Tuning Incommensurate Charge Order in Ba$_{1-x}$Sr$_x$Al$_4$ and Ba$_{1-y}$Eu$_y$Al$_4$

TL;DR

This study investigates how incommensurate charge density wave order in Ba$_{1-x}$Sr$_x$Al$_4$ and Ba$_{1-y}$Eu$_y$Al$_4$ evolves with substitution, revealing a universal correlation between transition temperature and wavevector, and confirming an electron-phonon mechanism.

Contribution

It provides the first detailed analysis of the evolution of incommensurate CDW order in these materials, linking charge order suppression to phonon instabilities and uncovering a universal behavior.

Findings

Incommensurate CDW with c-axis orientation in SrAl$_4$

Charge order wavevector shortens with Ba substitution

Charge order suppression correlates with phonon instability suppression

Abstract

The BaAl$_4$-type structure family is home to a vast landscape of interesting and exotic properties, with descendant crystal structures hosting a variety of electronic ground states including magnetic, superconducting and strongly correlated electron phenomena. BaAl$_4$ itself hosts a non-trivial topological band structure, but is otherwise a paramagnetic metal. However, the other members of the $A$Al$_4$ family ($A$= alkali earth), including SrAl$_4$ and EuAl$_4$, exhibit symmetry-breaking ground states including charge density wave (CDW) and magnetic orders. Here we investigate the properties of the solid solution series Ba$_{1-x}$Sr$_x$Al$_4$ and Ba$_{1-y}$Eu$_y$Al$_4$ using transport, thermodynamic and scattering experiments to study the evolution of the charge-ordered state as it is suppressed with Ba substitution to zero near 50% substitution in both systems. Neutron and x-ray diffraction measurements reveal an incommensurate CDW state in SrAl$_4$ with $c$-axis-oriented ordering vector (0, 0, 0.097) that evolves with Ba substitution toward a shorter wavelength. A similar progression is observed in the Ba$_{1-y}$Eu$_y$Al$_4$ series that also scales with the ordering temperature, revealing a universal correlation between charge-order transition temperature and ordering vector that points to a critical wavevector that stabilizes CDW order in both systems. We study the evolution of the phonon band structure in the Ba$_{1-x}$Sr$_x$Al$_4$ system, revealing the suppression of the CDW phase matches the suppression of a phonon instability at precisely the same momentum as observed in experiments, confirming the electron-phonon origin of charge order in this system.