Curvature-induced skyrmion deformation

We perform a systematic analysis of equilibrium solutions for Néel and Bloch skyrmions on a cylindrical shell and show that both experience a curvature-induced deformation. Considering the curvature as a small perturbation and applying first-order perturbation theory, we decompose the deformation into the radially symmetric and elliptical parts. The orientation of the elliptically deformed skyrmion shape depends on the skyrmion type. For the Néel skyrmion, the long half axis of the ellipse is oriented along or perpendicular to the cylinder generatrix, depending on the sign of the curvature and the Dzyaloshinskii–Moriya interaction. In contrast, the elliptical shape of the Bloch skyrmion forms an angle ±π/4 with the generatrix. The theoretically predicted skyrmion shapes are compared with those obtained from numerical spin lattice simulations. We also use simulations to investigate the nonlinear regime beyond the applicability of first-order perturbation theory. In particular, we show that the Néel skyrmion can collapse for sufficiently large curvature.