Incipient modulated phase in Sr$_{1-x}$Ca$_{x}$TiO$_3$

TL;DR

This study reveals that Sr$_{1-x}$Ca$_x$TiO$_3$ is close to developing a modulated phase due to strong coupling between dipolar fluctuations and lattice vibrations, influenced by calcium substitution.

Contribution

It provides experimental evidence of incipient modulated phases in Sr$_{1-x}$Ca$_x$TiO$_3$ driven by flexoelectric phonon coupling and calcium doping effects.

Findings

Dipolar fluctuations soften the $c_{44}$ transverse acoustic mode upon cooling.

Calcium substitution enhances the amplitude and wavevector of softening.

A characteristic length scale of modulation is identified through wavevector analysis.

Abstract

Nanometer-scale modulations can spontaneously emerge in complex materials when multiple degrees of freedom interact. Here we demonstrate that ferroelectric Sr$_{1-x}$Ca$_x$TiO$_3$ lies in close proximity to an incipient structurally modulated phase. Using inelastic neutron and X-ray scattering, we show that upon cooling, dipolar fluctuations strongly couple to and soften the $c_{44}$ transverse acoustic mode. We identify the wavevector at which this softening is maximal, thereby defining the characteristic length scale of the modulation. Calcium substitution enhances both the amplitude and the wavevector of the softening by strengthening the ferroelectric and antiferrodistortive instabilities. Our results demonstrate that nonlinear flexoelectric phonon coupling tends to stabilize a modulated state that cooperates with, rather than competes against, the other lattice instabilities in SrTiO$_3$.