Skyrmion in a real magnetic film

Skyrmions are the magnetic defects in an ultrathin magnetic film, similar to the bubble domains in the thicker films. Even weak uniaxial anisotropy determines its radius unambiguously. We consider the dynamics of the skyrmion decay. We show that the discreteness of the lattice in an isotropic 2D magnet leads to a slow rotation of the local magnetization in the skyrmion and, provided a small dissipation, 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.