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

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 $\text{ab initio}$ 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 $\text{ab initio}$ 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.

arXiv comment9 pages, 6 figures, published in Physical Review Research

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