Micromagnetic modelling of imperfect crystals

In paleomagnetism, practical measurements are rarely made using perfect, isolated, single-phase, ferromagnetic crystals. Experimental observations are typically made using magnetic materials formed by a variety of natural processes. In this thesis, we will look at bridging the gap between current numerical modelling capability and experimental observations. First, we work towards micromagnetic modelling of multi-phase magnetic materials, including magnetostriction, embedded in a rocky matrix, along with crystal defects. We present a derivation of the Boundary Element Method formulation used by the micromagnetics package, MERRILL, and provide an extension of this from single-phase materials to multi-phase. After discussing issues with previous approaches to modelling magnetostriction, we derive and present a more robust and flexible approach. This model of magnetostriction is suitable for non-uniformmagnetizations, for multi-phase materials, and for arbitrary boundary conditions, and can be incorporated into MERRILL.We then outline a method for extending our model to materials embedded in an infinite elastic matrix of arbitrary elasticity. Finally, we present a method for modelling the magnetic response of a material due to crystal defects, along with a concrete example of a magneto-dislocation coupling energy at a magnetite-ilmenite boundary where stress due to lattice misfit is eased by regular edge dislocations. Second, we work towards being able to verify micromagnetic models against nano-scale experimental data. To do this, we present two techniques for simulating electron holograms from micromagnetic modelling results, a technique capable of imaging magnetic structures at the nano-scale. We also present example electron holograms of commonly occurring magnetic structures in nano-scale rock and mineral magnetism, and highlight some distinguishing features, which may be useful for interpreting experimental electron holography data

Multi-scale three-dimensional characterization of iron particles in dusty olivine: Implications for paleomagnetism of chondritic meteorites

Dusty olivine (olivine containing multiple sub-micrometer inclusions of metallic iron) in chondritic meteorites is considered an ideal carrier of paleomagnetic remanence, capable of maintaining a faithful record of pre-accretionary magnetization acquired during chondrule formation. Here we show how the magnetic architecture of a single dusty olivine grain from the Semarkona LL3.0 ordinary chondrite meteorite can be fully characterised in three dimensions, using a combination of Focussed-Ion-Beam nanotomography (FIB-nT), electron tomography and finite-element micromagnetic modelling. We present a three-dimensional (3D) volume reconstruction of a dusty olivine grain, obtained by selective milling through a region of interest in a series of sequential 20 nm slices, which are then imaged using scanning electron microscopy. The data provide a quantitative description of the iron particle ensemble, including the distribution of particle sizes, shapes, interparticle spacings and orientations. Iron particles are predominantly oblate ellipsoids with average radii 242 ± 94 nm by 199 ± 80 nm by 123 ± 58 nm. Using analytical TEM we observe that the particles nucleate on sub-grain boundaries and are loosely arranged in a series of sheets parallel to (001) of the olivine host. This is in agreement with the orientation data collected using the FIB-nT, and highlights how the underlying texture of the dusty olivine is crystallographically constrained by the olivine host. The shortest dimension of the particles is oriented normal to the sheets and their longest dimension is preferentially aligned within the sheets. Individual particle geometries are converted to a finite-element mesh and used to perform micromagnetic simulations. The majority of particles adopt a single vortex state, with ‘bulk’ spins that rotate around a central vortex core. We observed no particles, which are in a true single domain state. The results of the micromagnetic simulations challenge some pre-conceived ideas about the remanence carrying properties of vortex states. There is often not a simple predictive relationship between the major, intermediate and minor axes of the particles and the remanence vector imparted in different fields. Although the orientation of the vortex core is determined largely by the ellipsoidal geometry (i.e., parallel to the major axis for prolate ellipsoids and parallel to the minor axis for oblate ellipsoids), the core and remanence vectors can sometimes lie at very large (tens of degree) angles to the principal axes. The subtle details of the morphology can control the overall remanence state, leading in some cases to a dominant contribution from the bulk spins to the net remanence, with profound implications for predicting the anisotropy of the sample. The particles have very high switching fields (several hundred mT), demonstrating their high stability and suitability for paleointensity studies.The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC grant agreements 291522-3DIMAGE (P.A.M.) and 320750 - Nanopaleomagnetism (J.F.E., R.J.H., and P.A.M.). BPW and RRF were supported by NASA Emerging Worlds program grant #NNX15AH72G, the NASA Solar System Exploration and Research Virtual Institute grant #NNA14AB01A, and a generous gift from Thomas F. Peterson, Jr. The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement No. 320832-Imagine. (W.W . and P.O.C.) W.W. was also supported for this research under NERC grant NE/J020966/1 - Predicting the reliability with which the geomagnetic field can be recorded in igneous rocks.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by the Mineralogical Society of America

Stability of equidimensional pseudo–single-domain magnetite over billion-year timescales

© 2017, National Academy of Sciences. All rights reserved. Interpretations of paleomagnetic 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 paleomagnetic signals in rocks are usually larger, nonuniformly 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 timescales. We examine in detail the thermal stability characteristics of equidimensional cuboctahedral magnetite and find that, contrary to previously published theories, such nonuniformly magnetized particles provide greater magnetic stability than their uniformly magnetized counterparts. Hence, nonuniformly magnetized grains, which are commonly the main remanence carrier in meteorites and rocks, can record and retain high-fidelity magnetic recordings over billions of years

Direct observation of the thermal demagnetization of magnetic vortex structures in non-ideal magnetite recorders

The thermal demagnetization of pseudo-single-domain (PSD) magnetite (Fe3O4) particles, which govern the magnetic signal in many igneous rocks, is examined using off-axis electron holography. Visualization of a vortex structure held by an individual Fe3O4 particle (~ 250 nm in diameter) during in situ heating is achieved through the construction and examination of magnetic-induction maps. Step-wise demagnetization of the remanence-induced Fe3O4 particle upon heating to above the Curie temperature, performed in a similar fashion to bulk thermal demagnetization measurements, revealed its vortex state remains stable under heating close to its unblocking temperature, and is recovered upon cooling with the same or reversed vorticity. Hence, the PSD Fe3O4 particle exhibits thermomagnetic behavior comparable to a single-domain carrier, and thus vortex-states are considered reliable magnetic recorders for paleomagnetic investigations

Magnetic vortex effects on first-order reversal curve (FORC) diagrams for greigite dispersions

First-order reversal curve (FORC) diagrams are used increasingly in geophysics for magnetic domain state identification. The domain state of a magnetic particle is highly sensitive to particle size, about which FORC diagrams provide valuable information. However, the FORC signal of particles with nonuniform magnetisations, which are the main carrier of natural remanent magnetisations in many systems, is still poorly understood. In this study, the properties of non-interacting, randomly oriented dispersions of greigite (Fe3S4) in the uniform single-domain (SD) to non-uniform single-vortex (SV) size range are investigated via micromagnetic calculations. Signals for SD particles () are found to be in excellent agreement with previous SD coherent-rotation studies. A transitional range from to is identified for which a mixture of SD and SV behaviour produces complex FORC diagrams. Particles have purely SV behaviour with the remanent state for all particles in the ensemble in the SV state. It is found that for SV ensembles the FORC diagram provides a map of vortex nucleation and annihilation fields and that the FORC distribution peak should not be interpreted as the coercivity of the sample, but as a vortex annihilation field on the path to saturation

The Vortex State in Geologic Materials: A Micromagnetic Perspective

A wide variety of Earth and planetary materials are very good recorders of paleomagnetic information. However most magnetic grains in these materials are not in the stable single (SD) domain grain size range, but are larger and in non-uniform vortex magnetization states. We provide a detailed account of vortex phenomena in geologic materials by simulating first-order reversal curves (FORCs) via finite-element micromagnetic modeling of magnetite nanoparticles with realistic morphologies. The particles have been reconstructed from focused ion beam nanotomography of magnetite-bearing obsidian, and accommodate single and multiple vortex structures. Single vortex (SV) grains have fingerprints with contributions to both the transient and transient-free zones of FORC diagrams. A fundamental feature of the SV fingerprint is a central ridge, representing a distribution of negative saturation vortex annihilation fields. SV irreversible events at multiple field values along different FORC branches determine the asymmetry in the upper and lower lobes of generic bulk FORC diagrams of natural materials with grains predominantly in the vortex state. Multi vortex (MV) FORC signatures are modeled here for the first time. MV grains contribute mostly to the transient-free zone of a FORC diagram, averaging out to create a broad central peak. The intensity of the central peak is higher than that of the lobes, implying that MV particles are more abundant than SV particles in geologic materials with vortex state fingerprints. The abundance of MV particles, as well as their SD-like properties point to MV grains being the main natural remanent magnetization carriers in geologic materials.European Research Counci

Micromagnetic simulations of first-order reversal curve (FORC) diagrams of framboidal greigite

Greigite is a sensitive environmental indicator and occurs commonly in nature as magnetostatically interacting framboids. Until now only the magnetic response of isolated non-interacting greigite particles have been modelled micromagnetically. We present here hysteresis and first-order reversal curve (FORC) simulations for framboidal greigite (Fe3S4), and compare results to those for isolated particles of a similar size. We demonstrate that these magnetostatic interactions alter significantly the framboid FORC response compared to isolated particles, which makes the magnetic response similar to that of much larger (multidomain) grains. We also demonstrate that framboidal signals plot in different regions of a FORC diagram, which facilitates differentiation between framboidal and isolated grain signals. Given that large greigite crystals are rarely observed in microscopy studies of natural samples, we suggest that identification of multidomain-like FORC signals in samples known to contain abundant greigite could be interpreted as evidence for framboidal greigite

Stability of equidimensional pseudo-single-domain magnetite over billion-year timescales

Interpretations of paleomagnetic 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 paleomagnetic signals in rocks are usually larger, nonuniformly 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 timescales. We examine in detail the thermal stability characteristics of equidimensional cuboctahedral magnetite and find that, contrary to previously published theories, such nonuniformly magnetized particles provide greater magnetic stability than their uniformly magnetized counterparts. Hence, nonuniformly magnetized grains, which are commonly the main remanence carrier in meteorites and rocks, can record and retain high-fidelity magnetic recordings over billions of years

D7.9: Hardware developments V

Update on "Hardware Developments IV" (https://doi.org/10.5281/zenodo.3256137) which covers:- Report on hardware developments that will affect the scientific areas of interest to E-CAM and detailed feedback to the project software developers;- discussion of project software needs with hardware and software vendors, completion of survey of what is already available for particular hardware platforms; and,- detailed output from direct face-to-face session between the project end users, developers and hardware vendors

Stability of equidimensional pseudo–single-domain magnetite over billion-year timescales

© 2017, National Academy of Sciences. All rights reserved. Interpretations of paleomagnetic 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 paleomagnetic signals in rocks are usually larger, nonuniformly 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 timescales. We examine in detail the thermal stability characteristics of equidimensional cuboctahedral magnetite and find that, contrary to previously published theories, such nonuniformly magnetized particles provide greater magnetic stability than their uniformly magnetized counterparts. Hence, nonuniformly magnetized grains, which are commonly the main remanence carrier in meteorites and rocks, can record and retain high-fidelity magnetic recordings over billions of years