Moduli spaces and breather dynamics of analytic solutions in Heisenberg exchange-free chiral magnets

We investigate the special case of the chiral magnet with vanishing Heisenberg exchange energy, whose axisymmetric Skyrmion solution has previously been found. The dynamical equations of this model look like inviscid fluid flow, and by investigating path lines of this flow we can construct explicit static and dynamic solutions. We find an infinite-dimensional family of static Skyrmions that are related to the axisymmetric Skyrmion by co-ordinate transformations thus discovering a new moduli space, and further infinite-dimensional families of axisymmetric and non-axisymmetric breather-like supercompactons.

💡 Research Summary

The authors investigate a highly simplified version of chiral magnetic materials in which the Heisenberg exchange term is set to zero. In this “restricted” limit the energy consists only of the Dzyaloshinskii‑Moriya interaction (DMI) and a scalar potential (Zeeman‑type and anisotropy). The Landau‑Lifshitz equation then reduces to a first‑order, inviscid‑fluid‑like equation \