Broken magnetic symmetry due to charge-order ferroelectricity discovered in (TMTTF)${}_{2}X$ salts by multifrequency ESR

We have investigated the charge-ordered state of the quasi-one-dimensional organic charge-transfer salts (TMTTF)${}_{2}X$ (where TMTTF stands for tetramethyltetrathiafulvalene and $X={\text{PF}}_6$ AsF${}_6$, SbF${}_6$, and SCN) by performing comprehensive electron-spin-resonance (ESR) experiments at several frequencies for $4\mathrm{K}<T<300$ K. At elevated temperatures all compounds show a linear increase of $\Delta H\left(T\right)$. Below the charge-ordering transition $T_{\mathrm{CO}}$ important anomalies are observed in both the temperature dependence and the anisotropy of the ESR linewidth. In the case of the centrosymmetric anions PF${}_6$, AsF${}_6$, and SbF${}_6$, the linewidth doubles its periodicity when rotated in a plane normal to the molecule axis; and it exhibits a significant frequency dependence. This enhanced linewidth is caused by anisotropic Zeeman interaction that we identify as a relaxation process in the charge-ordered state where magnetically inequivalent sites are present in adjacent stacks. Thus, charge order not only produces ferroelectricity but also breaks the symmetry of the magnetic degree of freedom in these organic quantum spin chains. For (TMTTF)${}_2$SCN charge order coincides with the ordering of the non-centrosymmetric anions; the large contribution of dipolar interaction dominates the relaxation process.

Figure 1

Crystal structure of (TMTTF)${}_2$SbF${}_6$ viewed (a) along the stacking direction $a$, (b) along the $b$ axis, and (c) along the $c$ direction. The TMTTF molecules are basically arranged in the direction $c+b$. The strongest couplings between the octahedral anions and the sulfur atoms are indicated by the red dashed lines I and II, which are related by inversion symmetry for $T>T_{\mathrm{CO}}$. In the charge-ordered state, not only do the TMTTF molecules develop a charge disproportionation with alternating charge-rich and charge-poor molecules along the stacks, the anions also are slightly deformed. The inversion symmetry is lifted and contact I becomes shorter than contact II. Also shown is the configuration between the TMTTF molecular structure and the principal axes of the $\mathbf{g}$ tensor. At elevated temperatures the $\mathbf{g}$ tensor (blue arrows indicate the principal magnetic directions $\tilde{a}$, $\tilde{b}$, and $\tilde{c}$) is determined by the molecular structure. The $\tilde{a}$ axis of the $\mathbf{g}$ tensor is normal to the molecular plane and basically along the stacking direction, while the $\tilde{c}$ axis points along to the longest molecule extension. For $T<T_{\mathrm{CO}}$ the principal axes of the $\mathbf{g}$ tensor rotate around the $\tilde{c}$ axis by an angle $\phi$ in opposite directions, resulting in the brown arrows.

Figure 2

Angular dependence of the ESR linewidth $\Delta H$ (HWHM) (top), and the $g$ value (bottom) of (TMTTF)${}_2$SbF${}_6$ at room temperature measured at $X$-band frequency when the static magnetic field $B_0$ is rotated within the $\tilde{a}\tilde{b}$ plane (green circles), the $\tilde{b}\tilde{c}$ plane (red squares), and the $\tilde{a}\tilde{c}$ plane (blue triangles). The least-squares fits of the linewidth and the $g$ value by Eqs. (1) and (2) are shown by the corresponding lines. The inset demonstrates the orientation of the different orthogonal directions within the TMTTF molecule. The $\tilde{a}$ axis is normal to the plane, the $\tilde{c}$ axis points in the long direction, and $\tilde{b}$ points along the intermediate short direction.

Figure 3

Temperature dependence of ESR parameters of (TMTTF)${}_2$PF${}_6$ measured by $X$-band spectroscopy along the three crystal orientations. (a) The linewidth $\Delta H$ and (b) the change in the $g$ value obtained along the $\tilde{a}$ axis (green solid dots), the $\tilde{b}$ direction (open red squares), and the $\tilde{c}$ direction (blue triangles). Basically no change in $\Delta H\left(T\right)$ and $\Delta g\left(T\right)$ is observed at the charge-ordering temperature $T_{\mathrm{CO}}=67$ K.

Figure 4

Temperature dependence of (a) the linewidth $\Delta H$, and (b) the change in the $g$ value for (TMTTF)${}_2$SbF${}_6$ measured by $X$-band ESR along the three crystal orientations. The green solid dots correspond to the $\tilde{a}$ axis, the open red squares indicate the $\tilde{b}$ direction, and the blue triangles are measured along the $\tilde{c}$ direction.

Figure 5

Temperature dependence of (a) the ESR linewidth $\Delta H$ and (b) the $g$ shift $\Delta g\left(T\right)=g\left(T\right)-2.002319$ for (TMTTF)${}_2$AsF${}_6$ measured by $X$-band spectroscopy along the three directions $\tilde{a}$ (green dots), $\tilde{b}$ (open red squares), and $\tilde{c}$ (blue triangles).

Figure 6

(a) ESR linewidth $\Delta H$ and (b) $\Delta g$ of (TMTTF)${}_2$SCN measured in the $X$ band as a function of temperature along the three principal directions as indicated.

Figure 7

Temperature dependence of the $W$-band ESR linewidth and the $g$ shift of (TMTTF)${}_2$SbF${}_6$ along the three principal magnetic axes $\tilde{a}$, $\tilde{b}$, and $\tilde{c}$. The insets show the ESR linewidth and the $g$ shift measured in the $Q$-band spectrometer along the $\tilde{a}$ axis. The solid green dots correspond to the $\tilde{a}$ axis, the open red squares to the $\tilde{b}$ direction, and the open blue triangles to the $\tilde{c}$ axis.

Figure 8

Temperature dependence of the $W$-band ESR linewidth and the $g$ shift of (TMTTF)${}_2$AsF${}_6$ along the three axes $\tilde{a}$, $\tilde{b}$, and $\tilde{c}$. The $Q$-band ESR linewidth and the $g$ shift ($\tilde{a}$ axis) are displayed in the insets, respectively.

Figure 9

Contributions to the ESR linewidth due to CO for the salts (TMTTF)${}_{2}X$ ($X={\text{SbF}}_6$, AsF${}_6$, and SCN) along the three main axes. Note the different scales of $\Delta H_{\mathrm{CO}}$. The excess linewidth $\Delta H_{\mathrm{CO}}\left(T\right)$ is given by $\Delta H\left(T\right)-\Delta H_{\mathrm{background}}\left(T\right)$ and explained in the text. Note, the data are shown for temperatures well above the magnetic ordering and spin Peierls transitions that occur for $T<20$ K.

Figure 10

Angular dependence of the ESR linewidth within the $\tilde{a}\tilde{b}$ plane of (TMTTF)${}_2$SbF${}_6$ measured at different temperatures above and below the CO transition $T_{\mathrm{CO}}=156$ K using $X$-band (blue crosses), $Q$-band (red stars), and $W$-band (green dots) spectrometers. The lines represent fits of the linewidth using Eqs. (4) and (5) (see text for more details).

Figure 11

Angular dependence of the $X$-band (blue crosses), $Q$-band (red stars), and $W$-band (green dots) ESR linewidth when rotated along the $\tilde{a}\tilde{b}$ plane measured in (TMTTF)${}_2$AsF${}_6$ ($T_{\mathrm{CO}}=$ 102 K) at different temperatures, as indicated in the frames. The lines represent fits of $\Delta H$ using Eqs. (4) or (5).

Figure 12

Angular dependence of the ESR linewidth within the $\tilde{a}\tilde{b}$ plane of (TMTTF)${}_2$PF${}_6$ measured at different temperatures $T=295$ K, 30 K, and 19 K using an $X$-band spectrometer. The line represents a fit of the linewidth using Eqs. (4) and (5).

Figure 13

Frequency dependence of the enhanced ESR linewidth $\Delta H_{\mathrm{en}}$ measured in the $\tilde{a}\tilde{b}$ plane along the diagonal direction ($\theta ={45}^{\circ }$). The data for (TMTTF)${}_2$SbF${}_6$ are shown at $T=10$ K (blue dots), 60 K (green triangles), and 130 K (red squares) for (TMTTF)${}_2$AsF${}_6$ at 10 K (blue dots) and 50 K (green triangles). The lines are fits using Eq. (7).

Figure 14

Angular dependence of the $g$ value of (TMTTF)${}_2$PF${}_6$, (TMTTF)${}_2$AsF${}_6$, and (TMTTF)${}_2$SbF${}_6$ single crystals determined at $T=29$ K, 50 K, and 60 K, respectively; the static magnetic field $B_0$ is rotated within the $\tilde{a}\tilde{b}$ plane, that is, perpendicular to the molecular axis as sketched in Fig. 1. The dotted lines indicate the calculated variation of the $g$ value of the two magnetically inequivalent sites ($g_1$ and $g_2$) using Eq. (9).

Figure 15

Double-logarithmic plot of the linewidth versus $T-T_N$ of (TMTTF)${}_2$SCN (top) and (TMTTF)${}_2$SbF${}_6$ (bottom) in the antiferromagnetic fluctuation region; the $X$-band data are taken at different directions, as indicated. The lines represent the fit to a power law $\Delta H\left(T\right)\propto {(T-T_N)}^{-\mu }$ given in Eq. (10) with the exponent $\mu =1.5$ for (TMTTF)${}_2$SCN and $\mu =0.5$ for (TMTTF)${}_2$SbF${}_6$, where $T_N=7$ K in the case of (TMTTF)${}_2$SCN and 8 K for (TMTTF)${}_2$SbF${}_6$.

Figure 16

Angular dependence of the linewidth $\Delta H\left(\theta \right)$ of (TMTTF)${}_2$SCN measured in the $X$ band along the $\tilde{a}\tilde{b}$ plane. The green open circles are data in the antiferromagnetic fluctuation region at $T=10$ K. The red dotted line represents a fit of the dipole-dipole interaction with $\Delta H_{d-d}=\Delta H_{\tilde{b}}{[3{\cos }^2\theta -1]}^{4/3}$, the blue dashed line a fit of the spin-phonon interaction by Eq. (4). The solid green line is the sum of both contributions and perfectly describes the data.