Mechanical properties and abnormal mechanical behaviors of ferroelectric hexagonal manganites

Hexagonal manganites (h-RMnO₃, R=Y, Ho-Lu) are emerging as advantageous multiferroic materials with structural ferroelectric topological defects. Strain has been proven as an effective means to control topological vortex cores. To further understand and utilize the mechanical manipulation mechanism, mechanical properties such as the Young's modulus are important; however, accurate values are still to be obtained for single-crystalline specimens. In this study, by combining contact resonance atomic force microscopy, nanoindentation, and density functional theory calculations, we systematically studied the Young's moduli of YMnO₃, ErMnO₃, and LuMnO₃ single crystals. The Young's moduli of LuMnO₃ obtained by the different methods were consistent, whereas for ErMnO₃ and YMnO₃, the abnormal mechanical behavior observed in the nanoindentation experiments deviated from the theoretical and experimental calculations. Through in-situ transmission electron microscopy, it was confirmed that lattice distortion plays a key role in resisting deformation, which is the origin of the abnormal mechanical behavior. Our work provides insights into an important mechanical parameter and the origin of the difference in the Young's modulus of h-RMnO₃, which is important for further theoretical investigations and potential applications.