Charge density waves and soft phonon evolution in the superconductor BaNi${}_2$(As${}_{1-x}$P${}_x$)${}_2$

Abstract

The superconductor BaNi${}_2$As${}_2$ exhibits a soft-phonon-driven, incommensurate charge density wave (I-CDW) which is accompanied by a small orthorhombic structural phase transition. Upon further cooling, BaNi${}_2$As${}_2$ undergoes a first-order structural transition to a triclinic phase in which a commensurate CDW (C-CDW) appears. The relationship and interplay between the I-CDW, C-CDW and structural phase transitions has remained elusive. To investigate this issue, we present a complementary study of thermal diffuse X-Ray scattering and inelastic X-Ray scattering for phosphorus substituted BaNi${}_2$(As${}_{1-x}$P${}_x$)${}_2$ $(x⪅0.12)$ and down to 2.2 K. We show that most of the diffuse scattering signal can be well described by first-principles lattice dynamics calculations. Furthermore, we find that although phosphorus substitution rapidly suppresses the structural transition temperatures, the temperature dependence of the correlation length of the I-CDW fluctuations and the formation of Bragg-like superstructure peaks associated with long-range ordering of this order depends only weakly on the substitution level. Finally, we present the absence of signatures of the I-CDW to C-CDW or triclinic transition in the lattice dynamics, indicating that these instabilities are not (soft) phonon driven.

12 pages, 8 figures, 17 pages supplemental material, 16 supplementary figures, accepted version of the manuscript