Giant Kohn Anomaly and the Phase Transition in Charge Density Wave ${\mathrm{ZrTe}}_3$

A strong Kohn anomaly in ${\mathrm{ZrTe}}_3$ is identified in the mostly transverse acoustic phonon branch along the modulation vector $q_P$ with polarization along the $a^{*}$ direction. This soft mode freezes to zero frequency at the transition temperature $T_P$, and the temperature dependence of the frequency is strongly affected by fluctuation effects. Diffuse x-ray scattering of the incommensurate superstructure shows a power-law scaling of the intensity and the correlation length that is compatible with an order parameter of dimension $n=2$.

Figure 1

Acoustic phonon along ${\overrightarrow{q}}_P$ at $T=100\mathrm{K}$. (a) Representative IXS spectra at momenta close to $(40\overline{1})$ at ${\overrightarrow{q}}_P$ ($a^{*}=3.93$) and across ${\overrightarrow{q}}_P$ on a logarithmic scale with arbitrary offset. Error bars are smaller than the symbols except for the outer data points. Solid lines below that data are (shifted) resolution functions that were summed to fit the data. (b) Phonon dispersion extracted from fits to the IXS data. The dashed line is a sinusoidal model dispersion ${\omega }_{ni}(\overrightarrow{q})$ that serves as a guide to the eye. The inset shows a portion of reciprocal space with the scan direction through ${\overrightarrow{q}}_P$ indicated.

Figure 2

Phonon dispersion from $(40\overline{1})$ in the direction of ${\overrightarrow{q}}_P$ at various temperatures $T>T_P$ above the transition. The inset shows the phonon energy $\hslash {\omega }_q$ at ${\overrightarrow{q}}_P$ as a function of reduced temperature $(T-T_P)/T_P$. The solid and dashed lines represent a $1/8$ and a $1/2$ power law, respectively.

Figure 3

Diffuse scattering along ${\overrightarrow{q}}_P$. (a) Symbols represent the intensities extracted from data fitting of the IXS spectra: central peak (triangles), phonon contribution (filled circles). The solid line is the total diffuse scattering intensity as measured with an energy-integrating detector. (b) Diffuse scattering intensities at three selected temperatures as indicated. (c) Scans of diffuse scattering across ${\overrightarrow{q}}_P$ along $b^{*}$ at various temperatures above $T_P$.

Figure 4

(a) Temperature dependence of superstructure intensity at — (left scale) and the width of the diffuse scattering along $b*$ (right scale). (b),(c) Double-logarithmic representations of the intensity and the width, respectively, versus the reduced temperature.