Texture-induced spin-orbit coupling and Skyrmion-electron bound states in a N\'eel antiferromagnet

TL;DR

This paper derives an effective electron Hamiltonian in Ne9el antiferromagnets with textured magnetization, revealing strong spin-orbit coupling effects and bound states in Skyrmion textures, enabling electric manipulation of Skyrmions.

Contribution

It introduces a novel effective-mass Hamiltonian capturing texture-induced spin-orbit coupling and bound states in Skyrmions within Ne9el antiferromagnets.

Findings

Texture produces strong spin-orbit coupling at band extrema.

Skyrmion textures host electron bound states with energy scale b.

Bound states enable electric control of Skyrmions.

Abstract

We derive effective-mass electron Hamiltonian for a N\'eel antiferromagnet in the presence of a smooth texture of the staggered magnetization. For certain locations of electron band extrema, the texture produces a peculiar and anomalously strong spin-orbit coupling of the scale $\hbar v / L$, with $v$ the Fermi velocity and $L$ the characteristic length scale of the texture. For a Skyrmion texture, this coupling generates electron bound states, whose energy scale is given by the gap $\Delta$ in the electron spectrum. With dopant carriers, such bound states turn the Skyrmion into a charged particle, that can be manipulated by electric field.