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 $2000\times 2000$ 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.

• Received 21 April 2012

DOI:https://doi.org/10.1103/PhysRevB.86.024429