## Project Details

### Layman's description

Much of the geological history of the Earth and our understanding of the physical process occurring deep within it, have been unravelled by studying the recordings of the geomagnetic field made by rocks that form on the Earth's surface. Without such information we would not be aware, for example, of the fact that the geomagnetic field has reversed, and would have little understanding of the physical and chemical processes that occur within the Earth's core. The mapping of the motions of the continental plates relies almost entirely on the detailed interpretation of rock-magnetic recordings in well dated rocks, whilst compiling the frequency and periods of geomagnetic field reversals through time provides a magneto-stratigraphic dating tool used extensively in the oil industry and in geological research. Unfortunately, magnetic recording properties are highly grain size dependent, and it is only for the smallest grains, with near uniform magnetisations called single-domain (SD) grains, that we fully understand their ability to record a magnetic field. Naturally occurring magnetic materials in rocks are in fact far from ideal magnetic recorders since, in general, they contain a variety of magnetic mineralogies and have a wide range of grains geometries and sizes. Frequently, most of the magnetic information recorded by the rocks will be carried by grains whose magnetisation is inhomogeneous, but nevertheless their contribution to the magnetic remanence (strength or recording) is almost as high as that of SD grains. Such particles are called pseudo-single-domain (PSD) grains. Despite the dominant contribution of these particles to rock-magnetic remanences, their fidelity of magnetic recoding is poorly understood. This project aims to address this problem by building a numerical model that is able to examine the magnetic properties of PSD grains and in particular the magnetisation in specific grain geometries of that are commonly found in natural samples. We will address the two most perplexing problems remaining in rock-magnetism. Firstly we will model magnetic grains that are sufficiently close to each other that they interact, in the same way as closely spaced bar magnetic might interact. Secondly we will examine the ability of PSD grains to hold an accurate recording of the geomagnetic field as a function of time and temperature, over geological timescales. In order to achieve these goals we must have a numerical model that is capable of the high spatial resolutions needed to accurately account for the inhomogeneous domain structures that occur not just in a single grain, but in a cluster of interacting grains. We also need to be able to determine their thermal stability by estimating, for any particular magnetic structure, the energy barrier preventing thermal fluctuations from destroying its magnetic remanence. Such models cannot be run using a single computer processor on any reasonable time frame (weeks of computation for one solution). Instead we must increase computational efficiency by spreading the calculations across many processors, particularly for the magnetostatic (interaction) field that requires the most computation. This project will develop such a parallelised micromagnetic model capable of detailing, for the first time, the magnetic fidelity of geomagnetic recordings in naturally occurring magnetic minerals.

### Key findings

A finite-element (FE) micromagnetic numerical model was built, and benchmarked against alternative approaches published on the mu-mag website (www.ctcms.nist.gov). At the time the initial release of the FE code in 2008 it was one of the most efficient publicly available magnetic modellling software, which allowed both a dynamic solution of the Landau-Lifshitz-Gilbert equation governing the atomic relaxation of magnetic moments, and a conjugate-gradient optimisation.

This allowed the search for stable magnetic structures to be found by a dual approach providing both efficiency of computation and robustness of the final solution.

Thermal fluctuations were incorporated using a stochastic integration (Huen method), however attempt to introduce a nudged elastic band approach to determining energy barriers to changes in magnetic domain states proved unstable.

Early attempts at parallelisation of the micromagnetic code were partially successful, but efficiency was limited by the automatic techniques used to partition the finite elements defining the model geometry.

This allowed the search for stable magnetic structures to be found by a dual approach providing both efficiency of computation and robustness of the final solution.

Thermal fluctuations were incorporated using a stochastic integration (Huen method), however attempt to introduce a nudged elastic band approach to determining energy barriers to changes in magnetic domain states proved unstable.

Early attempts at parallelisation of the micromagnetic code were partially successful, but efficiency was limited by the automatic techniques used to partition the finite elements defining the model geometry.

Status | Finished |
---|---|

Effective start/end date | 1/07/07 → 30/09/10 |

### Funding

- EPSRC: £163,835.00

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