  Magnetic skyrmions are whirls in the magnetization whose topological winding
number promises stability against thermal fluctuations and defects. They can
only decay via singular spin configurations. We analyze the corresponding
energy barriers of skyrmions in a magnetic monolayer for two distinct
stabilization mechanisms, i.e., Dzyaloshinskii-Moriya interaction (DMI) and
competing interactions. Based on our numerically calculated collapse paths on
an atomic lattice, we derive analytic expressions for the saddle point textures
and energy barriers of large skyrmions. The sign of the spin stiffness and the
sign of 4th-order derivative terms in the classical field theory determines the
nature of the saddle point and thus the height of the energy barrier. In the
most common case for DMI-stabilized skyrmions, positive stiffness and negative
4th-order term, the saddle point energy approaches a universal upper limit
described by an effective continuum theory. For skyrmions stabilized by
frustrating interactions, the stiffness is negative and the energy barrier
arises mainly from the core of a singular vortex configuration.
