# Quantum Phenomena Emerging Near a Ferroelectric Critical Point in a Donor–Acceptor Organic Charge-Transfer Complex

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## Abstract

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## 1. Introduction

## 2. Crystal Structures

## 3. Quantum Effects on Thermo-Equilibrium Properties Near the Ferroelectric QCP

#### 3.1. Phase Diagram

#### 3.2. Quantum Criticality Seen in Order-Parameter-Related Quantities

## 4. Quantum Effects on the Kinetics of Ferroelectric Domain Walls Near the Ferroelectric QCP

#### 4.1. Athermal Creep Motion of Domain Walls Near the QCP

#### 4.2. Effective Mass of the Ferroelectric Domain Wall Near the QCP

## 5. Conclusions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Chemical forms of donor and acceptor molecules that appear in this article. (

**b,c**) Schematic diagrams of the structure of the donor–acceptor mixed stack: with a uniform spacing (

**b**) and in a dimerized state (

**c**). Small arrows in (

**c**) indicate the shifts in the molecules that occur upon dimerization.

**Figure 2.**(

**a**) Pressure–temperature phase diagram of TTF-2,5-QBr${}_{2}$I${}_{2}$. (

**b**) Temperature dependence of the permittivity under various pressures. The applied pressure value, corrected considering its thermal change in the medium for each measurement, is represented by the value at the transition point or at the lowest temperature when the phase transition is absent. (

**c**) Pressure variations in the polarization hysteresis loop measured at the lowest temperature: $T/{T}_{\mathrm{c}}$ = 0.1 for 0.28, 0.31 and 0.34 GPa, and $T/{T}_{\mathrm{c}}$ = 0.3 for 0.26 GPa. (

**d**) ${T}_{\mathrm{c}}^{2}$ versus pressure plot, highlighting the quantum critical behavior of the ferroelectric-transition temperature. The blue line represents ${T}_{\mathrm{c}}$ ∼ ${(p-{p}_{\mathrm{c}})}^{0.5}$ with ${p}_{\mathrm{c}}$ ≈ 0.25–0.26 GPa. (

**e**) Inverse permittivity versus the square of the temperature. The broken lines represent $1/\u03f5$ ∝ ${T}^{2}$. (

**f**) ${P}_{\mathrm{s}}^{2}$ versus pressure plot, highlighting the quantum critical behavior of the spontaneous polarization. The red line represents ${P}_{\mathrm{s}}$ ∼ ${(p-{p}_{\mathrm{c}})}^{0.5}$ with ${p}_{\mathrm{c}}$ ≈ 0.25–0.26 GPa.

**Figure 3.**(

**a**) Structure in the case of a head-to-head domain wall. (

**b**) Shift of the domain wall under an applied electric field. TTF and 2,5-QBr${}_{2}$I${}_{2}$ are denoted by D (donor) and A (acceptor), respectively, and the underlines represent the dimerization of the two molecules. For simplicity, the domain wall is depicted as an atomically thin boundary, but in reality, it likely has a finite width, particularly when the system is located near the ferroelectric quantum critical point (QCP).

**Figure 4.**(

**a**,

**b**) Permittivity–temperature profiles measured under a.c. electric fields of different magnitudes: at 0.34 GPa (${T}_{\mathrm{c}}$ ≈ 64 K) (

**a**) and at 0.26 GPa (${T}_{\mathrm{c}}$ ≈ 13 K) (

**b**), the latter of which is close to the ferroelectric QCP. (

**c**) Temperature dependences of the coercive electric field at different pressures. In (

**a**–

**c**), the temperatures are represented in the form of reduced temperatures, $T/{T}_{\mathrm{c}}$.

**Figure 5.**(

**a**) Measurement protocol for probing the polarization decay. (

**b**) Typical polarization hysteresis loops with various delay times, measured at 0.34 GPa and $T/{T}_{\mathrm{c}}$ = 0.5. (

**c**) Delay-time dependences of the remnant polarization at select temperatures and 0.34 GPa (${T}_{\mathrm{c}}$ ≈ 64 K). (

**d**) Normalized relaxation behavior of the polarization decay at 0.34 GPa. (

**e**) Delay-time dependence of the remnant polarization at 0.26 GPa (${T}_{\mathrm{c}}$ ≈ 13 K), which is near the ferroelectric QCP. (

**f**) Normalized relaxation behavior of the polarization decay at 0.26 GPa. The lines in (

**c**–

**f**) represent fits to the standard relaxation equation; see Equation (1).

**Figure 6.**(

**a**) Classical-quantum crossover of the ferroelectric domain-wall dynamics. The lines represent fits to Matthiessen’s rule: 1/$\tau $ = 1/$\tau $${}_{\mathrm{classical}}$ + 1/$\tau $${}_{\mathrm{quantum}}$, where $\tau $${}_{\mathrm{classical}}$ follows the Arrhenius law and $\tau $${}_{\mathrm{quantum}}$ is constant at a given pressure. The inset shows a schematic diagram comparing the classical thermally activated creep (solid arrows) with the quantum tunneling creep (broken arrows) of a domain wall (modeled as a particle). The multi-valley schematic represents a multidimensional potential landscape. (

**b**) Pressure dependence of $\Delta $, derived from (

**a**).

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**MDPI and ACS Style**

Kagawa, F.; Horiuchi, S.; Tokura, Y. Quantum Phenomena Emerging Near a Ferroelectric Critical Point in a Donor–Acceptor Organic Charge-Transfer Complex. *Crystals* **2017**, *7*, 106.
https://doi.org/10.3390/cryst7040106

**AMA Style**

Kagawa F, Horiuchi S, Tokura Y. Quantum Phenomena Emerging Near a Ferroelectric Critical Point in a Donor–Acceptor Organic Charge-Transfer Complex. *Crystals*. 2017; 7(4):106.
https://doi.org/10.3390/cryst7040106

**Chicago/Turabian Style**

Kagawa, Fumitaka, Sachio Horiuchi, and Yoshinori Tokura. 2017. "Quantum Phenomena Emerging Near a Ferroelectric Critical Point in a Donor–Acceptor Organic Charge-Transfer Complex" *Crystals* 7, no. 4: 106.
https://doi.org/10.3390/cryst7040106