Charge density waves and soft phonon evolution in the superconductor BaNi 2 (As 1−x P <…

The superconductor <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>BaNi</a:mi><a:mn>2</a:mn></a:msub><a:msub><a:mi>As</a:mi><a:mn>2</a:mn></a:msub></a:mrow></a:math> exhibits a soft-phonon-driven, incommensurate charge density wave (I-CDW) which is accompanied by a small orthorhombic structural phase transition. Upon further cooling, <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msub><b:mi>BaNi</b:mi><b:mn>2</b:mn></b:msub><b:msub><b:mi>As</b:mi><b:mn>2</b:mn></b:msub></b:mrow></b:math> 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 have 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msub><c:mi>BaNi</c:mi><c:mn>2</c:mn></c:msub><c:msub><c:mrow><c:mo>(</c:mo><c:msub><c:mi>As</c:mi><c:mrow><c:mn>1</c:mn><c:mo>−</c:mo><c:mi mathvariant="normal">x</c:mi></c:mrow></c:msub><c:msub><c:mi mathvariant="normal">P</c:mi><c:mi mathvariant="normal">x</c:mi></c:msub><c:mo>)</c:mo></c:mrow><c:mn>2</c:mn></c:msub><c:mrow><c:mspace width="4pt"/><c:mo>(</c:mo><c:mi>x</c:mi><c:mo>≲</c:mo><c:mn>0.12</c:mn></c:mrow></c:mrow></c:math>) and down to <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mrow><h:mn>2.2</h:mn></h:mrow><h:mspace width="0.16em"/><h:mi mathvariant="normal">K</h:mi></h:mrow></h:math>. 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.