Collapse of skyrmions in two-dimensional ferromagnets and antiferromagnets

Collapse of a skyrmion due to the discreteness of a crystal lattice in isotropic two-dimensional ferromagnets 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.