Micromagnetic modelling of imperfect crystals

Abstract

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.