BaAl2O4 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 BaAl2O4 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 (TC) 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.
@article{arxiv.2602.01732,
title = {Degenerate Soft Modes and Selective Condensation in BaAl$_2$O$_4$ via Inelastic X-ray Scattering},
author = {Yui Ishii and Arisa Yamamoto and Alfred Q. R. Baron and Hiroshi Uchiyama and Naoki Sato},
journal= {arXiv preprint arXiv:2602.01732},
year = {2026}
}