Phonon softening and atomic modulations in EuAl4

<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>EuAl</a:mi><a:mn>4</a:mn></a:msub></a:math> is a rare-earth intermetallic in which competing itinerant and/or indirect exchange mechanisms give rise to a complex magnetic phase diagram, including a centrosymmetric skyrmion lattice. These phenomena arise not in the tetragonal parent structure but in the presence of a charge-density wave (CDW), which lowers the crystal symmetry and renormalizes the electronic structure. Microscopic knowledge of the corresponding atomic modulations and their driving mechanism is a prerequisite for a deeper understanding of the resulting equilibrium of electronic correlations and how it might be manipulated. Here, we use synchrotron single-crystal x-ray diffraction, inelastic x-ray scattering, and lattice-dynamics calculations to clarify the origin of the CDW in <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>EuAl</b:mi><b:mn>4</b:mn></b:msub></b:math>. We observe a broad softening of a transverse acoustic phonon mode that sets in well above room temperature and, at <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msub><c:mi>T</c:mi><c:mtext>CDW</c:mtext></c:msub><c:mo>=</c:mo><c:mn>142</c:mn></c:mrow></c:math> K, freezes out in an atomic displacement mode described by the superspace group <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>I</d:mi><d:mi>m</d:mi><d:mi>m</d:mi><d:mi>m</d:mi><d:mo>(</d:mo><d:mn>00</d:mn><d:mi>γ</d:mi><d:mo>)</d:mo><d:mi>s</d:mi><d:mn>00</d:mn></d:mrow></d:math>. In the context of previous work, our observation is a clear confirmation that the CDW in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:msub><e:mi>EuAl</e:mi><e:mn>4</e:mn></e:msub></e:math> is driven by electron-phonon coupling. This result is relevant for a wider family of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msub><f:mi>BaAl</f:mi><f:mn>4</f:mn></f:msub></f:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:msub><g:mi>ThCr</g:mi><g:mn>2</g:mn></g:msub><g:msub><g:mi>Si</g:mi><g:mn>2</g:mn></g:msub></g:mrow></g:math>-type rare-earth intermetallics known to combine CDW instabilities and complex magnetism. Published by the American Physical Society 2024