Phonon softening and slowing-down of charge density wave fluctuations in ${\mathrm{BaNi}}_2{\mathrm{As}}_2$

${\mathrm{BaNi}}_2{\mathrm{As}}_2$ is a nonmagnetic analog of the iron pnictide superconductors, and exhibits an incommensurate charge density wave (IC-CDW) and a sizable elastoresistance. In this Letter, phonons in ${\mathrm{BaNi}}_2{\mathrm{As}}_2$ associated with the IC-CDW and uniform in-plane lattice distortions are investigated using high-resolution inelastic x-ray scattering. The in-plane transverse acoustic phonons reveal no softening at temperatures where the elastoresistance increases strongly, indicating the latter to be electronically driven. Systematic phonon measurements suggest the IC-CDW occurs in two stages upon cooling: Underdamped phonons first soften to zero energy well above the IC-CDW ordering temperature, then the resulting quasielastic IC-CDW fluctuations gradually slow down and coalesce into the static IC-CDW order. A possible origin for our observations is the IC-CDW in ${\mathrm{BaNi}}_2{\mathrm{As}}_2$ being uniaxial, which provides an additional Ising degree of freedom favorable for disordered IC-CDW modulations, and accounts for the elastoresistance through a weak coupling to the lattice.

Figure 1

(a) Schematic evolution of ${\mathrm{BaNi}}_2{\mathrm{As}}_2$ with temperature. The IC-CDW order forms at $T_{\mathrm{IC}}$, and a structural transition occurs at $T_{\mathrm{S}}$. The insets in the three regions for $T>T_{\mathrm{S}}$ are schematic phonon dispersions around ${\mathbf{q}}_0$. (b) Schematic energy scans in ${\mathrm{BaNi}}_2{\mathrm{As}}_2$ at ${\mathbf{q}}_0$ for $T>T_{\mathrm{S}}$. (c) Schematic of the reciprocal space probed in this work. The light gray circles are IC-CDW peaks which occur for odd $L$, and the black arrow represents a line along $(1,K,5)$, where our measurements are carried out. The red arrows present measurements of the IPTA phonons, with lattice distortions in the $B_{1\mathrm{g}}$ and $B_{2\mathrm{g}}$ channels respectively probed by phonons at $(3+q,3-q,0)$ and $(4,k,0)$. (d) Color-coded intensity of elastic scans along $(1,K,5)$ as a function of temperature. Alignment in the tetragonal phase is used for scans in the triclinic phase. (e) Temperature dependence of the integrated intensity for scans in (d). The inset zooms in around 150 K.

Figure 2

Phonon measurements at several temperatures for (a) $\mathbf{Q}=(1,1.64,5)$, (b) $\mathbf{Q}=(1,1.69,5)$, (c) $\mathbf{Q}=(1,1.72,5)$, (d) $\mathbf{Q}=(1,1.75,5)$, and (e) $\mathbf{Q}=(1,1.80,5)$. The solid lines are fits to either the DHO model (thick lines with the same color as the symbols) or a Lorentzian model (thin black lines). The dashed lines are the elastic components in the DHO model, and the dotted lines are the inelastic components. The experimentally measured instrumental resolution is parametrized using a pseudo-Voigt function, and is represented as the shaded gray areas.

Figure 3

(a) Damping ratios $\gamma /\left(2E_0\right)$, and (b) phonon energies $E_{\mathrm{ph}}$, obtained by fitting the data in Fig. 2 to a general DHO. $E_{\mathrm{ph}}=0$ corresponds to critically damped or overdamped phonons. (c) Relaxation rates $\mathrm{\Gamma }$, and (d) the intensity scale factors $A_{\mathrm{L}}$, obtained by fitting the data in Figs. 2–2 to a Lorentzian model. The solid lines in (c) are a fit to Eq. (3), for data inclusively between 150 and 180 K. The solid lines in (d) are a fit to Eq. (4), with $A_0$ as the only free parameter and the other parameters are from the fit in (c).

Figure 4

Temperature evolution of acoustic phonons at $\mathbf{Q}=(3+q,3-q,0)$ with (a) $q=0.035$ and (b) $q=0.1$. (c) $E_{\mathrm{ph}}/q$ for phonons at $\mathbf{Q}=(3+q,3-q,0)$. The solid line is a fit to $E_{\mathrm{ph}}/q=Bsin\left(\pi Dq\right)/q$, and the dashed line is obtained by further multiplying $\sqrt{\frac{1+{\xi }_{\mathrm{nem}}^2{q}^2}{1+{\xi }_{\mathrm{nem}}^2(q^2+r)}}$ (using ${\xi }_{\mathrm{nem}}=5$ Å and $r=0.02$ Å${}^{-2}$ for ${\mathrm{Sr}}_{0.64}{\mathrm{Na}}_{0.36}{\mathrm{Fe}}_2{\mathrm{As}}_2$ at 147 K [38]), when there is a significant coupling between the lattice and nematic fluctuations. (d) Temperature evolution of acoustic phonons at $\mathbf{Q}=(4,k,0)$ for $k=0.05$. The solid lines in (a), (b), and (d) are fits to the DHO model.