Magnetic skyrmions, topology and spintronic memory devices

Magnetic skyrmions are nanoscale, topologically non-trivial structures in magnetic materials that behave in many respects like particles. Their topological structure gives them unusual stability and particle-like behaviour, while their small size and ability to be manipulated by electrical currents make them promising candidates for next-generation energy-efficient spintronic technologies, including magnetic memory and logic devices.

This project will develop a mathematical theory of magnetic skyrmions, focusing on their stability, interactions, and dynamics. The competition between different magnetic interactions produces a rich landscape of stable and metastable configurations, raising fundamental questions about the geometry and structure of the corresponding solution space. Skyrmions can interact, scatter, form bound states, and annihilate, with their behaviour shaped by their topology and the geometry of this space.

The dynamics of skyrmions are strongly influenced by their topology and internal structure. For example, a skyrmion driven by an electrical current acquires a transverse velocity, or Hall angle, determined by its topology. This project will investigate the extent to which such complicated dynamical behaviour can be captured by simpler mathematical descriptions. In particular, it will explore collective-coordinate reductions, in which skyrmion evolution is described by a small number of degrees of freedom, such as position and internal structure. Developing and analysing these reductions provides a bridge between nonlinear partial differential equations and finite-dimensional dynamical systems, while offering a framework for understanding interactions and collective behaviour in multi-skyrmion configurations.

The project will combine analytical and computational approaches, drawing on topology, differential geometry, nonlinear PDEs, variational methods, and dynamical systems. Numerical simulations will complement the analysis by allowing more complicated skyrmion configurations and dynamical regimes to be explored. The ultimate motivation is to understand how mathematical structure can be turned into technological function. Reliable skyrmion-based memory requires topological states that are stable enough to store information yet controllable enough to be created, moved, and erased. By uncovering the mathematical principles governing skyrmion stability and dynamics, this project will explore how topological magnetic structures can be harnessed for next-generation spintronic memory and information processing.

The successful candidate will join a large, vibrant international collaboration spanning pure mathematics, theoretical physics, and experimental science, with partners across the UK, Sweden, Greece, Spain, and China. There are substantial opportunities for travel to conferences, workshops, and extended research visits throughout Europe through the EU-wide COST Action CA23134, Topological Textures in Condensed Matter, reflecting the international recognition and momentum of this rapidly developing field.

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