Probing the ionic dielectric constant contribution in the ferroelectric phase of the Fabre salts

In strongly correlated organic materials it has been pointed out that charge ordering could also achieve electronic ferroelectricity at the same critical temperature $T_{co}$. A prototype of such phenomenon are the quasi-one-dimensional $({\mathrm{TMTTF})}_{2}X$ Fabre salts. However, the stabilization of a long-range ferroelectric ground state below $T_{co}$ requires the break of inversion symmetry, which should be accompanied by a lattice deformation. In this paper we investigate the role of the monovalent counteranion $X$ in such mechanism. For this purpose, we measured the quasistatic dielectric constant along the $c^{*}$-axis direction, where layers formed by donors and anions alternate. Our findings show that the ionic charge contribution is three orders of magnitude lower than the intrastack electronic response. The $c^{*}$ dielectric constant $\left({\epsilon }_{c^{*}}^{\prime }\right)$ probes directly the charge response of the monovalent anion $X$, since the anion mobility in the structure should help to stabilize the ferroelectric ground state. Furthermore, our ${\epsilon }_{c^{*}}^{\prime }$ measurements show that the dielectric response is thermally broaden below $T_{co}$ if the ferroelectric transition occurs in the temperature range where the anion movement begin to freeze in their methyl groups cavity. In the extreme case of the ${\mathrm{PF}}_6\text{−}{\mathrm{H}}_{12}$ salt, where $T_{co}$ occurs at the freezing point, a relaxor-type ferroelectricity is observed. Also, because of the slow kinetics of the anion sublattice, global hysteresis effects and reduction of the charge response upon successive cycling are observed. In this context, we propose that anions control the order-disorder or relaxation character of the ferroelectric transition of the Fabre salts. Yet, our results show that x-ray irradiation damages change the well-defined ferroelectric response of the ${\mathrm{AsF}}_6$ pristine salt into a relaxor.

Figure 1

Projection of the structure of $({\mathrm{TMTTF})}_{2}X$ with octahedral counter-anion $X$ in the $(a,c)$ plane. Donors and anions alternate along the $c^{*}$ direction perpendicular to $a$. Dimers are indicated by the dotted vertical segments in the left stack. Details in the main text.

Figure 2

Scheme of the CO/ferroelectric of (a) the TMTTF chain and (b)–(e) its various types of disorder. Green arrows represent the anion shift and the vertical black segments the dimer. Charge-rich (poor) donors are in red (blue). ${\mathrm{TMTTF}}^{+}$ is in brown, ${\mathrm{TMTTF}}^0$ is in black, and the horizontal black dotted segment represents a broken TMTTF.

Figure 3

Temperature dependence of the real part of the $c^{*}$ dielectric constant ${\epsilon }_{c^{*}}^{\prime }$ of the ${\mathrm{AsF}}_6\text{−}{\mathrm{H}}_{12},{\mathrm{SbF}}_6\text{−}{\mathrm{H}}_{12},{\mathrm{PF}}_6\text{−}{\mathrm{D}}_{12}$, and ${\mathrm{PF}}_6\text{−}{\mathrm{H}}_{12}$ Sample No. 2 salts measured at fixed 1 kHz upon cooling. For a proper comparison between the various salts, the data for the ${\mathrm{PF}}_6\text{−}{\mathrm{H}}_{12}$ was divided by a factor of 5 and the ${\mathrm{SbF}}_6$ multiplied by a factor of 3.

Figure 4

(a) Dielectric constant as a function of temperature for the fully hydrogenated $({\mathrm{TMTTF})}_2{\mathrm{PF}}_6$ salt (Sample No. 2) showing a maximum dielectric response at about 57 K both in the heating and cooling processes with employed rate of $\pm 7\mathrm{K}$/h and 50 mV/cm of applied electric field. Also, the various observed jumps indicate the formation of ferroelectric clusters, details in the main text. (b) Dielectric constant as a function of temperature for the fully hydrogenated $({\mathrm{TMTTF})}_2{\mathrm{PF}}_6$ salt (Sample No. 1) showing a broad maximum of dielectric response around 55 K in both heating and cooling measurements with an employed rate of $\pm 6\mathrm{K}$/h and 150 mV/cm of applied electric field.

Figure 5

Dielectric constant of ${\mathrm{PF}}_6\text{−}{\mathrm{H}}_{12}$ (Sample No. 2) measured during four successive cooling runs. The green data set was measured employing a rate of $-7\mathrm{K}$/h, while for the orange, yellow and gray data sets a rate of $-10\mathrm{K}$/h was employed.

Figure 6

Dielectric constant $\left({\epsilon }^{\prime }\right)$ as a function of temperature for the pristine $({\mathrm{TMTTF})}_2{\mathrm{AsF}}_6$ system (red data set), 12 h irradiated (blue) and three days irradiated (gray). The red dashed line, which refers to the smooth data of the pristine variant, was multiplied by a factor of 1.4 for a proper comparison with the 12 h irradiated variant. The measurements were carried out in warming up employing a rate of $+12\mathrm{K}$/h and with 50 mV/cm of applied electric field. The temperature scale $T/T_{co}$ is expressed in a fraction of the ferroelectric critical temperature of our pristine ${\mathrm{AsF}}_6$ sample $\left(T_{co}=105\mathrm{K}\right)$. For clarity the data have been shifted vertically (the base line of each shifted data is indicated on the left side of the figure).

Figure 7

Curie-Weiss plot, i.e., 1/${\epsilon }^{\prime }$ as a function of $T$ upon cooling for: (a) ${\mathrm{H}}_{12}$ Sample No. 2 (green) and ${\mathrm{D}}_{12}$ (pink) ${\mathrm{PF}}_6$; (b) the pristine $({\mathrm{TMTTF})}_2{\mathrm{AsF}}_6$ system (red data set), 12 h irradiated (blue), ${\mathrm{SbF}}_6$ (dark yellow), cf. label. The solid lines indicate the expected slopes in the frame of the mean-field approximation. The solid lines above $T_{co}$ are obtained from a mean-square fit of the raw data for the various salts. Details in the main text.