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

Abstract

Skyrmion crystals (SkX) are 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 SkX bring 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 SkX. Here we systematically study the long wavelength emergent phonons of SkX distorted by (a) a negative exchange anisotropy, and (b) a tilted magnetic field. In both cases, deformation and structural transitions of SkX thoroughly influence the frequency, anisotropy of vibrational pattern and dispersion relation, and coupling between 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.

Lagrangian formulation for emergent elastic waves in magnetic emergent crystals

“…Based on the formulation established here, we systematically study the long wavelength emergent phonon excita-tions for isotropic hexagonal SkX [29] and distorted SkX due to presence of anisotropic effects [30].…”

Emergent elastic waves in skyrmion crystals with finite frequencies at long wavelength limit

“…( 1) is isotropic in the x − y plane. The effect of anisotropy is discussed in a subsequent work of ours [20]. Deformable SkX with long range order permits the following Fourier expansion of m [15,21] m = l m q e l e iq l (ε e ij , ω e )•r ,…”

“…Further research in this direction not only helps us in understanding the discrepancies between emergent crystalline states and ordinary crystals in terms of their dynamics, but may also stimulate novel applications. We construct a reliable and analytical framework to study the collective spin excitations in magnetic emergent crystals, which can easily be extended to cases where they are deformed [20].…”