Relaxor ferroelectricity in the polar ${\mathrm{M}}_2\text{P-TCNQ}$ charge-transfer crystal at the neutral-ionic interface

We investigated the mixed-stack charge-transfer crystal, N,N'-dimethylphenazine-TCNQ (${\mathrm{M}}_2\mathrm{P}$-TCNQ), which is polar at room temperature and just at the neutral-to-ionic interface (ionicity $\rho \approx 0.5$). We detect the typical dielectric signature of a relaxor ferroelectric and an asymmetric positive-up-negative-down behavior. While relaxor ferroelectricity is usually ascribed to disorder in the crystal, we find no evidence for structural disorder in the investigated crystals. To elucidate the origin of ${\mathrm{M}}_2\mathrm{P}$-TCNQ's dielectric properties we perform parallel structural and spectroscopic measurements, associated with theoretical modeling and quantum-mechanical calculations. Our combined effort points to a highly polarizable electronic system that is strongly coupled to lattice vibrations. The found indications for polarization reversal imply flipping of the bent conformation of the ${\mathrm{M}}_2\mathrm{P}$ molecule with an associated energy barrier of a few tens of an eV, broadly consistent with an Arrhenius fit of the dielectric relaxation times. While the polarization is mostly of electronic origin, its possible reversal implies slow collective motions that are affected by solid-state intermolecular interactions.

Figure 1

Structure of ${\mathrm{M}}_2\mathrm{P}$-TCNQ viewed along the $b$ crystal axis.

Figure 2

(a) Temperature dependence of the real part of the dielectric constant ${\varepsilon }^{\prime }\left(T\right)$. The solid lines are guides to the eyes, while the dashed line indicates Curie-Weiss behavior of the right flanks of the peaks, representing the static dielectric constant. (b) Temperature dependence of the conductivity ${\sigma }^{\prime }\left(T\right)$.

Figure 3

Frequency-dependent plot of the dielectric constant ${\varepsilon }^{\prime }\left(\nu \right)$ of ${\mathrm{M}}_2\mathrm{P}$-TCNQ at various temperatures, revealing a steplike decrease which shifts to lower frequencies with decreasing temperature. Lines are fits to the data with the phenomenological Cole-Cole equation.

Figure 4

Temperature evolution of ${\mathrm{M}}_2\mathrm{P}$-TCNQ's relaxation time in an Arrhenius plot. Fitting with the linear Arrhenius equation ($\tau ={\tau }_0\exp \left[E_{\mathrm{a}}/\left(k_{\mathrm{B}}T\right)\right]$) yields an activation energy of $E_a\approx 0.52$ eV and a pre-exponential factor ${\tau }_0=1.9\times {10}^{-12}$ s.

Figure 5

Examples of polarization curves of ${\mathrm{M}}_2\mathrm{P}$-TCNQ at (a) 5 K and 100 Hz and (b) at 155 K and 11 Hz.

Figure 6

Positive-up-negative-down (PUND) measurement of ${\mathrm{M}}_2\mathrm{P}$-TCNQ with (a) applied electric fields $E$ of 50 kV/cm resulting in (b) current density pulses $j=I/A$ ($A=0.0625 {\mathrm{mm}}^2$), of which 1 and 5 are larger than 2. The negative pulses, 3 and 4, are virtually identical and smaller than the positive ones. The dashed lines show the differential current density (i.e., 2 subtracted from 1 and 5, and 3 subtracted from 4). Measured at a frequency of 0.166 Hz, a temperature of 200 K, and with a very short interval between pulses of 1 ms.

Figure 7

(a) Low-frequency Raman spectra of ${\mathrm{M}}_2\mathrm{P}$-TCNQ, $(c,c$) polarization, as a function of temperature, exciting line: 752 nm and (b) Temperature evolution of the frequencies of selected bands.

Figure 8

${\mathrm{M}}_2\mathrm{P}$-TCNQ polarized Raman spectra recorded with different exciting lines, $T=300$ K. Red line: ($c,c$) polarization; Black line: ($\perp c,\perp c$) polarization.

Figure 9

Experimental (752 nm excitation) and calculated low-frequency Raman spectrum of ${\mathrm{M}}_2\mathrm{P}$-TCNQ, ($cc$) polarization. The eigenvectors of the two most intense Raman bands, corresponding to the prominent experimentally observed bands, are shown at the bottom.

Figure 10

Energy profile to invert the v-like conformation of ${\mathrm{M}}_2\mathrm{P}$ (a) in the gas phase and (b),(c) in the crystal. Results from relaxed scans with a constraint on the dihedral angle connecting the two N atoms of ${\mathrm{M}}_2\mathrm{P}$. The upper sketches (${\mathrm{M}}_2\mathrm{P}$ in red, TCNQ in blue) illustrate the flipping procedure. (b) Energy scan to simultaneously flip all ${\mathrm{M}}_2\mathrm{P}$ molecules in the crystal obtained with periodic DFT calculations. (c) Energy scan to flip one ${\mathrm{M}}_2\mathrm{P}$ molecules in the crystal from QM/MM calculations. The central ${\mathrm{M}}_2\mathrm{P}$ molecule and the two neighboring TCNQ along the stack were relaxed at the DFT level, in the field of the other molecules in the crystal (gray molecules in the sketch) that were kept frozen and described with point charges and Lennard-Jones potential. Lines are guides to the eyes.