Minimal Radius of Magnetic Skyrmions: Statics and Dynamics
  In a broad range of applied magnetic fields and material parameters isolated magnetic skyrmions condense into skyrmion lattices. While the geometry of isolated skyrmions and their lattice counterparts strongly depend on field and Dzyaloshinski-Moriya interaction, this issue has not been adequately addressed in previous studies. Meanwhile, this information is extremely important for applications, because the skyrmion size and the interskyrmion distance have to be tuned for skyrmion based memory and logic devices. In this investigation we elucidate the size and density-dependent phase diagram showing traditional phases in field vs. material parameters space by means of Monte-Carlo simulations on a discrete lattice. The obtained diagram permits us to establish that, in contrast to the continuum limit, skyrmions on a discrete lattice cannot be smaller than some critical size and have a very specific shape. These minimal skyrmions correspond to the micromagnetic configuration at the energy barrier between the ferromagnetic and the skyrmionic states. Furthermore, we use atomistic Landau-Lifshitz-Gilbert simulations to study dynamics of the skyrmion annihilation. It is shown that this procees consists of two stages: the continuous skyrmion contraction and its discontinuous annihilation. The detailed analysis of this dynamical process is given. 
A. Siemens, Y. Zhang, J. Hagemeister, E. Y. Vedmedenko, R.   Wiesendanger
cond-mat.mes-hall