  It is common for the local inversion symmetry to break in crystals, even
though the whole crystal has global inversion symmetry. This local inversion
symmetry breaking allows for a local Dzyaloshinsky-Moriya interaction (DMI) in
magnetic crystals. Here we show that the local DMI can stabilize a skyrmion as
a metastable excitation or as a skyrmion crystal in equilibrium. We consider
the crystal structure with layered structure as an example, where local
inversion is violated in each layer but a global inversion center exists in the
middle of the two layers. These skyrmions come in pairs that are related by
inversion symmetry. The two skyrmions with opposite helicity in a pair form a
bound state. We study the properties of a skyrmion pair in the ferromagnetic
background and determine the equilibrium phase diagram, where a robust lattice
of skyrmion pairs is stabilized. Our results point to a new direction to search
for the skyrmion lattice in centrosymmetric magnets.
