Electron-phonon coupling in EuAl4 under hydrostatic pressure

Abstract

In the intermetallid rare-earth tetragonal EuAl4 system, competing itinerant exchange mechanisms lead to a complex magnetic phase diagram, featuring a centrosymmetric skyrmion lattice. Previous inelastic x-ray scattering (IXS) experiments revealed that the incommensurate charge-density wave (CDW) transition in EuAl4 (TCDW = 142 K) is driven by momentum-dependent electron-phonon coupling (EPC). We present the results of IXS under high hydrostatic pressure induced by diaond anvils and show how the EPC in EuAl4 is renormalized and suppressed in the material's temperature-pressure phase diagram. Our findings highlight the crucial role of momentum-dependent EPC in the formation of the CDW in EuAl4 and provide further insights into how external pressure can be used to tune charge ordering in quantum materials.

Figures (5)

• Figure 1: The $(T$--$P)$ phase diagram of EuAl$_4$. The CDW transition is shown as reported by Nakamura et al., Ref. Nakamura:2015aa. The measurements at the $(T$--$P)$ points studied in the present paper are marked by red diamonds.
• Figure 2: Inelastic X-ray scattering at $T = 293$ K. (a) The data collected at the momentum (3 0 0.1) at high pressure of 0.5 GPa, compared to the previous measurements at ambient pressure PhysRevB.110.045102. (b) The data at (3 0 0.8). The open symbols are data and the solid lines are the pseudo-Voigt fits. The shaded areas illustrate the individual peak contributions into the net fitting curve. The black marks highlight the peak positions. (c) The extracted phonon dispersions at 0 and 0.5 GPa. The solid symbols are the fit results, and the solid lines describe the model given in Eq. \ref{['eq:eq1']}. (d) The real part of the phonon self energy at ambient pressure, according to Eq. \ref{['eq:eq1']}, with the shaded band showing the $1\sigma$ margin of uncertainty
• Figure 3: Inelastic X-ray scattering at $T = 150$ K. (a) The data collected at the momentum (3 0 0) at 1.1 GPa, as compared to the previous measurements at ambient pressure PhysRevB.110.045102. (b) The data at (3 0 0.5). The open symbols are data, the solid lines are the pseudo-Voigt fits. The shaded areas illustrate the individual peak contributions to the net fitting curve. The black markers highlight the peak positions. (c) The extracted phonon dispersions at 0 and 1.1 GPa. The solid symbols are the fit results, and the solid lines describe the model given in Eq. \ref{['eq:eq1']}. (d) The real part of the phonon self energy for 0 and 1.1 GPa, with shaded bands showing the $1\sigma$ margin of uncertainty.
• Figure 4: The results of the ab initio calculations. (a) The sketch of the atomic displacements of the TA phonon at the momentum (0 0 0.2) r.l.u. The red dotted lines show which Al atoms form the zigzag chains. (b) The pressure-induced change of the relative atomic phases in the mode. (c) The calculated TA mode dispersion under different pressures.
• Figure 5: (a) Temperature dependence of the scale parameter $A$ of Eq. \ref{['eq:eq2']}, proportional to the EPC strength, for different pressures. For each $P$, the green symbols mark the values $A_{\text{max}}$, at which the softened mode freezes out, and the green solid line is a guide to the eye indicating this limit. (b) The corresponding contours of constant $A$ within the $(T$--$P)$ phase diagram of EuAl$_4$. (c) The similarity of the phonon dispersion measured under different $T$ and $P$ conditions, as suggested by (b).