Lattice instabilities in cubic pyrochlore Bi$_2$Ti$_2$O$_7$

TL;DR

This study uses first-principles calculations to identify lattice instabilities in cubic Bi$_2$Ti$_2$O$_7$, revealing a tendency towards ferroelectric distortion despite experimental cubic stability, highlighting the role of soft polar modes.

Contribution

The paper uncovers lattice instabilities in cubic Bi$_2$Ti$_2$O$_7$ and predicts a ferroelectric ground state, providing new insights into its dielectric behavior.

Findings

Identification of lattice instabilities via phonon calculations

Prediction of a ferroelectric ground state

Role of soft polar modes in dielectric properties

Abstract

The oxide pyrochlore Bi$_2$Ti$_2$O$_7$ is in some ways analogous to perovskite PbTiO$_3$, in that Bi$_2$Ti$_2$O$_7$ has two cations, Bi$^{3+}$ and Ti$^{4+}$ in oxidation states that are normally associated with a propensity to off-center. However, unlike PbTiO$_3$, Bi$_2$Ti$_2$O$_7$ is experimentally observed to remain cubic down to 2 K, while the only observed ionic displacements are local and incoherent. Here we report first-principles calculations of the zone-center phonons of the ordered cubic pyrochlore which reveal several lattice instabilities. An analysis of the structural energetics suggest that the ordered cubic pyrochlore is unstable with respect to distortion towards a ferroelectric ground state with a large polarization. Our results suggest a key role of a frustrated soft polar mode in the dielectric properties of bismuth pyrochlores.