Wyn Williams

A GENERALIZATION OF THE DEMAGNETIZING TENSOR FOR NONUNIFORM MAGNETIZATION

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.

Critical superparamagnetic/single-domain grain sizes in interacting magnetite particles: implications for magnetosome crystals

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.

Simulation of magnetic hysteresis in pseudo‐single‐domain grains of magnetite

Magnetic hysteresis has been simulated in grains of magnetite for the size range 0.1–0.7 μm. This was achieved using an unconstrained three-dimensional micromagnetic model of single grains of magnetite with cubic magnetocrystalline anisotropy. Hysteresis loops were obtained for fields applied along both the easy and hard magnetocrystalline axes. Both discrete (Barkhausen) jumps and gradual changes in the magnetic structure are seen, and the reversal of the magnetization can be followed from near saturation in a normal field to a similar state in a reverse field. Predictions of coercivity agree well with published experimental data for unstressed cubic grains of magnetite.

Three‐dimensional micromagnetic analysis of stability in fine magnetic grains

We examine the stability of magnetic remanences in grains of magnetite near the critical single-domain grain size (d0). The magnetic structure of a grain is followed during a 180° magnetization reversal, and it is shown that noncoherent reversals can occur even in grains smaller than d0. The energy barrier to noncoherent revesal is much lower than that of coherent rotation, so that pseudo-single-domain grain behavior will be exhibited by grains significantly smaller than d0.

Critical single‐domain/multidomain grain sizes in noninteracting and interacting elongated magnetite particles: Implications for magnetosomes

[i] The critical size for stable single-domain (SD) behavior has been calculated as a function of grain elongation for magnetite grains using a numerical micromagnetic algorithm. Importantly, for the first time, we consider the contribution of intergrain magnetostatic interactions on the SD/multidomain (MD) critical size (do). For individual grains our numerical estimates for d 0 for elongated grains are lower than that determined by previous analytical and numerical calculations. Nevertheless, the inclusion of magnetostatic interactions into the model was found to increase do to values significantly higher than any previously published estimates of d 0 for individual grains. Therefore the model calculations show that there is a relatively wide range of grain sizes within which depending on the degree of magnetostatic interactions and elongation, a grain can be either SD or MD. The model results are compared to observations of magnetosomes found in magnetotactic bacteria. The newly calculated upper d 0 limit for the interacting grains now accommodates the largest magnetosomes reported in the literature. These large magnetosomes were previously thought to be MD, suggesting that evolutionary processes are highly efficient at optimizing magnetosome grain size and spatial distribution.

Magnetostatic interaction fields in first-order-reversal-curve diagrams

The contribution of magnetostatic interaction fields in magnetic systems during first-order-reversal-curve (FORC) simulations has been systematically addressed using a dynamic micromagnetic algorithm. The interaction field distributions (IFD) display a nonlinear dependency on the field history and intergrain spacing, and are commonly asymmetric. The IFDs tend to be more Gaussian on average than Cauchian as predicted analytically for disordered systems, due to ordering during FORC diagram determination. The spreading of the FORC distribution in the vertical direction of the FORC diagram is shown to be directly related to the mean standard deviation of the IFD during the FORC measurement, with a small offset related to the smoothing factor.

Low-temperature magnetic properties of magnetite

Although several studies have recommended removal of secondary components of magnetic remanence by zero-field cycling from room temperature to a temperature much lower than the low temperature transition for magnetite (about 120 K), the method has not become a standard routine technique. This is partly due to the poor understanding of the behavior of magnetite particles at the low-temperature transition zone. Previous experiments by other researchers have used magnetite powders. In such powders it is always possible to attribute any discrepancy between the results observed and theory to possible existence of magnetostatic interaction effects or existence of elongated particles in samples presumed to contain only equant particles. Such factors need to be eliminated in order to have a better understanding of the low temperature behavior of magnetite particles. Low-temperature magnetic properties of lithographically produced arrays of both interacting and noninteracting cubic magnetite particles as well as those from powder particles have been measured as part of this study. A gradual increase in the amount of saturation isothermal remanent magnetization (SIRM) lost at the Verwey transition Tv with increasing particle size in the pseudo-single-domain size range has been observed. This behavior is consistent with the vortex state domain structure. The grain size dependence of the amount of SIRM lost at Tv is most probably what previous researchers reported as a magnetic memory particle-size-dependent trend. Magnetic memory measured during the cooling and warming process is shown to be a stress-related phenomenon. Such measurements could be useful in assessing the nature of stress in a magnetite sample.

Micromagnetic modeling of first-order reversal curve (FORC) diagrams for single-domain and pseudo-single-domain magnetite

First-order reversal curve (FORC) diagrams have been experimentally shown to be a better way of discriminating domain states in a sample compared to the straightforward use of major hysteresis loops. In order to better understand the fundamental behavior of assemblages of single-domain (SD) grains, we used a micromagnetic model witha conjugate gradient algorith m to calculate FORC diagrams for isolated grains of magnetite as well as for arrays of grains. In the case of individual elongated grains, we found that the FORC diagram consists of a single peak centered on the coercive force Hc if the grain is SD. For a pseudo-single-domain (PSD) grain with vortex structure, we observe multiple peaks on the FORC diagram. The modeling of arrays of elongated SD particles reveals two distinct types of patterns depending on the spacing between particles. In a 2U2U2 array of particles, a secondary branchon the reversal curves appears if the spacing between particles is less than about twice the particle length. This feature translates into the appearance of one negative and three positive peaks on the FORC diagram. In the case of a 3U3U3 array of particles, we again observe several secondary branches when the spacing between grains is less than about twice the particle length, leading to the appearance of multiple peaks on the FORC diagram. Splitting of the central peak on the Hu axis when particles interact could explain the vertical spread of FORC distributions of natural interacting samples as an effect of superposition of multiple peaks caused by the random orientation and distributions of particle spacing and switching fields of a large number of grains. The presence of symmetric peaks on a FORC diagram can be an indicator of the presence of either small PSD grains or magnetic interactions in an ensemble of grains.

Magnetostatic interactions in a natural magnetite‐ulvöspinel system

[ 1] Magnetostatic interactions have been investigated in anintergrown material consisting of similar to 200-nm magnetite blocksseparated by similar to 30-nm-wide ulvospinel lamellae. First-orderreversal curve (FORC) measurements provide a direct measure of theinteraction fields, giving a value for the full width at half maximum

High‐resolution micromagnetic models of fine grains of magnetite

High resolution three dimensional models are presented of cubic grains of magnetite in the grain size range 0.03 μm to 4.0 μm, achieved using a resolution of up to 262,144 elements to represent a single grain. Previous models have been limited in the maximum grain size that could be investigated because of the lack of resolution and increase in complexity of domain structure with grain size. This paper confirms the simple flower and vortex states found previously, but the classical two-domain (with closure domains) Kittel structure is shown not to be a local energy minimum state for magnetite. The concept of a single-domain to two-domain transition is now seen as a gradual unwinding of a flower state, and pseudo-single domain grains are shown to be vortex and multiple-vortex states. For grains greater than about 2 μm in size the center of vortices act a nucleation centers for the formation of domain walls. At the largest grains size modeled (4.0 μm), the expected features of multidomain grains are seen, with well-defined domain walls, and body domains with their magnetization aligned along the easy magnetocrystalline anisotropy axis.