Soft tilt and rotational modes in the hybrid improper ferroelectric Ca$_{3}$Mn$_{2}$O$_{7}$

TL;DR

This study uses Raman spectroscopy to investigate soft tilt and rotational modes in the hybrid improper ferroelectric Ca$_{3}$Mn$_{2}$O$_{7}$, revealing their critical role in phase transitions and material properties.

Contribution

It provides direct experimental evidence of soft tilt and rotational modes and their evolution across phase transitions in Ca$_{3}$Mn$_{2}$O$_{7}.

Findings

Giant softening of the tilting mode by 26 cm$^{-1}$ during phase transition.

Small softening of the rotational mode by 6 cm$^{-1}$.

Coexistence of soft modes with different symmetries in the intermediate phase.

Abstract

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 Ca$_3$Mn$_2$O$_7$. We observe a giant softening of the 107-cm$^{-1}$ octahedron tilting mode by 26~cm$^{-1}$, 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 6~cm$^{-1}$. 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 Ca$_3$Mn$_2$O$_7$.