Orthorhombic charge density wave on the tetragonal lattice of EuAl₄

Abstract

EuAl4 possesses the BaAl4 crystal structure type with tetragonal symmetry I4/mmm. It undergoes a charge density wave (CDW) transition at T CDW = 145 K and features four consecutive antiferromagnetic phase transitions below 16 K. Here we use single-crystal X-ray diffraction to determine the incommensurately modulated crystal structure of EuAl4 in its CDW state. The CDW is shown to be incommensurate with modulation wave vector q = (0,0,0.1781 (3)) at 70 K. The symmetry of the incommensurately modulated crystal structure is orthorhombic with superspace group Fmmm(00σ)s00, where Fmmm is a subgroup of I4/mmm of index 2. Both the lattice and the atomic coordinates of the basic structure remain tetragonal. Symmetry breaking is entirely due to the modulation wave, where atoms Eu and Al1 have displacements exclusively along a, while the fourfold rotation would require equal displacement amplitudes along a and b. The calculated band structure of the basic structure and interatomic distances in the modulated crystal structure both indicate the Al atoms as the location of the CDW. The temperature dependence of the specific heat reveals an anomaly at T CDW = 145 K of a magnitude similar to canonical CDW systems. The present discovery of orthorhombic symmetry for the CDW state of EuAl4 leads to the suggestion of monoclinic instead of orthorhombic symmetry for the third AFM state.

Spontaneous reversal of spin chirality and competing phases in the topological magnet EuAl4

“…In performing these calculations, we assumed that the Eu ions do not contribute to the periodic distortion of the lattice that gives rise to the CDW satellites, in accordance with Ref. [21,22] that suggests it is the Al ions that displace. We note changing the magnitude of k0q did not change the qualitative results of the calculations, and hence these results are valid for the AFM2, AFM3 and AFM4 phases.…”

“…We label the Eu ion at the vertex Eu11, and the Eu ion at the body center as Eu12. Below TCDW = 145 K the onset of charge density wave order occurs with propagation vector (0,0,τ) τ = 0.1781 (3) [19][20][21]. Single crystal neutron diffraction studies demonstrated that the four magnetically ordered phases of EuAl4, which we label as AFM1, AFM2, AFM3 and AFM4 with onset temperatures of T1 = 15.4 K, T2 = 13.2 K, T3 = 12.2 K and T4 ∼10 K respectively, ordered with multiple magnetic propagation vectors [22].…”

Atomic Resolution Cryogenic 4D-STEM Imaging via Robust Distortion Correction

“…EuAl 4 was chosen as the primary material for this study to demonstrate the effectiveness of our correction algorithm. EuAl 4 is attracting increasing attention as it develops a charge density wave at around 145 K and exhibits four successive magnetic transitions below 16 K. − Precisely identifying the atomic positions in EuAl 4 below the charge density wave transition temperature helps to understand the charge density wave ordering in the material and its complicated magnetic behavior at lower temperatures. The initial effort to procure a cryogenic 4D-STEM data set along the [100] zone axis of EuAl 4 at 100 K is presented in Figure .…”

Coupling between Charge Density Wave Ordering and Magnetism in Ho2Ir3Si5

“…More recently, alternative mechanisms were proposed that explain, for example, the formation of CDWs by q -dependent electron–phonon coupling (EPC) in three-dimensional (3D) CDW compounds. Examples of 3D metals with CDWs include α-uranium, CuV 2 S 4 , − La 3 Co 4 Sn 13 , − R Te 3 ( R = La, Sm, Gd, Tb, Dy, Ho, Er, Tm), − R Te 2 ( R = La, Ce), , R 5 Ir 4 Si 10 ( R = Dy, Ho, Er, Yb, Lu), Sm 2 Ru 3 Ge 5 , EuAl 4 , − and CuIr 2– x Cr x Te 4 . In several of these compounds, a coexistence and competition exist between the CDW and antiferromagnetic (AFM) order or superconductivity (SC).…”