  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.
