Topological solitons in two-dimensional chiral magnets

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Chiral skyrmions are topological field configurations occurring in magnets of broken chiral symmetry. These novel magnetic nanostructures emerge as isolated solitons or arranged in regular lattices, which amounts to a new magnetic order in the style of the vortex state in superconductivity. Chiral skyrmions have been predicted theoretically about 25 years ago on the basis of a remarkably simple energy functional. The key effect is chirality induced Dzyaloshinskii-Moriya interaction, which is the anti-symmetric counterpart of Heisenberg exchange and expressed in terms of helicity type functionals. The unexpected recent experimental discovery of chiral skyrmions in a variety of material systems has boosted the interest and activity and opened a new direction in physics. Owing to their outstanding stability properties and efficient dynamic coupling to electric currents, chiral skyrmions became a promising candidate as information carrier in future spintronic devices.The project is concerned with the formation, structure and dynamics of topological patterns arising from chiral interaction in the spatially two-dimensional context. We shall address the occurrence and stability of skyrmionic structures in models of chiral magnets by means of global variational calculus. A major challenge we shall meet is the comprehensive understanding of the governing phase diagram. The current theoretical prediction is mainly based on numerical minimization of the energy functional or ad-hoc optimization of a specific Ansatz. Therefore a global mathematical approach to rigorously characterize critical fields would be desirable. With improved knowledge on the energetics and internal structure of isolated chiral skyrmions, we aim to examine the dynamic stability and effective dynamics arising from the Landau-Lifshitz-Gilbert equation coupled to spin- torque effects. We expect that the mathematical insight achieved and methods developed within this project will also contribute to the exploration of new aspects in the physics of chiral skyrmions and to the search of new mechanisms to stabilize topological solitons in magnetism.