Broken inversion symmetry in the charge density wave phase in EuAl₄

EuAl₄ exhibits a complex phase diagram, including the development of a charge density wave (CDW) below TCDW = 145 K. Below TN=15.4 K, a series of antiferromagnetically (AFM) ordered phases appear, while non-trivial 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. EuAl₄ at room temperature has tetragonal symmetry with space group $I4/mmm$. The CDW phase has an incommensurately modulated crystal structure described by the modulation wave vector q ≈ 0.17c*. 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 EuAl₄ could be centrosymmetric orthorhombic, non-centrosymmetric orthorhombic or non-centrosymmetric 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 non-centrosymmetric symmetry according to the orthorhombic superspace group $F222(0\,0\,σ)00s$.Essential for this finding is the availability of a sufficient number of second-order (2q) 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.