Stability of skyrmions on curved surfaces in the presence of a magnetic field

We study the stability and energetics associated to skyrmions appearing as excitations on curved surfaces. Using a continuum model we show that the presence of cylindrically radial and azimuthal fields destabilize the skyrmions that appear in the absence of an external field. Weak fields generate fractional skyrmions while strong magnetic fields yield stable 2π-skyrmions, which have their widths diminished by the magnetic field strength. Under azimuthal fields vortex appears as stable state on the curved surface. - Highlights: • Stability of skyrmions on curved surfaces in the presence of a magnetic field. • Weak fields can destabilize skyrmions. • Strong magnetic fields yield the appearing of 2π-skyrmions. • The width of skyrmions is determined by the curvature and magnetic field strength. • Under azimuthal fields vortex appears as stable states