Hidden phonon-assisted charge density wave transition in BaFe2Al9 revealed by ultrafast optical spectroscopy

TL;DR

The paper investigates the microscopic origin of the charge-density wave in BaFe$_2$Al$_9$, addressing whether nesting or electron-phonon coupling dominates in a three-dimensional system. Using polarization-resolved ultrafast optical spectroscopy together with first-principles calculations of phonons and electron-phonon coupling, the authors observe a sharp, first-order CDW transition near $T_c \approx 110$ K and a single coherent mode at $f \approx 1.6$ THz that emerges only in the CDW phase. This mode is identified as a Ba-dominated precursor phonon at the CDW wave vector $q_{\rm CDW}$ with strong EPC, activated via a displacive mechanism and not visible in Raman spectra, explaining the atypical amplitude-mode behavior. The results demonstrate a phonon-assisted, electronically driven CDW in a 3D intermetallic and underscore the role of hidden, strongly coupled phonons in CDW formation, offering a framework for exploring similar systems.

Abstract

The interplay between electronic and lattice degrees of freedom is fundamental to charge density wave (CDW) formation, yet the microscopic origin often remains elusive. Here, we investigate the transient optical response of the intermetallic compound BaFe2Al9 using polarization-resolved ultrafast optical spectroscopy. We identify a discontinuous sign reversal in the transient reflectivity at Tc ~ 110 K, providing unambiguous evidence for the first-order transition. The anisotropic quasiparticle relaxation establishes the three-dimensional nature of the ordered state. Below Tc, a single coherent 1.6 THz oscillation appears abruptly and remains confined to the CDW phase. This mode exhibits weak temperature dependence with negligible softening and is absent in Raman spectra. First-principles calculations imply that it is a precursor phonon at the CDW wave vector with strong electron-phonon coupling. Our results indicate that the CDW in BaFe2Al9 arises from intertwined electronic and lattice instabilities, assisted by a displacive mechanism mediated by a hidden strongly coupled phonon, distinct from conventional amplitude-mode softening scenarios.

Figures (4)

• Figure 1: Temperature-dependent ultrafast dynamics for BaFe$_2$Al$_9$. Two-dimensional color maps of the transient reflectivity change, $\Delta R/R$, as a function of pump-probe time delay and temperature for (a) E // c and (b) E $\perp$ c. The horizontal dashed lines mark the CDW transition temperature. (c) Representative transients at 10 K (upper) and 300 K (lower) for both polarizations up to 10 ps. Dash curves are the fits to the three exponential relaxation background. Inset: schematic of the polarization-resolved pump-probe experiment.
• Figure 2: Quantitative analysis of the quasiparticle relaxation. Temperature dependence of the (a-c) amplitudes and (d-f) relaxation times extracted from the three exponential fit to the experimental data. Error bands indicate fit uncertainties.
• Figure 3: Coherent phonon spectroscopy in the CDW phase. (a) Oscillatory component of the transient reflectivity for E // c at various temperatures below T$_C$, isolated by subtracting the multi-exponential background. (b) Comparison of the FFT spectrum of the oscillatory signal at 10 K with experimental Raman spectra. Arrows mark the observed Raman-active phonon modes, with their assignments guided by first-principles calculations. Dash line highlights the dominant 1.6 THz mode, absent in the Raman spectra. (c-d) Temperature dependence of the oscillation frequency $f$ and damping rate $\gamma$ for both polarizations. Error bands indicate fit uncertainties.
• Figure 4: First-principles analysis of the phonon dispersion and EPC for BaFe$_2$Al$_9$ in the high temperature P6/mmm phase. (a) Phonon dispersion superimposed by the mode-resolved EPC (blue circles, Eq. \ref{['eq:mode_EPC']}), with radius proportional to the coupling magnitude. A horizontal dashed line highlights the 1.6 THz frequency. Inset: The Brillouin zone with high symmetry points. The U$_4$ point lies on the L-M line at fractional coordinates (0.5, 0, 0.3). (b) Cumulative EPC parameter (blue curve, Eq. \ref{['eq:lambda_def']}) and the marginal contribution to $\lambda$ (red curve, Eq. \ref{['eq:lambda_diff']}), magnified by 10 times for clarify. (c) Real-space visualization of the atomic displacements for the 1.6 THz phonon mode at the U$_4$ point, highlighting the dominant sine-modulated in-plane vibrations of the Ba atoms. The dashed rectangle denotes the unit cell of the high-temperature phase.