Degenerate Soft Modes and Selective Condensation in BaAl$_2$O$_4$ via Inelastic X-ray Scattering

TL;DR

This study provides direct experimental evidence of two soft phonon modes in BaAl$_2$O$_4$ using inelastic X-ray scattering, elucidating their roles in the material's structural phase transition and quantum criticality.

Contribution

First direct observation of soft modes in BaAl$_2$O$_4$ via inelastic X-ray scattering, confirming their involvement in the ferroelectric phase transition.

Findings

Soft modes at M and K points are nearly degenerate in energy.

The K-point mode softens toward the transition temperature.

The phase transition occurs only at the M point, with mode stabilization.

Abstract

BaAl$_2$O$_4$ is a ferroelectric material that exhibits structural quantum criticality through chemical composition tuning. Although theoretical calculations and several diffraction experiments have suggested the involvement of a soft mode in its ferroelectric structural phase transition, direct experimental verification is still lacking. In this study, we successfully observed two soft modes of BaAl$_2$O$_4$ using x-ray inelastic scattering, providing direct experimental evidence for their role in the structural phase transition. Furthermore, we reveal that the soft modes at the M and K points are nearly degenerate in energy, indicating a delicate balance in which either mode could potentially freeze. The K-point mode simultaneously softens toward the transition temperature ($T_{\rm C}$) in a manner nearly identical to the M-point mode. However, the phase transition condenses only at the M point, with the M-point mode stabilizing as an acoustic mode in the low-temperature structure and the K-point mode hardening as temperature decreases.