Noncentrosymmetric, transverse structural modulation in Sr Al 4 , and elucidation of its origin in the Ba Al 4 family of compounds

At ambient conditions SrAl 4 adopts the BaAl 4 structure type with space group I 4 / m m m . It undergoes a charge-density-wave (CDW) transition at T CDW = 243 K, followed by a structural transition at T S = 87 K. Temperature-dependent single-crystal x-ray diffraction (SXRD) leads to the observation of incommensurate superlattice reflections at q = σ c * with σ = 0.1116 at 200 K. The CDW has orthorhombic symmetry with the noncentrosymmetric superspace group F 222 ( 0 0 σ ) 00 s , where F 222 is a subgroup of F m m m as well as of I 4 / m m m . Atomic displacements mainly represent a transverse wave, with displacements that are 90 deg out of phase between the two diagonal directions of the I -centered unit cell, resulting in a helical wave. Small longitudinal displacements are provided by the second harmonic modulation. The orthorhombic phase realized in SrAl 4 is similar to that found in EuAl 4 , except that no second harmonic could be determined for the latter compound. Electronic structure calculations and phonon calculations by density functional theory (DFT) have failed to reveal the mechanism of CDW formation. No clear Fermi surface nesting, electron-phonon coupling, or involvement of Dirac points could be established. However, DFT reveals that Al atoms dominate the density of states near the Fermi level, thus corroborating the SXRD measurements. SrAl 4 remains incommensurately modulated at the structural transition, where the symmetry lowers from orthorhombic to b -unique monoclinic. The present work draws a comparison on the modulated structures of nonmagnetic SrAl 4 and magnetic EuAl 4 elucidating their similarities and differences, and firmly establishing that although substitution of Eu to Sr plays little to no role in the structure, the transition temperatures are affected by the atomic sizes. We have identified a simple criterion that correlates the presence of a phase transition with the interatomic distances. Only those compounds X Al 4 − x Ga x ( X = Ba , Eu , Sr , Ca ; 0 < x < 4 ) undergo phase transitions, for which the ratio c / a falls within the narrow range 2.51 < c / a < 2.54 .