Long-wavelength emergent phonons in Bloch skyrmion crystals distorted by exchange anisotropy and tilted magnetic fields

摘要

Skyrmion crystals (SkXs) are a periodic alignment of magnetic skyrmions, i.e., a type of topologically protected spin textures. Compared with ordinary crystals, they can be drastically deformed under anisotropic effects because they are composed of field patterns whose deformation does not cause any bond-breaking This exotic ductility of SkXs brings about great tunability of its collective excitations, called emergent phonons, which are vital for magnonics application. The question is how to quantitatively determine the emergent phonons of distorted SkXs. Here we systematically study the long-wavelength emergent phonons of SkXs distorted by (a) a negative exchange anisotropy and (b) a tilted magnetic field. In both cases, deformation and structural transitions of SkXs thoroughly influence the frequency, anisotropy of vibrational pattern, dispersion relation, and coupling between the lattice vibration and in-lattice vibration for all modes. Tilted magnetic fields are very effective in tuning the emergent phonons, such that all modes except the Goldstone mode can be excited by AC magnetic fields when a tilted bias field is presented.