Complex phase transitions in hexagonal manganites: the Landau theoretical approach*

Improper ferroelectric hexagonal manganites have been extensively investigated for the coexistence of ferroelectricity and magnetism and the potential for ferroelectric memory. However, the exact understanding about the experienced phases and their sequence in the phase transition in hexagonal manganites has been the subject of much debate. In the line with the well-established Landau theory YMnO₃, we find that the competition between the anisotropy of the trimerization and the coupling of the trimerization to the polarization plays a key role in the determination of the low-temperature structure of hexagonal manganites. By adding a higher order term on Q to the existing expression of Landau free energy, the P3c1 structure which is allowed to emerge at low temperature based on group theoretical analysis is accessed. A kind of topological twelvefold vortex domain pattern corresponding to the P3c1 phase is achieved using phase-field simulation. Our result provides a new prospective for revealing the mystery of the complex phase transition in hexagonal manganites.