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Magnetic skyrmions are whirls in the magnetization whose topological windingnumber promises stability against thermal fluctuations and defects. They canonly decay via singular spin configurations. We analyze the correspondingenergy barriers of skyrmions in a magnetic monolayer for two distinctstabilization mechanisms, i.e., Dzyaloshinskii-Moriya interaction (DMI) andcompeting interactions. Based on our numerically calculated collapse paths onan atomic lattice, we derive analytic expressions for the saddle point texturesand energy barriers of large skyrmions. The sign of the spin stiffness and thesign of 4th-order derivative terms in the classical field theory determines thenature of the saddle point and thus the height of the energy barrier. In themost common case for DMI-stabilized skyrmions, positive stiffness and negative4th-order term, the saddle point energy approaches a universal upper limitdescribed by an effective continuum theory. For skyrmions stabilized byfrustrating interactions, the stiffness is negative and the energy barrierarises mainly from the core of a singular vortex configuration.

Universality of annihilation barriers of large magnetic skyrmions in chiral and frustrated magnets