  A magnetic skyrmion crystal (SkX) with a swirling spin configuration, which
is one of topological spin crystals as a consequence of an interference between
multiple spin density waves, shows a variety of noncoplanar spin patterns
depending on a way of superposing the waves. By focusing on a phase degree of
freedom among the constituent waves in the SkX, we theoretically investigate a
position of the skyrmion core on a discrete lattice, which is relevant with the
symmetry of the SkX. The results are obtained for the double exchange
(classical Kondo lattice) model on a discrete triangular lattice by the
variational calculations. We find that the skyrmion cores in both two SkXs with
the skyrmion number of one and two are locked at the interstitial site on the
triangular lattice, while it is located at the onsite by introducing a
relatively large easy-axis single-ion anisotropy. The variational parameters
and the resultant Fermi surfaces in each SkX spin texture are also discussed.
The different symmetry of the Fermi surfaces depending on the core position is
obtained when the skyrmion crystal is commensurate with the lattice. The
different Fermi-surface topology is directly distinguished by an electric probe
of angle-resolved photoemission spectroscopy. Furthermore, we show that the
SkXs obtained by the variational calculations are also confirmed by numerical
simulations on the basis of the kernel polynomial method and the Langevin
dynamics for the double exchange model and the simulated annealing for an
effective spin model.
