Skyrmions are magnetic defects in ultrathin magnetic films, similar to the bubble domains in the thicker films. Even weak uniaxial anisotropy determines their radii unambiguously. We derive equations of slow dynamics for Skyrmions. We show that the discreteness of the lattice in an isotropic two-dimensional magnet leads to a slow rotation of the local magnetization in the Skyrmion and even a small dissipation leads to decay of the Skyrmion. The radius of such a Skyrmion as a function of time is calculated. We prove that uniaxial anisotropy stabilizes the Skyrmion and study the relaxation process. 1998 The American Physical Society.
