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Collapse of a skyrmion due to the discreteness of a crystal lattice inisotropic two-dimensional ferro- and antiferromagnets has been studiedanalytically and by numerical solution of equations of motion for up to 2000 x2000 classical spins on a square lattice coupled via Heisenberg exchangeinteraction. Excellent agreement between analytical and numerical results hasbeen 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 inantiferromagnets, with a being the lattice parameter. This makesantiferromagnetic skyrmions significantly shorter lived than ferromagneticskyrmions.

Collapse of Skyrmions in 2d Ferro- and Antiferromagnets