked) only at high temperatures, retain magnetic recordings from the time of their mineral crystallization, possibly as far back in time as four billion years ago.However, in the 1970s and 80s the widespread use of hysteresis parameters to characterize magnetic mineralogy (5) found that the majority of magnetic particles in rocks are not in uniform magnetic states, but are larger in size (80 -1000 nm) and contain complex magnetic states that are not described by either SD theory or the multidomain theory of micron-sized particles (2, 6). The term pseudo-single-domain (PSD) was coined for such particles and much effort was spent in determining the origin of their magnetic fidelity (Dunlop Psark, 1977, Moon and Merrill, 1985). Due to the complexity of the problem it has not been possible to determine the temporal stability of magnetisation in PSD grains on geological time scales fro...