For the last months I have been working on a joint project with Markus Garst in which we studied the magnon scattering from a skyrmion texture. Today we submitted a draft of the paper to the preprint arxiv (arXiv:1405.1568).
Skyrmions in chiral magnets are topological magnetisation configurations stabilized due to the Dzyaloshinskii-Moriya interaction (a result of the lack of inversion symmetry in the atomic unit cell). When a thin film of chiral magnetic material is immersed in a sufficiently large applied magnetic field one finds that the action is minimized by the fully polarized state. In this regime skyrmions can be considered as large amplitude excitations of the field-polarized state which are protected due to their topology.
We investigated analytically the interaction between the skyrmion excitation and the magnons in a clean two-dimensional chiral magnet. We analyzed the magnon spectrum and found that the magnon spectrum is gapped (due to the applied magnetic field) with a discrete set of localized bound states below the gap energy and a continous spectrum exteded scattering states above. Interestingly, due to the skyrmion topology, the magnons scatter from an Aharonov-Bohm flux density that leads to skew scattering: Magnons are not symmetrically scattered by a skyrmion texture, but scatter predominantly to one side (determined by the sign of the Berry phase; see picture below). As a consequence of the skew scattering, a finite density of skyrmions will generate a topological magnon Hall effect. Using the conservation law for the energy-momentum tensor, we demonstrated that the magnons also transfer momentum to the skyrmion. A magnon current therefore leads to magnon pressure reflected in a momentum-transfer force in the Thiele equation of motion for the skyrmion. This force is reactive and governed by the scattering cross sections of the skyrmion; it causes not only a finite skyrmion velocity but also a large skyrmion Hall effect.