PhD project opportunity: Computer Simulation of Magnetic Skyrmions (fully funded)
Figure 0: a) Magnetic nanotechnology device, b) and c) isolated Skyrmions (see Figure 2), d) helical state, e) mixed helical and skyrmion state, f) array of skyrmions (See Figure 1). Computer simulation of Magnetic SkyrmionsBackground and Context Ferromagnetic nanostructures underpin a wide range of technology, including hard disks, actuators and sensors, and provide scope for fundamental materials and physics research. The magnetisation vector field in such nanostructures is dominated by: (i) the strong and short-range exchange interaction that favours parallel alignment of the magnetisation, (ii) the weak and long-range demagnetisation interaction field that favours antiparallel alignment of domains of magnetisation, (iii) the local crystal anisotropies that favour particular directions in the crystal lattice and (iv) the locally acting external field. The theory often used to describe these affects at the length scale of micrometres and below is called Micromagnetics. Nowadays computer simulation of micromagnetic systems using codes such as OOMMF, Nmag and others, has become a key tool in industry and academia to understand and predict the behaviour of ferromagnetic nanostructures and devices, as it provides insight and guidance for design decisions where analytical theory can not be applied. Recently, a new kind of interaction has been predicted and found to exist in magnetic materials: the (v) short-range and strong Dzyaloshinskii-Moriya Interaction (abbreviated as DM interaction or DMI) which favours 'curvature' in the magnetisation. The DM interaction is in direct competition with the exchange interaction: the exchange interactions wants to achieve a uniform vectorfield configuration and the DMI tries to twist the magnetisation: neighbouring magnetic moments would like to point in perpendicular directions. Just from the competition of the DMI and the exchange (which favours neighbouring magnetic moments to point in the same direction), together with an applied (uniform) external magnetic field, a number of new phases is observed (Figure 0 above), including regular arrangements of skyrmions (Figure 1 below) and helical magnetisation patterns and mixed configurations (see Figure 0d) and 0e) above). A particularly interesting and potentially very useful magnetisation vector field is that which looks a little bit like a vortex and which is known as a Skyrmion - see for example Nature Physics 7, 673-674, 2011 for an introductory summary on skyrmions in magnetic nanostructures. Inspired by this recent experimental discovery of skyrmions in magnetic systems, further works have shown remarkable properties of skyrmions: due to the unexpected stability of the skyrmion lattice, they could potentially be used to record data at the nanoscale. It has also been found that a very low electric currents can drive the skyrmions through the film, which opens the door for a low-energy realisation of the currently much researched race-track memory device which has the potential to replace harddisks with a new technology that combines high capacity with low power requirements, and can sustain an unlimited number of read-write cycles. This research project Figure 2 (left) shows a single skyrmion in a small disk which as just large enough to accommodate that skyrmion (here the diametre is 120nm, and the material is FeGe), and a result from our work at Southampton [1]. A number of innovative suggestions have been made, how these skyrmions could create a step-change in mankind's data storage and processing capabilities. There is a multitude of interesting studies possible, including static and dynamics of skyrmions, and their interaction with spatially confined structures (leading the path towards logic networks). We will collaborate with academic and industrial partners where appropriate, to complement the simulation work with analytical theory and experimental work, and progress with good understanding of industry design constraints. Methods In this project, we extend and apply the established micromagnetic framework with the interaction terms that allow to observe and study the skyrmion phase using computer simulation. The micromagnetic code that will be used and extended is the successor of the open source tool Nmag, uses a finite-element discretisation of space and employs the Fenics library. We use Python as the main tool to drive the simulation, combined with C/C++ code where necessary. Prerequisits: You need to have some programming experience. Knowledge of one or more of the following are beneficial but can be acquired as part of the training we provide: Python, finite elements, material science/condensed matter, parallel programming, visualisation. 
Figure 1: A array of skyrmions in a thin magnetic film. The arrows show local magnetisation direction. The objects looking like vortices are skyrmions. Skyrmions act like particles and repel each other. In an infinite film, they would form a ordered hexagonal lattice to minimise their energy. In the example shown above (from a Metropolic Monte Carlo simulation), perfect hexagonal order can not be established due to the finite size and given shape of the simulated square. The sample is exposed to an external field applied into the screen plane which is necessary to stabilise this skyrmion state. 
Figure 2: A single Skyrmion confined in a disk (left) and square-like (right) structure. We have shown [1] that the boundaries of such small systems stabilise skyrmions, and that these can exist without applied magnetic fields. This is of great importance for data storage and processing applications, and will be explored further in this project. [1] http://arxiv.org/abs/1312.7665 If you wish to discuss any details of the project informally, please contact Hans Fangohr, CED research group, Email: h.fangohr@soton.ac.uk, Tel: +44 (0) 2380 59 8345 Application deadline: applications are invited as soon as possible Funding: This project can be funded (fees and studentship) through the Centre for Doctoral Training in Next Generation Computational Modelling (see http://www.ngcm.soton.ac.uk). The project will start in September 2015. Eligibility: Please see http://www.ngcm.soton.ac.uk/studentships.html Contact and Applications: Please contact Hans Fangohr <fangohr@soton.ac.uk> for informal queries, expressions of interest or applications.
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