# Origin and evolution of ferroelectricity in the layered rare-earth-titanate, $R_2$Ti$_2$O$_{7}$, Lichtenberg phases

## TL;DR

This study uses first-principles calculations to analyze the structural and ferroelectric properties of $R_2$Ti$_2$O$_{7}$ oxides, revealing the mechanisms behind their ferroelectricity and polarization trends across different rare-earth elements.

## Contribution

It provides a detailed first-principles analysis of the origin and evolution of ferroelectricity in $R_2$Ti$_2$O$_{7}$, clarifying polarization values and the role of structural distortions.

## Key findings

- Ferroelectric distortion driven by a single polar soft mode involving octahedral rotations and displacements.
- Secondary centrosymmetric distortion significantly lowers the energy of the ground state.
- The materials are confirmed as proper geometric ferroelectrics.

## Abstract

We report a systematic first-principles study based on density functional theory (DFT) of the structural and ferroelectric properties of the $R_2$Ti$_2$O$_{7}$ perovskite-related oxides with $R=$ La, Ce, Pr, and Nd. We show that, in all cases, the ferroelectric distortion to the ground-state polar $P2_1$ structure from its parent centrosymmetric $P2_1/m$ phase is driven by a single polar soft mode consisting of rotations and tilts of the TiO$_6$ octahedra combined with displacements of the $R$ ions. A secondary centrosymmetric distortion, which is stable in the parent structure, contributes substantially to the energy lowering of the ground state. We evaluate the trends in structure and polarization across the series as a function of $R$ and reconcile discrepancies in reported values of polarization in the literature. Our results confirm that the family of $R_2$Ti$_2$O$_{7}$ materials belong to the class of proper geometric ferroelectrics.