Lifetime of Skyrmions in Cuprates and Other Layered Materials

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$\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.