  Collapse of a skyrmion due to the discreteness of a crystal lattice in
isotropic two-dimensional ferro- and antiferromagnets has been studied
analytically and by numerical solution of equations of motion for up to 2000 x
2000 classical spins on a square lattice coupled via Heisenberg exchange
interaction. Excellent agreement between analytical and numerical results has
been achieved. The lifetime of the skyrmion scales with its initial size,
lambda_0, as(lambda_0/a)^5 in ferromagnets and as (lambda_0/a)^2.15 in
antiferromagnets, with a being the lattice parameter. This makes
antiferromagnetic skyrmions significantly shorter lived than ferromagnetic
skyrmions.
