Fast computation of magnetostatic fields by Non-uniform Fast Fourier Transforms

The bottleneck of micromagnetic simulations is the computation of the long-ranged magnetostatic fields. This can be tackled on regular N-node grids with Fast Fourier Transforms in time N logN, whereas the geometrically more versatile finite element methods (FEM) are bounded to N^4/3 in the best case. We report the implementation of a Non-uniform Fast Fourier Transform algorithm which brings a N logN convergence to FEM, with no loss of accuracy in the results

magnum.fe: A micromagnetic finite-element simulation code based on FEniCS

We have developed a finite-element micromagnetic simulation code based on the FEniCS package called magnum.fe. Here we describe the numerical methods that are applied as well as their implementation with FEniCS. We apply a transformation method for the solution of the demagnetization-field problem. A semi-implicit weak formulation is used for the integration of the Landau-Lifshitz-Gilbert equation. Numerical experiments show the validity of simulation results. magnum.fe is open source and well documented. The broad feature range of the FEniCS package makes magnum.fe a good choice for the implementation of novel micromagnetic finite-element algorithms

Micromagnetic Simulations of High-Speed Magnonic Devices

An emerging field of research in recent years has been magnonics, the manipulation of coherent spin excitations, spin-waves, in magnetically ordered materials. Recent advances in experimental techniques for high-frequency magnetisation dynamics and the advent of micromagnetic simulations has led to the propositions of functional magnetic devices based upon the control of spin-waves. This thesis presents work for characterisation and future development of high-speed magnonic devices derived from micromagnetic simulations, and numerical techniques for the solution of the Landau-Lifshitz equation for micromagnetic simulations in the finite-difference time-domain approach. In chapter 3, spin-waves were controlled in the propagation along a thin film magnonic waveguide via resonant scattering from a mesoscale chiral magnetic resonator, in the backwards volume, forwards volume and Damon-Eshbach geometries. The scattering interaction demonstrated non-reciprocity associated with devices acting as spin-wave diodes. Additionally, such devices demonstrated the possibility of phase-shifting. The results obtained were numerically fit and interpreted in terms of a phenomenological model of resonant chiral scattering. The origin of the chiral coupling was discussed in terms of the stray field. In chapter 4, the phenomenon of spin-wave confinement, wavelength conversion and Möbius mode formation was demonstrated in the backwards volume configuration of thin-film magnetic waveguides. The presence of magnetic field gradients or thickness gradients modified the position of the Γ-point of the dispersion relation for Backwards Volume Dipolar-Exchange Spin-Waves (BVDESW), such that back-scattering and wavelength conversion occurred from the field/thickness gradients due to the “valleys” of the spin-wave dispersion. This work highlights a basis for not only experimental observation of such phenomena, but the potential for devices based upon valleytronics, an exploitation of the valley degree-of-freedom due to the spin-wave dispersion. In chapter 5, motivated by numerical error encountered in previous work in the thesis, the validity of implicit methods formulated for the numerical solution of the Landau-Lifshitz equation for finite-difference time-domain micromagnetic simulations were demonstrated. The implicit methods were tested for single spin precession in an external field, the μMAG standard problems and additional test cases. A source of numerical instability in explicit integration methods, numerical stiffness in systems of differential equations, was demonstrated to occur in existing explicit numerical methods, applied to the Landau-Lifshitz equation, common to popular micromagnetic software. The stability of implicit methods was demonstrated to be advantageous over explicit methods in micromagnetic scenarios where numerical stiffness could occur. Additionally, it was demonstrated that the quality of the numerical results was improved compared to explicit methods when the implicit method possessed L-stability, a damping of stiff, high wave number spin waves in the simulation.Engineering and Physical Sciences Research Council (EPSRC

Micromagnetics and spintronics: Models and numerical methods

Computational micromagnetics has become an indispensable tool for the theoretical investigation of magnetic structures. Classical micromagnetics has been successfully applied to a wide range of applications including magnetic storage media, magnetic sensors, permanent magnets and more. The recent advent of spintronics devices has lead to various extensions to the micromagnetic model in order to account for spin-transport effects. This article aims to give an overview over the analytical micromagnetic model as well as its numerical implementation. The main focus is put on the integration of spin-transport effects with classical micromagnetics

Fast stray field computation on tensor grids

A direct integration algorithm is described to compute the magnetostatic field and energy for given magnetization distributions on not necessarily uniform tensor grids. We use an analytically-based tensor approximation approach for function-related tensors, which reduces calculations to multilinear algebra operations. The algorithm scales with N^(4/3) for N computational cells used and with N^(2/3) (sublinear) when magnetization is given in canonical tensor format. In the final section we confirm our theoretical results concerning computing times and accuracy by means of numerical examples.Comment: 16 pages, 1 figure, submitted to the Journal of Computational Physic

Numerical study of magnetic processes: extending the Landau-Lifshitz-Gilbert approach from nanoscale to microscale

The micromagnetic theory describes the magnetic processes in magnetic materials on a microscopic time and space length. Therefore, micromagnetic models are since long employed in the design of for instants magnetic storage media as magnetic tapes and Random Access Memory elements, used in computers. The use of efficient numerical techniques and the availability of powerful computers now make it possible to apply the same micromagnetic models on larger and more complex material systems with the aim of increasing our insight in the experimentally observed magnetic phenomena. In this PhD research, an efficient numerical micromagnetic model is developed that enables the analysis of magnetic processes starting from the nanometer space scale up to the micrometer space scale. Therefore, efficient algorithms are presented on the one hand to simulate the ultra fast dynamics of the magnetic processes as described by the Landau-Lifshitz-Gilbert equation. On the other hand, powerful numerical techniques are developed to evaluate the magnetic fields, characteristic to the micromagnetic description, in a fast way. The developed micromagnetic model is validated extensively in comparative studies with other micromagnetic and macroscopic magnetic material models. Moreover, the model is successfully applied in different magnetic research domains: magnetic switching processes in classical samples with nanometer dimensions are analysed, magnetic domains are studied in structures with order micrometer dimensions and magnetic hysteresis properties are investigated