Vector vorticity of skyrmionic texture: an internal degree of freedom tunable by magnetic field

TL;DR

This paper introduces a vector vorticity concept for skyrmionic textures in centrosymmetric magnets, enabling continuous internal degree of freedom control via magnetic and electric fields, with implications for dynamic behavior and potential applications.

Contribution

It extends scalar vorticity to a vector form, allowing full internal rotation description and tunability of skyrmionic textures in centrosymmetric magnets.

Findings

Vector vorticity allows continuous internal rotation control.

Magnetic field tunes vorticity in skyrmionic textures.

Vorticity modulation influences skyrmion dynamics.

Abstract

Different from the skyrmion driven by the Dzyaloshinskii-Moriya interaction in non-centrosymmetric materials, the skyrmionic texture in centrosymmetric magnet may possess the extra internal degrees of freedom, which greatly enrich its morphologies, imply the continuous deformation allowed by topological protection, and enable flexible tunability and potential functionality. To describe the internal degree of freedom to full extent, the conventional integer-valued scalar vorticity is extended into a vector vorticity with continuous rotation allowed. The further simplified vorticity angle, together with helicity angle, represents the whole rotation freedom of spin space. The centrosymmetric magnet with frustration provides a perfect platform for realizing a controllable manipulation on these internal degrees of freedom, where the magnetic field can be applied to tune vorticity continuously in both crystal and isolated forms of skyrmionic texture, and the helicity can be further controlled by electric field. Moreover, the simulation reveals the distinctive dynamic effects related to the vorticity modulation, namely, a straight motion can be generated by rotating magnetic field to tune vorticity, and the vorticity can also be controlled to modulate the dynamics induced by the spin polarized current.