EPSRC Reference: 
EP/Y033256/1 
Title: 
Skyrmion lattices in chiral ferromagnets 
Principal Investigator: 
Speight, Professor JM 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Pure Mathematics 
Organisation: 
University of Leeds 
Scheme: 
Standard Research  NR1 
Starts: 
01 June 2024 
Ends: 
28 February 2025 
Value (£): 
74,416

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


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Summary on Grant Application Form 
Ferromagnets are materials made up of molecules each of which behaves like a tiny magnet, which interact with one another so that neighbouring molecules want their magnets to align. The state of such a material can be represented by a unit length vector field called the magnetization vector, which records the direction of the magnet at each point in space. If the underlying molecules lack reflexion symmetry, the ferromagnet is said to be chiral. In this case, the lowest energy configuration of the ferromagnet, when exposed to an external magnetic field, may not be the obvious state in which the magnetization vector aligns with the field, but a rather more mysterious state called a skyrmion. This is a configuration in which the magnetization vector ties itself up in a twodimensional analogue of a knot, ranging through all possible orientations as one moves in space. The knottedness cannot be undone by any continuous deformation of the system  in mathematical language, this is a topological soliton. One dimensional arrays of magnetic skyrmions are the basis of proposed nextgeneration data storage devices (socalled race track memory). Their mathematical study has focussed almost exclusively on single isolated skyrmions, or small isolated clusters of skyrmions. But in real ferromagnetic systems, skyrmions occur spontaneously in regular two dimensional arrays  skyrmion lattices. Remarkably, there has been no systematic mathematical study of such lattices. We propose to study the existence, stability, genericity, and geometry of skyrmion lattices, focussing in particular on how these properties depend on the strength and direction of the applied magnetic field. To do this, we will adapt mathematical ideas developed originally in models of nuclear physics and superconductivity, implementing these in largescale computer simulations.

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http://www.leeds.ac.uk 