# Electrodynamics in Organic Dimer Insulators Close to Mott Critical Point

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## Abstract

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## 1. Introduction

## 2. Antiferromagnet with Ferroelectric Character $\mathit{\kappa}$-(BEDT-TTF)${}_{\mathbf{2}}$Cu[N(CN)${}_{\mathbf{2}}$]Cl

## 3. Quantum Spin Liquids in Disordered $\mathit{\kappa}$-(BEDT-TTF)${}_{\mathbf{2}}$Cu${}_{\mathbf{2}}$(CN)${}_{\mathbf{3}}$ and $\mathit{\kappa}$-(BEDT-TTF)${}_{\mathbf{2}}$Ag${}_{\mathbf{2}}$(CN)${}_{\mathbf{3}}$

## 4. Van de Waals Interactions in $\mathit{\kappa}$-(BEDT-TTF)${}_{\mathbf{2}}\mathit{X}$; $\mathit{X}$ = Cu[N(CN)${}_{\mathbf{2}}$]Cl, Cu${}_{\mathbf{2}}$(CN)${}_{\mathbf{3}}$ and Ag${}_{\mathbf{2}}$(CN)${}_{\mathbf{3}}$

## 5. Materials and Methods

## 6. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The crystal structure of the three layered organic charge-transfer salts. The lines mark the unit cell. Carbon, sulfur and hydrogen atoms of the BEDT-TTF molecule are colored in dark gray, yellow and light gray, respectively. In the anion network, chlorine, cooper, silver, carbon and nitrogen are colored in green, red, pink, dark grey and violet, respectively. (

**Left**) Unit cell of $\kappa $-Cl. The space group is ${P}_{nma}$. In each of two organic layers, related by mirror symmetry, all four BEDT-TTF molecules are equivalent. (

**Middle**,

**Right**) Extended unit cell of $\kappa $-CuCN and $\kappa $-AgCN, respectively. The space group is commonly solved in $P{2}_{1}/c$ in which all four BEDT-TTF molecules are equivalent.

**Figure 2.**View of BEDT-TTF dimers arranged in anisotropic triangles in the three layered organic charge-transfer salts: (

**Left**) $\kappa $-Cl, projection of one of the layers is shown along the [110] direction; (

**Middle**) $\kappa $-CuCN, projected along the [100] direction; and (

**Right**) $\kappa $-AgCN, projected along the [10-1] direction. Neighboring dimers are rotated by ${90}^{\circ}$ with respect to each other. The interdimer transfer integrals are denoted by t and ${t}^{\prime}$, and the intradimer transfer integral by ${t}_{\mathrm{d}}$. The ratio ${t}^{\prime}/t$ measures the degree of frustration. ${t}^{\prime}/t\approx 0.5$ indicates medium frustration for $\kappa $-Cl, while ${t}^{\prime}/t\approx 0.85$ indicates high frustration for $\kappa $-CuCN and $\kappa $-AgCN.

**Figure 3.**(

**Left**) Distinct behaviors of the resistivity along the b axis below 100 K for three single crystals of $\kappa $-Cl: S1 (red), S2 (blue) and S3 (black). Data for S3 are after [18]. The inset displays the resistivity behavior in the whole temperature range demonstrating a weak activated behavior similar for all three samples. (

**Right**) Logarithmic resistivity derivative versus temperature.

**Figure 4.**Real part of the dielectric function ${\epsilon}^{\prime}$ as a function of temperature with the ac electric field applied $\mathbf{E}\parallel b$ for three representative single crystals of $\kappa $-Cl: S1 (

**Left**); S2 (

**Middle**); and S3, after [18] (

**Right panel**) The full lines in (

**Right**) are guides for the eye.

**Figure 5.**Magnetic field influence on sample S2 of $\kappa $-Cl. (

**Left**) Conductivity $\sigma $ measured at 500 Hz for $\mathbf{E}\parallel b$ versus temperature measured at different magnetic field strengths ($\mathbf{H}\parallel b$). At $\mathbf{H}$ = 0 T there is a rise in conductivity below 12 K, while the application of magnetic field shifts the onset of conductivity rise to lower temperatures, thus indicating a superconducting phase transition at ${T}_{\mathrm{SC}}\approx $ 12 K. (

**Right**) Real part of the dielectric function ${\epsilon}^{\prime}$ as a function of temperature with the ac electric field applied $\mathbf{E}\parallel b$, and measured at different magnetic field strengths ($\mathbf{H}\parallel b$). The effect of the magnetic field can be seen only below 12 K. Increasing magnetic field lowers the peak amplitude.

**Figure 6.**Susceptibility $\chi $ of sample S2 of $\kappa $-Cl as a function of temperature measured in a magnetic field of 500 Oe applied $\mathbf{H}\parallel ac$-plane.

**Figure 7.**(

**Left**) Temperature evolution of the intramolecular vibration ${\nu}_{27}$ in sample S2 of $\kappa $-Cl. (

**Right**) Temperature dependence of the resonance frequency and damping obtained by Fano function fit of the mode.

**Figure 8.**View of the anion layer of $\kappa $-Cl in the $ac$ plane projected along the b-axis. Copper is colored in red, and chlorine in green. Carbon and nitrogen are colored in blue and orange, respectively. The unit cell is marked as a rectangle.

**Figure 9.**Real part of the dielectric function ${\epsilon}^{\prime}$ as a function of temperature with the ac electric field applied $\mathbf{E}\parallel {a}^{*}$ for single crystals of: $\kappa $-CuCN (

**Left**); and $\kappa $-AgCN (

**Right**).

**Figure 10.**(

**Left**) Temperature evolution of the intramolecular vibration ${\nu}_{27}$ of $\kappa $-CuCN. (

**Right**) Temperature dependence of the resonance frequency and damping obtained by Fano function fit of the mode.

**Figure 11.**(

**Left**) Temperature evolution of the intramolecular vibration ${\nu}_{27}$ of $\kappa $-AgCN. The two Fano functions required to fit the spectra indicate two crystallographically distinct sites. (

**Right**) Temperature dependence of the resonance frequency and damping obtained by the fit using two Fano functions.

**Figure 12.**View of the anion network of $\kappa $-CuCN (

**Left**) and $\kappa $-AgCN (

**Right**) in the $bc$ plane projected along the ${a}^{*}$-axis. Cooper and silver are colored in red and violet, respectively. Carbon and nitrogen of ordered CN${}^{-}$ groups are colored in blue and orange, while they are colored in black for CN${}^{-}$ groups located at inversion centers. The unit cell is marked as a rectangle.

**Figure 13.**Perspective view of zigzag polymeric anion chains as obtained by structural refinements of X-ray data assuming either: $\kappa $-Cl (

**Left**); or $\kappa $-Br (

**Right**). View shows the ac plane. Copper, carbon and nitrogen are shown in red, blue and orange, respectively. Chlorine and bromine ligands on each copper atom are colored in dark and light green, respectively. All atoms are drawn with 50% probability ellipsoids of anisotropic thermal displacement parameters. Unit cell is marked as a rectangle.

**Figure 14.**Energy Dispersive X-ray Spectra (EDXS) recorded at 300 K. Only characteristic lines for C, N, S and Cu, and in particular for ClK$\alpha $ at 2.59 keV and for ClK$\beta $ at 2.83 keV were observed with intensities that correspond to the chemical formula of $\kappa $-Cl. On the other hand, no significant intensity for lines BrK$\alpha $1 and BrK$\alpha $2 at 11.92 keV, for BrK$\beta $ at 13.29 keV, and for BrL$\alpha $ at 1.49 keV were observed, which would be expected in the presence of Br.

**Table 1.**Unit cell parameters of $\kappa $-CuCN obtained from X-ray diffraction measurements at 100 K (left column), ab initio calculations based solely on PBE functional (central column) and on vdW-DF functional (right column). Relative deviations from experimental values are given in parentheses.

Unit Cell Parameters | Exp | Calc:PBE | Calc:vdW-DF |
---|---|---|---|

a | 15.9644 Å | 16.9706 Å (+6.3%) | 16.1809 Å (+1.4%) |

b | 8.5618 Å | 8.75745 Å (+2.3%) | 8.62586 Å (+0.8%) |

c | 13.2662 Å | 13.6497 Å (+2.9%) | 13.3523 Å (+0.7%) |

$\alpha $ | 90.000${}^{\circ}$ | 89.9968${}^{\circ}$ | 90.0037${}^{\circ}$ |

$\beta $ | 114.067${}^{\circ}$ | 116.409${}^{\circ}$ | 114.088${}^{\circ}$ |

$\gamma $ | 90.000${}^{\circ}$ | 90.0037${}^{\circ}$ | 89.9994${}^{\circ}$ |

V | 1655.65 Å${}^{3}$ | 1816.90 Å${}^{3}$ (+9.7%) | 1701.35 Å${}^{3}$ (+2.8%) |

**Table 2.**Unit cell parameters of $\kappa $-AgCN obtained from X-ray diffraction measurements at 150 K (left column), ab initio calculations based solely on PBE functional (central column) and on vdW-DF functional (right column). Relative deviations from experimental values are given in parentheses.

Unit Cell Parameters | Exp | Calc:PBE | Calc:vdW-DF |
---|---|---|---|

a | 14.969900 Å | 15.6693 Å (+4.7%) | 15.1161 Å (+0.98%) |

b | 8.656500 Å | 9.04653 Å (+4.5%) | 8.72513 Å (+0.79%) |

c | 13.216900 Å | 13.8238 Å (+4.6%) | 13.3487 Å (+1.0%) |

$\alpha $ | 90.000000${}^{\circ}$ | 90.0000${}^{\circ}$ | 90.0000${}^{\circ}$ |

$\beta $ | 91.389000${}^{\circ}$ | 94.6823${}^{\circ}$ | 91.3952${}^{\circ}$ |

$\gamma $ | 90.000000${}^{\circ}$ | 90.0000${}^{\circ}$ | 90.0000${}^{\circ}$ |

V | 1712.23 Å${}^{3}$ | 1953.03 Å${}^{3}$ (+14.1%) | 1760.03 Å${}^{3}$ (+2.8%) |

**Table 3.**Unit cell parameters of $\kappa $-Cl obtained from X-ray diffraction measurements at 100 K (left column), ab initio calculations based solely on PBE functional (central column) and on vdW-DF functional (right column). Relative deviations from experimental values are given in parentheses.

Unit Cell Parameters | Exp | Calc:PBE | Calc:vdW-DF |
---|---|---|---|

a | 12.885200 Å | 12.9769 Å (+0.7%) | 12.8334 Å (−0.4%) |

b | 29.575899 Å | 29.6637 Å (+0.3%) | 29.5323 Å (−0.2%) |

c | 8.416100 Å | 8.45028 Å (+0.4%) | 8.23316 Å (−2.2%) |

$\alpha $ | 90.000000${}^{\circ}$ | 90.0000${}^{\circ}$ | 90.0000${}^{\circ}$ |

$\beta $ | 90.000000${}^{\circ}$ | 90.0000${}^{\circ}$ | 90.0000${}^{\circ}$ |

$\gamma $ | 90.000000${}^{\circ}$ | 90.0000${}^{\circ}$ | 90.0000${}^{\circ}$ |

V | 3207.303 Å${}^{3}$ | 3252.875 Å${}^{3}$ (+1.4%) | 3120.366 Å${}^{3}(-2.7\%)$ |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Pinterić, M.; Rivas Góngora, D.; Rapljenović, Ž.; Ivek, T.; Čulo, M.; Korin-Hamzić, B.; Milat, O.; Gumhalter, B.; Lazić, P.; Sanz Alonso, M.;
et al. Electrodynamics in Organic Dimer Insulators Close to Mott Critical Point. *Crystals* **2018**, *8*, 190.
https://doi.org/10.3390/cryst8050190

**AMA Style**

Pinterić M, Rivas Góngora D, Rapljenović Ž, Ivek T, Čulo M, Korin-Hamzić B, Milat O, Gumhalter B, Lazić P, Sanz Alonso M,
et al. Electrodynamics in Organic Dimer Insulators Close to Mott Critical Point. *Crystals*. 2018; 8(5):190.
https://doi.org/10.3390/cryst8050190

**Chicago/Turabian Style**

Pinterić, Marko, David Rivas Góngora, Željko Rapljenović, Tomislav Ivek, Matija Čulo, Bojana Korin-Hamzić, Ognjen Milat, Branko Gumhalter, Predrag Lazić, Miriam Sanz Alonso,
and et al. 2018. "Electrodynamics in Organic Dimer Insulators Close to Mott Critical Point" *Crystals* 8, no. 5: 190.
https://doi.org/10.3390/cryst8050190