Skyrmions and spin waves in frustrated ferromagnets at low applied magnetic field

A continuum model of frustrated ferromagnets is analyzed in detail in the regime of low applied magnetic field, ${H}₀<1/4$, where the ground state is a spatially varying conical spiral. By changing variables to a corotating spin field, the model is reformulated as a gauged $\ensuremath{\sigma}$ model in a fixed background gauge, allowing the construction of stable isolated skyrmions, and stable multiskyrmion clusters, which approach the conical ground state at spatial infinity. Due to the spatial anisotropy induced by the ground state, these skyrmions exhibit only discrete symmetries, and are of neither N\'eel nor Bloch type. These skyrmions are continuously connected to the more familiar solutions in the high-field regime (${H}₀>1/4$), acquiring axial symmetry in the limit ${H}₀\ensuremath{\rightarrow}1/4$. The propagation of small-amplitude spin waves through the conical ground state is also analyzed and is found to depend strongly on both ${H}₀$ and the propagation direction relative to the ground state. In contrast to spin waves in the high-field regime (${H}₀>1/4$), there is no spectral gap: waves may propagate with any angular frequency.