Domain-size effects on the dynamics of a charge density wave in $1\mathrm{T}\text{−}{\mathrm{TaS}}_2$

Recent experiments have shown that the high-temperature incommensurate (I) charge density wave (CDW) phase of 1T-${\mathrm{TaS}}_2$ can be photoinduced from the lower-temperature, nearly commensurate CDW state. Here we report a time-resolved x-ray diffraction study of the growth process of the photoinduced I-CDW domains. The layered nature of the material results in a marked anisotropy in the size of the photoinduced domains of the I-phase. These are found to grow self-similarly, their shape remaining unchanged throughout the growth process. The photoinduced dynamics of the newly formed I-CDW phase was probed at various stages of the growth process using a double pump scheme, where a first pump creates I-CDW domains and a second pump excites the newly formed I-CDW state. We observe larger magnitudes of the coherently excited I-CDW amplitude mode in smaller domains, which suggests that the incommensurate lattice distortion is less stable for smaller domain sizes.

Figure 1

Experimental setup. (a) Optical pump x-ray probe experimental setup. (b) Ewald sphere for the NC and I satellite peaks. The rotation scan around the surface normal $\left(\phi \right)$ is represented. (c) Schematic representation of the superlattice peaks in the ab plane as a function of temperature.

Figure 2

Double pump scheme. The first pump creates the I phase whereas the second pump perturbs the I phase in order to probe its dynamics.

Figure 3

3D representation of the photoinduced I-phase superlattice peak in reciprocal space. The projections in all three planes are represented for (a) 50 ps delay and (b) 9 ns delay. The color scale is adapted for the two delays but the relative numbers are consistent.

Figure 4

$\phi$ rotation scan of the I-satellite peak for different delays obtained at 230 K for an absorbed fluence of 10.5 mJ ${\mathrm{cm}}^{-2}$. The intensity was integrated over a region of the detector.

Figure 5

Intensity and width of the I-satellite peak versus delay obtained at 230 K for an absorbed fluence of 10.5 mJ ${\mathrm{cm}}^{-2}$. (a) Widths in the $hk$ plane. (b) Width in the $l$ direction. (c) Integrated intensity. The widths and intensity are fitted with a power law in the 0–1 ns delay range. (d) Correlation length of the I-CDW versus time delay along different real-space directions. The widths measured in the different directions exhibit the same relative changes as a function of $\mathrm{\Delta }t$, but different absolute values. The experimental resolution is $1\times 1\times 1.1{10}^{-3}$ in $\mathrm{h}\times \mathrm{k}\times \mathrm{l}$ r.l.u. (see Appendix pp1). The statistical uncertainties for these data are too small to be represented.

Figure 6

Intensity and width of the I-satellite peak versus delay obtained at 265 K for a fluence of 4.6 mJ ${\mathrm{cm}}^{-2}$. (a) Widths in the $hk$ plane, (b) Width in the $l$ direction. (c) Integrated intensity. The widths and intensity are fitted with a power law in the 0–1 ns delay range. (d) correlation length of the I-CDW versus delay along different real-space directions.

Figure 7

Double pump experiment results. (a) Time evolution of the intensity of the I satellite peak versus delay between P2 and probe $\left(\mathrm{\Delta }t\right)$, for various P1-P2 delays. (b)–(c) Refined values of the fit parameters within the adapted displacive excitation model (see text), for different P1-P2 delays. The amplitude of the displacement is very sensitive to the P1-P2 delay as well as the final displacement.

Figure 8

Magnitude of the coherently excited amplitude mode versus domain volume of the I phase for the double pump experiment. The relation between the magnitude and the volume is linear.

Figure 9

Growth velocity along different real-space directions versus delay (a) for 10.5 mJ ${\mathrm{cm}}^{-2}$ and (b) for 4.6 mJ ${\mathrm{cm}}^{-2}$.