Ultrafast opto-protonics in a hydrogen-bonded π-molecular ferroelectric crystal

Ferroelectrics have various beneficial functions in practical applications, such as storing electric energy and information and interconverting thermal or mechanical energy into electrical energy. Therefore, the development of highly performing ferroelectrics is one of the most important themes in materials science. Organic ferroelectrics have been expected to be the candidates for realizing environmentally benign (lead-free), lightweight, flexible, and biocompatible ferroelectric devices. In particular, ferroelectricity of the hydrogen-bonded π-molecular compounds¹ has been attracting attention because of their large ferroelectric polarization and excellent thermal stability. The ferroelectricity is triggered by the ordering of protons that connect the constituent molecules by hydrogen bonding. Meanwhile, most of its large polarization originates from a quantum mechanical mechanism due to the simultaneous deformation of highly polarizable π-orbitals in real space. Therefore, knowing the proton dynamics and its modulation with external stimuli for controlling the ferroelectricity is useful to clarify the mechanism of ferroelectricity in this system and to develop and improve its ferroelectric functions by the quantum π-electrons.

Furthermore, recent advances in laser technology have made it possible to generate intense and ultrashort optical pulses in the near-to-mid-infrared region and terahertz band, making it possible to control the electronic state of materials on an ultrafast time scale.² In fact, studies on the optical control of ferroelectricity using state-of-the-art femtosecond laser technology have been reported for various organic^3–5 and inorganic ferroelectrics.^6–9 Among the numerous ferroelectric materials, in this study, we focus on hydrogen-bonded π-molecular ferroelectrics, which can exhibit excellent polarization performance^1,10 and nonlinear optical properties¹¹ due to the strong correlation between protons and π-electron systems. We investigate the time evolution of the ferroelectricity of the system by exciting the proton-coupled with the π-electrons using ultrafast laser pulses and by probing the degree of deviation from inversion symmetry through nonlinear optical techniques. This is an attempt to control ferroelectricity by directly modulating protons with a laser pulse and can be called a new type of opto-protonics.

The hydrogen-bonded supramolecular ferroelectrics focused on in this study is a co-crystal formed by alternating sequences of two types of π-conjugated molecules, namely, the proton donors and acceptors. Notably, the intermolecular hydrogen bonds have two stability points for respective protons. The asymmetric long-range ordering of protons causes crystal polarity. The externally applied electric field can collectively hop the protons to the other equilibrium position, enabling polarization reversal in low electric fields. The co-crystal Hdppz–Hca described in this paper consists of a protonated 2,3-di (2-pyridinyl) pyrazine (Hdppz) molecule and a deprotonated chloranilic acid (Hca) molecule. It has a ferroelectric transition temperature far above room temperature (Curie point T_c = 402 K). Specifically, the thermal stability of ferroelectricity is excellent among organic ferroelectrics.¹² To begin with, let us discuss the dielectric properties of this Hdppz–Hca. Figure 1(a) shows the chemical formula of Hdppz and Hca molecules and the crystal structure of the co-crystal at room temperature. As shown in the figure, Hdppz and Hca molecules are alternately linked by intermolecular hydrogen bonds to form one-dimensional chains along the crystallographic c-direction; at temperatures below T_c, the protons (H⁺) indicated by black circles in the figure are ordered.

What is the origin of ferroelectricity in this system? The key points are shown in Fig. 1(b). There are hydrogen bonds on both sides of each molecule. The protons are asymmetrically ordered at room temperature, with one side carrying O–H⋯N-type hydrogen bonds and the other N–H⁺⋯O⁻ type. The protons are off-centered by about 0.3 Å considering the O⋯N distances (2.74 Å for O–H⋯N bond and 2.63 Å for N–H⁺⋯O⁻ bond).¹² This leads to the appearance of polarity along the one-dimensional molecular chain due to the bond modulation of the π-electron system in the Hdppz and Hca molecules. In addition, the equilibrium position of the proton ordered at each hydrogen bond switches to the other equilibrium position upon application of an external field, enabling the polarization to be inverted. Above T_c, on the other hand, the protons become disordered [Fig. 1(c)], and inversion symmetry is restored.

To see the ferroelectric nature of Hdppz–Hca, for reference, Figs. 2(a) and 2(b) show the temperature dependence of the relative permittivity (ε_r) and the polarization-electric field (P-E) curve at room temperature, respectively.^12,13 The ε_r is relatively large (20–30) at room temperature and increases monotonically as temperature increases because the thermal fluctuations of the polarization and polarization domains become more pronounced as the transition temperature (T_c = 402 K) is approached. The P-E curve shows a hysteresis loop characteristic of the ferroelectrics. The spontaneous polarization of about 5.3 µC/cm² is larger than that of conventional small molecular systems and comparable to that of polymer ferroelectrics.¹ Note that the majority of this large spontaneous polarization has a quantum mechanical origin:^10,13,14 the theoretical estimate based on the Berry phase model suggests that at least more than half¹³ of the experimentally observed polarization originates from the quantum mechanical charge-density modulation of the π-electron system. The other unique feature of “ferroelectricity by proton transfer” is a very low operating electric field of 2–3 kV/cm, less than one-hundredth that of polymer ferroelectrics.

In addition to the dielectric properties, second harmonic generation (SHG) is one of the important ferroelectric functionalities categorized in second-order nonlinear optical effects, caused by the inversion symmetry breaking of the material. This is a phenomenon in which frequency-doubled light (or light with a half-wavelength) is emitted. Since the second-order nonlinearity completely disappears in materials with inversion symmetry, SHG measurements can probe the presence or absence of inversion symmetry breaking in the system more sensitively than diffraction experiments.

How would the SHG of Hdppz–Hca be observed? Figure 3 shows the incident light intensity dependence of SHG light (wavelength: 400 nm) emitted when irradiated with a laser pulse of 800 nm.¹⁵ Unlike ordinary reflected light, a signal proportional to almost the square of the incident light intensity, which is a characteristic of SHG light, is observed.

The inset in Fig. 3 shows the relationship between the polarization angle (θ) of the incident pulse and the SHG signal generated in the direction of the polarization axis (c-axis) of the Hdppz–Hca crystal.¹⁵ The numbers on the circumference represent the angle between the polarization of the incident light and the crystal axis. The laser field E is parallel to the c-axis when θ = 90° and parallel to the a* axis when θ = 0°.¹⁶ 

The observed SHG intensity shows an angular dependence reflecting the crystal structural symmetry, forming four leaf-like patterns in the directions parallel and perpendicular to the c-direction. We can know the second-order nonlinear susceptibility tensor (d_ij) contracted when the point group of the crystal is given; considering that the crystal symmetry of Hdppz–Hca is a monoclinic system with space group Cc and point group m,¹² the azimuth angle dependence of the observed SHG intensity (I_SH) can be described as follows:

The results of the fitting analysis based on Eq. (1) show that a good fit can be achieved, as shown by the solid line in the inset of Fig. 3. The obtained values of the ratio of the components are d₃₁/d₃₃ ≈ −0.99 and d₃₅ ≈ 0.

This paper describes how the SHG signal observed in Hdppz–Hca changes in real-time when its proton oscillations are excited by mid-infrared light pulses. First, we describe the femtosecond laser source used for this purpose. Figure 4(a) shows the real-time electric field waveform of the mid-infrared light pulse used to excite the crystal, measured by electro-optic sampling. In the “envelope” of the photoelectric field of ≈70 fs, fine electric field oscillations due to a carrier wave with a period of ≈10 fs are visible, indicating that the pulse is mid-infrared light oscillating at ≈80 THz.

Note that the mid-infrared light pulse used in this experiment has a carrier-envelope phase (CEP) that is always fixed with respect to the envelope of the optical electric field. In commercially available femtosecond laser light sources, although the shape of the envelope of the optical field covering the entire pulse is fixed, this CEP differs from pulse to pulse emitted from the device. It is impossible to know what is happening within the time width of the envelope as long as the integrated measurement is performed using such an optical pulse. To solve this problem, we developed mid-infrared oscillating electric field pulses with fixed CEP.¹⁷ 

The near-infrared pulsed laser light (≈790 nm, pulse width ≈70 fs, repetition rate ≈450 Hz) emitted from a Ti:sapphire chirped-pulse amplifier was divided into three pulses by beam splitters to form a two-stage optical parametric amplifier (OPA),¹⁷ and the final idler light of ∼3500 nm was extracted. Since the Idler light obtained in the last OPA process is obtained in the difference frequency generation process, the difference in the initial phase is canceled out, and the pulse always has a fixed CEP. The output pulse was further spectrally broadened and compressed using Si and CaF₂ plates to reduce the pulse width to ≈25 fs, which was used in this experiment.

Furthermore, to detect the electric field oscillations in this CEP-stable pulse shown in Fig. 4(a), we generated ultrashort pulses in the visible region (photon energy about 2.1 eV, pulse width about 5.0 fs) by filamentation using a Kr-filled gas cell under 6 bar and dispersion compensation with chirped mirrors.¹⁸ The electric field waveform of the mid-infrared pulse was measured by electro-optical sampling using an ultrashort pulse of ≈5.0 fs.

What does this CEP-stable electromagnetic wave excite in the crystal? The red line in Fig. 5 is the power spectrum obtained by Fourier transforming the electric field oscillation shown in Fig. 4(a). The spectrum forms a broad peak centered at about 2800 cm⁻¹. The black line in Fig. 5 shows the c-axis polarized optical conductivity spectrum [σ(ω)]. The structure in σ(ω) at ≈2800 cm⁻¹ is assigned as absorption from proton vibrations associated with the hydrogen bond in the crystal, and such a broad structure due to a proton in the mid-infrared region is observed in similar proton-transfer co-crystals.¹⁴ The electric field oscillation of the CEP stable pulse used in this study completely covers the proton vibration and can directly excite the proton motion responsible for the ferroelectricity.

We have previously investigated SHG changes by exciting vibrations of Hca molecules in Hdppz–Hca crystal using a broad 100 fs pulse, also CEP-locked, covering 1200 to 1600 cm⁻¹.¹⁹ In the experiment, however, the excitation pulse used there simultaneously excited several different vibration modes of the Hca molecule,^20–22 though the protons were indirectly excited, and the role of the proton vibration in the ferroelectricity has not been unraveled yet. The purpose of this paper is to reveal how the ferroelectricity of the system changes on the time scale of the electric field oscillations when the proton vibrations in the crystal are directly excited by CEP-stable pulses. This method of measuring ultrafast response within one oscillation of an optical electric field is called “subcycle spectroscopy” and has been commonly used in spectroscopy in the terahertz to near-infrared region. Using the optical pulse, we demonstrate ultrafast ferroelectric control at room temperature that can be viewed as opto-protonics.

The single crystals of Hdppz–Hca used in the experiment are shiny black ones crystallized by the diffusion method¹² in acetone solution and are elongated along the crystallographic c direction. The raw materials, dppz and H₂ca, are commercially available and were purified in advance by repeating the recrystallization and vacuum sublimation. The orientation of the crystal axes of the crystal samples was identified by x-ray diffraction and polarized reflection spectroscopy. The spatial dependence of the SHG signal and reflectance was hardly observed, suggesting that these crystals have a large domain size with very few ferroelectric domain walls.

The relative changes in SHG intensity and reflectance due to the excitation of mid-infrared pulses were measured by the pump-probe method. A schematic of the measurement is shown in Fig. 6. The laser beam emitted from the Ti:sapphire laser source is divided into two pulses: one is the pump beam used to excite the sample, and the other is the probe beam used to examine the SHG emitted from the sample.

The pump light is converted into a CEP-stable mid-infrared pulse by using a two-stage OPA as described in Sec. I C. The probe light is also converted into a 6.5 fs pulse by third-order nonlinear optical effects, as described above. The SHG light generated by the irradiation of the probe pulse is detected by a photomultiplier tube after the fundamental pulse is removed by a high-pass filter and a grating-type monochromator.

The timing of the irradiation of the pump and probe light to the sample was controlled by a delay stage, and a time profile of SHG and reflectance change was obtained after the photoirradiation. All measurements were performed at room temperature in the air.

Figure 4(b) shows the time dependence of the relative rate of change in SHG intensity (ΔI_SH/I_SH) of Hdppz–Hca obtained by applying the mid-infrared pulse in Fig. 4(a). As mentioned earlier, the incident electric field pulses used for excitation have a nearly symmetric shape in the positive and negative directions, but the observed ΔI_SH/I_SH profile is only observed in the positive direction (i.e., ΔI_SH > 0), indicating that a significant enhancement of SHG was observed within the time of the applied pulse and that the ferroelectricity of the system, i.e., the second-order nonlinear susceptibility χ⁽²⁾ of the system, is instantaneously enhanced within the pulse due to the pulsed excitation. Such a positively biased SHG change in this system has also been observed by exciting C–O⁻stretching vibrations of the Hca molecule,¹⁹ but what is noteworthy is the magnitude of the rate of change: by exciting C–O⁻stretching vibrations, a maximum SHG enhancement of ≈18% was observed with an applied electric field of ≈25 MV/cm, whereas by exciting proton vibrations, an increase of up to ≈100% was observed at the same level of field application. This clearly shows that direct excitation of proton vibration can enhance the ferroelectricity of the system more significantly and efficiently than exciting molecular vibrations.

In addition to Hdppz–Hca, several experiments have been reported on infrared photoexcitation with fixed CEP to a ferroelectric crystal. Changes in SHG intensity upon optical pulse excitation with the frequency of the terahertz region (≈1 THz) have been reported for Hdppz–Hca,¹⁹ and the charge–transfer complex, tetrathiafulvalene-p-chloranil (TTF-CA),⁴ but both show changes that perfectly follow the time profile of the excitation pulse. This is in contrast to the present experimental results, which suggest that in fast oscillating electric fields, the change in the SHG intensity of the system does not entirely follow the oscillation speed of the excitation pulse and changes nonlinearly. In addition, in a typical oxide ferroelectric LiNbO₃ crystal,⁹ where the SHG intensity change due to CEP stable ≈17.5 THz mid-infrared excitation has been investigated, an average decrease in the SHG intensity within the incident pulse is observed.⁹ This is in contrast to the rate of change of SHG intensity in Hdppz–Hca, which shows an average positive change (i.e., SHG enhancement) within the pulse.

Next, the time dependence of the reflectance change of the probe light upon the application of the excitation pulse is shown in Fig. 4(c); unlike the SHG case, the change in reflectance after excitation is tiny, less than 0.05%, compared with the ≈100% SHG change. This suggests that the excitation of proton vibrations modulates the value of the second-order nonlinear susceptibility χ⁽²⁾ rather than the linear refractive index and that the observed SHG enhancement is not simply caused by a change in a linear refractive index or absorption coefficient by the pulse excitation.

Furthermore, the SHG and reflectance changes become slightly negative as time elapses beyond the pulse duration. This negative change occurs due to the real excitation of the electron system caused by multiphoton absorption induced by the strong electric field of the mid-infrared pulse and the associated relaxation process,²² which was also observed in excitation experiments of C–O⁻ stretching vibrations.¹⁹ 

The inversion symmetry breaking in this system decreases as the temperature increases above room temperature. Therefore, one might consider the temperature rise effect can cause the observed decrease in SHG. However, it is noteworthy that this decrease in SHG appears to occur at least within 50 fs after the sub-30 fs pulse irradiation. This can be considered to be the time scale in which molecular vibrations, especially around the terahertz region in the Hdppz–Hca, have not yet finished, indicating that the system has not yet reached the thermal equilibrium state. The phenomenon observed here is an effect at a time earlier than the temperature can exactly be defined, and a simple temperature increase effect cannot explain the decrease in SHG.

Figure 7 shows the ΔI_SH/I_SH time profiles as the maximum electric field intensity of the applied pulse is varied from ≈28 MV/cm (a), ≈20 MV/cm (b), ≈13 MV/cm (c), and ≈6.5 MV/cm (d), as indicated by black circles. As mentioned above, in case (a), the SHG change is biased toward the positive direction, but as the applied electric field intensity is decreased, the magnitude of the change decreases, and the time profile changes to a symmetric shape in the positive and negative directions similar to the applied electric field waveform.

Here, let us consider the microscopic origin of the ultrafast SHG changes induced by mid-infrared excitation. In general, the relative SHG changes arise from the modulation of χ⁽²⁾. As demonstrated in Fig. 5, the mid-IR pulses directly excite proton vibrations in this system. It is reasonable to consider that the mid-IR excitation strongly affects proton molecular vibrations, resulting in a change in SHG intensity.

To investigate the effect of the vibrational electric field on the molecular vibration more quantitatively, the following nonlinear equation of motion for proton vibration was analyzed according to the literature:¹⁹ 

X(t) is the change in amplitude of the oscillation and can be regarded as an indicator of proton displacement, and E_MIR(t) is the mid-infrared electric field shown in Fig. 4(a). Moreover, μ, Ω, and q are the mass, frequency, and effective charge of the proton, respectively. a is the anharmonic term, and γ is the damping factor.

If the amplitude of the proton vibration is not so large, χ⁽²⁾ and ΔI_SH/I_SH can be expanded in terms of X(t). Taking the lowest order term, ΔI_SH/I_SH is proportional to X(t) [i.e., ΔI_SH/I_SH = kX(t)]. We then attempted to fit the ΔI_SH/I_SH time profile by solving Eq. (2) numerically, using a, γ, and k as fitting parameters. The obtained results are shown in Fig. 7(a) by red lines, to which ΔI_SH/I_SH profiles were well fitted. The parameters obtained from the fitting were a ≈ −33.0 Å⁻¹ fs⁻², γ ≈ 0.47 eV, and k ≈ 78 Å⁻¹. These results indicate that the protons are shifted from the equilibrium point by an order of ≈0.01 Å at most with an electric field of ≈28 MV/cm. Note that this additional shift corresponds to ≈1/30 of off-centering proton displacement (≈0.3 Å) in the ferroelectric state. This suggests that a simple polarization change cannot explain the observed large SHG intensification with this additional proton displacement alone, but a successive variation of π-electrons induced by the dynamical repositioning of the protons should be considered.

Next, using the parameters obtained by fitting the ΔI_SH/I_SH profiles obtained under the ≈28 MV/cm applied electric field, we calculated X(t) obtained with other mid-infrared oscillating electric fields, and the results are shown in Figs. 7(b)–7(d) as red lines. Comparing the calculated results with the experimental ones (black circles), three points were qualitatively reproduced by the calculated result without varying the parameters obtained in Fig. 7(a): (i) the same periodic structure in ΔI_SH/I_SH profile as the mid-infrared pulse, (ii) the excitation intensity dependence of the ΔI_SH/I_SH, and (iii) the positively biased change in SHG with an application of the strong symmetric field.

It is worth noting that a difference exists between the calculated and experimental profiles, especially in Figs. 7(b)–7(d); while the ΔI_SH/I_SH profile is almost scaled with the envelope of X(t), X(t) bears the fast cycle identical to E_MIR(t). This suggests the semi-classical model of Eq. (2) is still insufficient to describe the experiment quantitatively. The reason for the discrepancy is not clear at this stage, but one possible reason is that the origin of the SHG change is the simultaneous deformation of the π electron system rather than the proton dynamics that triggers it. To understand this point precisely, it is necessary to calculate the quantum π-electron state that also takes into account mid-infrared electromagnetic wave oscillations (i.e., π-electron Floquet state²³), and this deserves to be further studied from a theoretical viewpoint.

Figures 8(a) and 8(b) summarize the dynamics of protons due to CEP stable electric field excitation obtained by the above discussion. As shown in Fig. 8(a), before photoexcitation or under weak excitation, the proton (empty circles) oscillates almost harmonically around the equilibrium point (X₀) in the potential curve U. By contrast, when the proton is strongly excited, the proton begins to clearly exhibit anharmonic oscillations, and the stable position of the proton seems to move from X₀ to a new metastable position (X′) during the pulse width (about 25 fs), as if the potential curve effectively changes its center of vibration as shown by the dashed line. This dynamical proton repositioning is thought to cause a change in the polarity of the π-electrons,²⁴ resulting in an increase in the ferroelectricity as well as the SHG intensity of the system.

It is noteworthy that such dynamical repositioning occurs only within the incident electric field pulse, which enables us to generate ultrafast switching of the ferroelectricity of the system on the time scale of the applied pulse width. Ishikawa et al.²⁵ have recently demonstrated that electron hopping in a crystal can be reduced by using an ultrafast pulse, signaling dynamical localization of electrons, and the resultant reduction of conductivity as the Floquet state.²³ The idea can be extended to the proton (or π-electron caused by the proton oscillation) and the electron system in a solid crystal. The nonequilibrium Floquet state driven by an ultrafast pulse observed in this study brings about switching in the proton state on timescales of less than 100 fs, resulting in an ultrafast response of more than 10 THz in frequency, which will shed important light on the future application of novel ferroelectric devices.

We have focused on the molecular ferroelectric Hdppz–Hca co-crystal, whose ferroelectricity originates from the ordering of protons on hydrogen bonds and the resulting quantum mechanical modulation of π-electron system. We excited protons in the crystal with CEP-stable mid-infrared pulses with a maximum field strength of ≈25 MV/cm, which resonates with proton oscillations, and investigated the effect on ferroelectricity from the viewpoint of SHG measurements. Two points were revealed: (i) the SHG intensity increases by up to about 100% at room temperature when irradiated with mid-infrared pulses; (ii) the large SHG change exhibits extremely fast changes only during the applied sub-30 fs pulse. Analysis of these results based on a semi-classical nonlinear motion of equation model reveals that the amplitude of proton motion during excitation is consistent with the SHG change profile, including even the excitation intensity dependence. This suggests that the ferroelectricity of the system is greatly enhanced as the protons acquire a new stability point within the ultrafast pulses of the oscillating mid-infrared electric field.

Those obtained results that could be detected only by CEP-locked intense ultrashort pulses indicate that the electric field oscillations of laser pulses can improve the ferroelectric function significantly and quickly at room temperature. This study provides clues to the improvement and ultrafast response of ferroelectrics by direct optical control of protons, paving the way for new opto-protonics.

The authors thank T. Umanodan, Y. Kanemitsu, H. Hirori, K. Tanaka, K. Takeuchi, N. Ishii, and K. Kaneshima for their discussions at the early stage of this work. This research was supported by JSPS KAKENHI (Grant Nos. 16H04000, 18H05208, and 22H01153).

The authors have no conflicts to disclose.

Yoichi Okimoto: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Peiyu Xia: Investigation (equal). Jiro Itatani: Conceptualization (equal); Funding acquisition (equal); Resources (equal); Writing – original draft (equal). Haruka Matsushima: Formal analysis (equal); Investigation (equal). Tadahiko Ishikawa: Investigation (equal). Shin-ya Koshihara: Investigation (equal). Sachio Horiuchi: Conceptualization (equal); Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.