  An incommensurate phase refers to a solid state in which the period of a
superstructure is incommensurable with the primitive unit cell. Recently the
incommensurate phase is induced by applying an in-plane strain to hexagonal
manganites, which demonstrates single chiral modulation of six domain variants.
Here we employ Landau theory in combination with the phase-field method to
investigate the incommensurate phase in hexagonal manganites. It is shown that
the equilibrium wave length of the incommensurate phase is determined by
temperature and the magnitude of the applied strain, and a temperature-strain
phase diagram is constructed for the stability of the incommensurate phase.
Temporal evolution of domain structures reveals that the applied strain not
only produces the force pulling the vortices and anti-vortices in opposite
directions, but also results in the creation and annihilation of
vortex-antivortex pairs.
