Broken inversion symmetry in the charge density wave phase 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> exhibits a complex phase diagram, including the development of a charge density wave (CDW) below <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msub><b:mi>T</b:mi><b:mi>CDW</b:mi></b:msub><b:mo>=</b:mo><b:mn>145</b:mn><b:mspace width="0.16em"/><b:mi mathvariant="normal">K</b:mi></b:mrow></b:math>. Below <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:msub><e:mi>T</e:mi><e:mi>N</e:mi></e:msub><e:mo>=</e:mo><e:mn>15.4</e:mn><e:mspace width="0.16em"/><e:mi mathvariant="normal">K</e:mi></e:mrow></e:math>, a series of antiferromagnetically (AFM) ordered phases appear, while nontrivial topological phases, like skyrmion lattices, are stabilized under an applied magnetic field. The symmetries of the variously ordered phases are a major issue concerning the understanding of the stabilization of the ordered phases as well as concerning the interplay between the various types of order. <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:msub><h:mi>EuAl</h:mi><h:mn>4</h:mn></h:msub></h:math> at room temperature has tetragonal symmetry with space group <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mi>I</i:mi><i:mn>4</i:mn><i:mo>/</i:mo><i:mi>m</i:mi><i:mi>m</i:mi><i:mi>m</i:mi></i:mrow></i:math>. The CDW phase has an incommensurately modulated crystal structure described by the modulation wave vector <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:mi mathvariant="bold">q</j:mi><j:mo>≈</j:mo><j:mn>0.17</j:mn><j:mspace width="0.16em"/><j:msup><j:mi mathvariant="bold">c</j:mi><j:mo>*</j:mo></j:msup></j:mrow></j:math>. On the basis of various experiments, including elastic and inelastic x-ray scattering, and second-harmonic generation, it has been proposed that the symmetry of the CDW phase of <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"><n:msub><n:mi>EuAl</n:mi><n:mn>4</n:mn></n:msub></n:math> could be centrosymmetric orthorhombic, noncentrosymmetric orthorhombic or noncentrosymmetric tetragonal. Here, we report temperature-dependent, single-crystal x-ray diffraction experiments that show that the CDW is a transverse CDW with phason disorder, and with noncentrosymmetric symmetry according to the orthorhombic superspace group <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"><o:mrow><o:mi>F</o:mi><o:mn>222</o:mn><o:mo>(</o:mo><o:mn>0</o:mn><o:mspace width="0.16em"/><o:mn>0</o:mn><o:mspace width="0.16em"/><o:mi>σ</o:mi><o:mo>)</o:mo><o:mn>00</o:mn><o:mi>s</o:mi></o:mrow></o:math>. Essential for this finding is the availability of a sufficient number of second-order (<r:math xmlns:r="http://www.w3.org/1998/Math/MathML"><r:mrow><r:mn>2</r:mn><r:mi mathvariant="bold">q</r:mi></r:mrow></r:math>) satellite reflections in the x-ray diffraction data set. The broken inversion symmetry implies that skyrmions might form due to Dzyaloshinskii-Moriya (DM) interactions, instead of a more exotic mechanism as it is required for centrosymmetric structures.