PhD project opportunity: 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 shortrange exchange interaction that favours parallel alignment of the magnetisation, (ii) the weak and longrange 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 or Micromagnetism. In recent decades, computer simulation of Micromagnetic systems has become a key tool in industry and academia to understand and predict the behaviour of ferromagnetic nanostructures and devices, as it provides insight 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) shortrange and strong DzyaloshinskiiMoriya 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. Just from the competition of the DMI and the exchange, together with an applied (uniform) external magnetic field, a number of new phases is observed, including regular arrangements of skyrmions as shown in Figure 1. This research project 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 (see Nature Physics 7, 673674, 2011 for an introductory summary on skyrmions in magnetic nanostructures). Figure 2 shows a skyrmion in a small disk which as just large enough to accommodate that skyrmion (here the diametre is 120nm, and the material is irongermanium, FeGe). A number of innovative suggestions have been made, how these skyrmions could create a stepchange in mankind's data storage and processing capabilities. In this project, we study the existence and stability of skyrmions in finite size nanostructures which are key to realise any devices based on chiral nanomagnetic technology, and explore possible applications. 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. 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, experimental work and design constraints. We use Python combined with C/C++ code where necessary. The micromagnetic code that will be used and extended is the successor of the open source tool Nmag, uses a finiteelement discretisation of space and employs the Fenics library. 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). Prerequisits: You need to have some programming experience. Knowledge of Python, finite elements and material science are beneficial but can be acquired as part of the training we provide. 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 repell 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. A single Skyrmion confined in a disk (left) and squarelike (right) structure. We have shown (http://arxiv.org/abs/1312.7665) 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. 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 Eligibility: Please see http://www.ngcm.soton.ac.uk/studentships.html Please contact Hans Fangohr <fangohr@soton.ac.uk> for informal queries, expressions of interest or applications.

