Electric properties of the twelve-fold vortex structure in hexagonal manganites

Abstract

Hexagonal manganites, as a functional ferroelectric (FE) material, receive considerable attention due to their improper ferroelectricity and topological vortex structures. This family exhibits three low-symmetry states accompanied by distinct vortex domain structures. In addition to the FE P63 cm and anti-FE (AFE) P-3c1 states accompanied by dual six-fold vortex structures, there is another FE P3c1 state accompanied by a twelve-fold vortex structure. The responses of FE materials to external stimuli, such as external electric fields, are the core ingredients in the physics of FEs and are significant for technological applications. Under external electric fields, the responses of FE materials are determined by special FE domain structures. The electric properties of the FE P63 cm and AFE P-3c1 states are very different. However, the electric properties of the FE P3c1 state, which only stabilizes in Ga-substituted In(Mn, Ga)O3, are unclear. The present work studies the electric properties of the FE P3c1 state. The electric-field-driven transition of the FE P3c1 state is found to follow two sequences, i.e. (1) twelve-fold P3c1 → nine-fold P3c1 + P63 cm → three-fold P63 cm, and (2) twelve-fold P3c1 → six-fold P3c1 → three-fold P63 cm. The variation of average polarization with E for the FE P3c1 state with the second transition sequence manifests as an unusual triple-hysteresis loop, different from the usual single-hysteresis loop of FE materials. The results are related to the coexistence of the FE and non-FE domain walls in the FE P3c1 state. Furthermore, it is found that the FE P3c1 state at substitution concentration 0.39 exhibits the highest dielectric response. The results advance our understanding of topological vortex structures in hexagonal manganites.