Broken inversion symmetry in the charge density wave phase in EuAl$_4$

TL;DR

This study reveals that EuAl4's charge density wave phase breaks inversion symmetry, which could enable skyrmion formation via Dzyaloshinskii-Moriya interactions, advancing understanding of its complex magnetic and topological phases.

Contribution

The paper provides direct experimental evidence that the CDW phase in EuAl4 has non-centrosymmetric symmetry, clarifying the nature of its ordered phases and potential for skyrmion stabilization.

Findings

The CDW in EuAl4 is a transverse, non-centrosymmetric phase.

Broken inversion symmetry suggests Dzyaloshinskii-Moriya interactions enable skyrmion formation.

Temperature-dependent x-ray diffraction confirms the non-centrosymmetric orthorhombic symmetry.

Abstract

EuAl$_4$ exhibits a complex phase diagram, including the development of a charge density wave (CDW) below $T_{CDW} = 145$ K. Below $T_{N}=15.4$ 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. EuAl$_4$ 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 $\mathbf{q} \approx 0.17\mathbf{c}^{*}$. 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 EuAl$_4$ 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 $F222(0\,0\,\sigma)00s$.Essential for this finding is the availability of a sufficient number of second-order ($2\mathbf{q}$) 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.