One-Dimensional Fluctuating Nanodomains in the Charge-Transfer Molecular System TTF-CA and their First-Order Crystallization

We report on the direct observation by x-ray diffuse scattering measurements of thermally induced one-dimensional nanoscale ordered fluctuations in the mixed-stack charge-transfer molecular system tetrathiafulvalene-$p$ chloranil (TTF-CA), the prototype for the neutral-ionic phase transition. The unusual physical properties of this compound are considered to be driven by such one-dimensional excitations. The results are discussed in relation to previous experimental and theoretical experiments both at thermal equilibrium and under light irradiation.

Figure 1

Diffuse planes observed at 84 K ($T_{N\mathrm{\text{−}}I}+2\mathrm{K}$) in the diffraction pattern for different values of Miller index $h$ indicated at the image bottom (left). The stacking axis $\mathbf{a}$ is horizontal and the projections of the intersection of the (${\mathbf{b}}^{*},{\mathbf{c}}^{*}$) planes with the Ewald sphere correspond to the diffuse curves on the image plate as schematically shown (right). W22 beam line on DCI at LURE.

Figure 2

Diffuse scattering intensity at 84 K around (3 1 $-1$) in the (${\mathbf{a}}^{*},{\mathbf{b}}^{*}$) plane (left) and around (3 1 0.5) in the (${\mathbf{a}}^{*},{\mathbf{c}}^{*}$) planes (right). For clarity, the maximum intensity of the Bragg peaks has been cut. Just above the phase transition, no transverse modulation of the scattering is observed.

Figure 3

Scan through the diffuse plane along ${\mathbf{a}}^{*}$ at 84 K. The line corresponds to the fit with a Lorentzian function $I(Q)=I_0+I_M/(1+[(Q-3)/{\xi }_{1\mathrm{D}}{]}^2)$, from which is extracted the 1D correlation length ${\xi }_{1\mathrm{D}}$ associated with the characteristic size of the strings and the intensity at maximum $I_M$.

Figure 4

Inverse correlation length ${\xi }_{1\mathrm{D}}^{-1}$ (top) along ${\mathbf{a}}^{*}$ and x-ray intensity at maximum $I_M$ (bottom) versus temperature. Above the first order phase transition occurring at 82 K, purely 1D fluctuations are observed. The lines result from a fit using the transfer integral approach [14] according to ${\xi }_{1\mathrm{D}}^{-1}=\beta \sqrt{{\delta }^{\prime 2}+8t_0^2}$ and $I_M$ proportional to $\frac{1}{\beta }\frac{\sqrt{{\delta }^{\prime 2}+8t_0^2}-{\delta }^{\prime }}{{\delta }^{\prime 2}+8t_0^2}$, where $\beta =\frac{E_{\mathrm{DW}}}{k_{\mathrm{B}}T}$ and $t_0=\frac{1}{\beta }\exp (-\beta )$. The area between the discontinuous lines corresponds to the thermal hysteresis where neutral and ionic phases coexist.