Soft tilt and rotational modes in the hybrid improper ferroelectric Ca3Mn2 O7

Raman spectroscopy is employed to probe directly the soft rotation and tilting modes, which are two primary order parameters predicted in the hybrid improper ferroelectric material Ca3Mn2O7. We observe a giant softening of the 107-cm-1 octahedron tilting mode by 26cm-1 on heating through the structural transition from a ferroelectric to paraelectric orthorhombic phase. This is contrasted by a small softening of the 150-cm-1 rotational mode by 6cm-1. In the intermediate phase, the competing soft modes with different symmetries coexist, bringing about many-faceted anomalies in spin excitations and lattice vibrations. Our work demonstrates that the soft rotation and tilt patterns, relying on a phase-transition path, are a key factor in determining ferroelectric, magnetic, and lattice properties of Ca3Mn2O7.