Local structure and its implications for the relaxor ferroelectric Cd$_2$Nb$_2$O$_7$

TL;DR

This study combines x-ray pair distribution function measurements and first-principles calculations to clarify the local and global structural behavior of Cd$_2$Nb$_2$O$_7$, revealing the dominant phonon modes and their implications for relaxor ferroelectricity.

Contribution

It resolves the ambiguity between competing phonon mode roles in Cd$_2$Nb$_2$O$_7$ by demonstrating local dominance of $ extGamma_4^-$ and global dominance of $ extGamma_5^-$ modes through combined experimental and theoretical analysis.

Findings

Locally, $ extGamma_4^-$ dominates; globally, $ extGamma_5^-$ dominates.

Energy surfaces for distortion modes are nearly isotropic, explaining structural transitions.

Results suggest a Heisenberg-like dipolar fluctuation behavior rather than Ising.

Abstract

The relaxor ferroelectric transition in Cd$_2$Nb$_2$O$_7$ is thought to be described by the unusual condensation of two $\Gamma$-centered phonon modes, $\Gamma_4^-$ and $\Gamma_5^-$. However, their respective roles have proven to be ambiguous, with disagreement between $\textit{ab initio}$ studies, which favor $\Gamma_4^-$ as the primary mode, and global crystal refinements, which point to $\Gamma_5^-$ instead. Here, we resolve this issue by demonstrating from x-ray pair distribution function measurements that locally, $\Gamma_4^-$ dominates, but globally, $\Gamma_5^-$ dominates. This behavior is consistent with the near degeneracy of the energy surfaces associated with these two distortion modes found in our own $\textit{ab initio}$ simulations. Our first-principles calculations also show that these energy surfaces are almost isotropic, providing an explanation for the numerous structural transitions found in Cd$_2$Nb$_2$O$_7$, as well as its relaxor behavior. Our results point to several candidate descriptions of the local structure, some of which demonstrate two-in/two-out behavior for Nb displacements within a given Nb tetrahedron. Although this suggests the possibility of a charge analog of spin ice in Cd$_2$Nb$_2$O$_7$, our results are more consistent with a Heisenberg-like description for dipolar fluctuations rather than an Ising one. We hope this encourages future experimental investigations of the Nb and Cd dipolar fluctuations, along with their associated mode dynamics.