Strain-induced incommensurate phases in hexagonal manganites

An incommensurate phase refers to a solid state in which the period of a superstructure is incommensurable with its primitive unit cell. It was recently shown that an incommensurate phase, which displays a single chiral modulation of six domain variants, could be induced by applying an in-plane strain to a hexagonal manganite. Here we combine Landau theory description of thermodynamics and the phase-field method to investigate and understand the formation of the incommensurate phase in hexagonal manganites. It is shown that the equilibrium wavelength of the incommensurate phase is determined by both the temperature and the magnitude of the applied strain, and a temperature-strain phase diagram is constructed for graphically displaying the temperature and strain conditions 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 antivortices in opposite directions, but also results in the creation and annihilation of vortex-antivortex pairs.