Topological solitons in two-dimensional chiral magnets
Final Report Abstract
Chiral magnets are a paradigm for condensed matter systems featuring topological solitons. The prototype are chiral skyrmions, vortex-like nanostructures and building block of topological patterns in chiral magnetism. Their unexpected experimental dis- covery in a variety of material systems and promise to serve as information carrier in future spintronic devices has boosted the interest and activity and opened a new direction in physics. Our project has been among the first initiatives to develop mathe- matical foundations of chiral magnetism with the ambition to contribute to the physical understanding and the discovery of new spin-orbit based phenomena and application. Most analytical and computational approaches to chiral skyrmions are based on the assumption of axial symmetry. Proving symmetry in nonlinear field theories, however, is a notoriously difficult task. We proved that axially symmetric chiral skyrmions are indeed local energy minimizers. The analysis kicked off a detailed investigation of the skyrmion profile, elucidating its fine properties and multiscale structure. We have pro- vided precise asymptotic formulae for the skyrmion radius and energy, which are crucial ingredients to the assessment of the mathematical model. Understanding symmetry through equivariance offers a functional analytic characterization by means of an ab- stract notion of spin and orbital angular momentum assigned to a magnetization field. We have shown that deviation from equivariance is related to dynamic excitations in form of rotating skyrmions. Remarkably, an emergent spin-orbit coupling arising from reduced symmetry is revealed on the dynamic level. In the area of topological patterns, we have developed a mathematical framework for lattice solutions, i.e. magnetic analogues of Abrikosov vortex lattices in supercon- ductivity, based on symmetry breaking bifurcation methods. Our analysis revealed a surprisingly large variety of patterns occurring in chiral magnetism. Beyond hexagonal lattice configurations, which are ubiquitous in pattern forming systems, we have shown that chiral magnets host stable vortex-antivortex configurations arranged in a quadratic lattice. Beyond mathematical theory the project contributed to the exploration of new topologi- cal structures in the physics of chiral magnets. In a joint endeavor between mathemat- ics and physics we have predicted the occurrence of novel skyrmionic configurations of negative winding, so-called antiskyrmions, in certain magnetic layers. Surprisingly, our analysis revealed the unexpected co-existence of skyrmions and antiskyrmions in such material systems. Our findings may help to realize novel devices for low-energy data storage in tiny space.
Publications
- Antiskyrmions stabilized at interfaces by anisotropic Dzyaloshinskii- Moriya interaction. Nature Communications 8, 308 (2017)
Hoffmann, M., Zimmermann, B., Muller, G., Schurhoff, D., Kiselev, N.S., Melcher, C., Blugel, S.
(See online at https://doi.org/10.1038/s41467-017-00313-0) - Stability of axisymmetric chiral skyrmions. Journal of Functional Analysis 275 (2018), no. 10, 2817–2844
Li, X., Melcher, C.
(See online at https://doi.org/10.1016/j.jfa.2018.01.019) - Curvature stabilized skyrmions with angular momentum. Letters in Mathematical Physics 109 (2019), no. 10, 2291–2304
Melcher, C., Sakellaris Z.N.
(See online at https://doi.org/10.1007/s11005-019-01188-6) - Traveling domain walls in chiral ferromagnets. Nonlinearity 32 (2019), no. 7, 2392–2412
Komineas, S., Melcher, C., Venakides, S.
(See online at https://doi.org/10.1088/1361-6544/ab1430) - The profile of chiral skyrmions of small radius. Nonlinearity
Komineas, S., Melcher, C., Venakides, S.
(See online at https://doi.org/10.1088/1361-6544/ab81eb)
