Introduction

Photoinduced phase transitions of correlated electron systems, in which electronic and crystal structures are changed by irradiating solids with a femtosecond laser pulse, have been actively investigated1,2,3. The dynamics of nonequilibrium excited states can provide insights into the interplay in electron, spin, and lattice systems, which cannot be obtained via steady-state measurements. In most studies, visible pulses beyond the optical gap have been used for excitations4,5,6,7,8,9,10,11,12,13,14,15,16,17. In these investigations, photoexcitation-induced interband transitions or intermolecular electron transfers caused macroscopic electronic-state changes via strong electron-electron, electron-lattice, and spin-lattice interactions. However, their dynamics are complicated because high-energy electronic excited states induce large temperature increases in systems during their relaxation processes.

Recently, electronic-state controls using a mid-infrared (MIR) pulse have attracted attention as an approach for addressing the drawbacks of visible-pulse excitations18,19,20,21,22,23,24,25,26,27,28,29. Using an MIR pulse, it is possible to generate a strong electric field of the order of 10 MV cm−1, which can induce nonperturbative responses such as quantum tunneling processes30,31. If molecular or lattice vibrations that interact strongly with an electronic system are resonantly excited using an MIR pulse, periodic charge or spin modulation can be induced19,20,21,22,24,26,27,28. This can facilitate efficient electronic- and spin-state control, which is called Floquet engineering32,33,34,35,36,37,38,39. Although studies on vibrational excitations have been reported from this perspective, for example, the observation of high order phonon harmonics in LiNbO3 (ref. 24), modulation of on-site Coulomb repulsion19,20, observation of light-induced superconductivity21, and observation of phonon-dressed Floquet states in molecular solids28, there are limited examples of electronic-phase control in solids.

Here, we focus on the control of electron and spin states in molecular solids using vibrational excitations. Figure 1a shows a schematic of a dimer of molecules with singly occupied molecular orbitals (SOMO) and totally symmetric intramolecular vibration (ag mode) (blue open arrows). The ag mode is not IR-active in isolated molecules. However, given that it modulates the SOMO energy up and down, an out-of-phase ag-mode vibration in a dimer induces intermolecular electron transfer that is synchronized with the vibration and becomes IR-active for an electric field E along the direction of molecular stacking40. Such an interaction between electrons and the ag mode vibrations is called electron-intramolecular-vibration (EMV) coupling. Thus, the excitation of the IR-active ag mode can give rise to coherent electron- and spin-density oscillations in each dimer, which corresponds to a generation of a charge-spin modulated Floquet state.

Fig. 1: Charge and spin modulation by an intramolecular vibrational excitation with a mid-infrared (MIR) pulse in a spin-Peierls system of K-tetracyanoquinodimethane (TCNQ).
figure 1

a Schematic of an out-of-phase totally symmetric intramolecular vibration (ag mode) (blue open arrows) in a molecular dimer with one electron in each molecular orbital, which can be excited by an MIR pulse. Energy modulations of two singly occupied molecular orbitals (SOMO) coupled with ag-mode vibrations induce partial charge transfers, ∆ρ, in a molecular dimer, resulting in spin-density modulations in each molecule as shown in the lower part. b The crystal structure of K-TCNQ. The thin lines represent unit cell. c, d Schematics of c Mott-insulator phase and d spin-Peierls phase with molecular dimerizations in K-TCNQ. TC = 395 K is the critical temperature.

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To induce an electronic-state change using this type of Floquet state, we chose a spin-Peierls system of potassium-tetracyanoquinodimethane (K-TCNQ). Figure 1b shows the crystal structure of K-TCNQ. In this compound, an electron is transferred from K to TCNQ, and each TCNQ− has a SOMO. TCNQ− molecules are stacked along the a-axis, forming a half-filled one-dimensional electronic system owing to the molecular orbital overlap between neighboring molecules41. The on-site Coulomb repulsion U (∼1.5 eV) of TCNQ is large relative to the intermolecular transfer integral t0 (∼0.2 eV), thus, the system is a Mott insulator42,43,44. The electron spin (S = 1/2) on TCNQ− forms an antiferromagnetic chain (red arrows in Fig. 1c). Below the critical temperature Tc = 395 K, molecules dimerize to form a spin singlet state in each dimer (Fig. 1d), which is called a spin-Peierls transition41,45. A previous study revealed that visible femtosecond-pulse irradiation destabilized the spin-Peierls phase and decreased molecular dimerization8,46. The electron carriers (doublons) and hole carriers (holons) generated by the photoexcitation do not have spin and thus breaks up the antiferromagnetic spin chain. It was suggested that the fragment of spin chains resulted in the suppression of the spin-Peierls mechanism and reduction in the dimer molecular displacements8,46. The excitation of the ag-mode vibrations with EMV couplings (Fig. 1a) by an MIR pulse should induce the spin-density modulation as well as the charge-density one. The spin-density modulation is expected to destabilize the spin-Peierls phase since it hybridizes the antiferromagnetic ground state with the non-magnetic state.

In this study, we detected the ultrafast dynamics in the destabilization of the spin-Peierls phase via the formation of the charge-spin modulated Floquet state by a subcycle spectroscopy using a phase-locked MIR pump pulse and an ultrashort visible probe pulse. The analyses of the reflectivity changes in the intramolecular transition band revealed that the electron and spin density of each molecule are synchronously modulated with intramolecular vibrations. Additionally, we demonstrated that such a charge-spin modulation induces dimerization reduction, as observed in transient reflectivity changes of the Mott-gap transition band. This approach using an intramolecular vibrational excitation is an example of Floquet engineering and can be applied to drive various phase transitions in other molecular solids with strong electron-phonon couplings.

Results

Steady-state polarized reflectivity spectra

Figure 2a shows the polarized reflectivity (R) spectra on the ab plane. The broad peak at 1 eV for the electric field of light E parallel to the a axis (E//a) corresponds to the Mott-gap transition (orange arrow in the inset)43,44. The sharp peaks below 0.3 eV are the aforementioned ag-mode vibrations of TCNQ− (refs. 47,48). The atomic motions in TCNQ in mode 1 with Ω1 = 1178 cm−1 and mode 2 with Ω2 = 1330 cm−1 are illustrated in the inset28,47. The band at 2 eV for E perpendicular to the a axis (E ⊥ a) is the intramolecular transition (IMT) from the highest occupied molecular orbital of TCNQ− to SOMO (blue arrow in the inset)43,44,49. The intensity of this transition is sensitive to the electron and spin densities of the SOMO.

Fig. 2: Experimental condition of mid-infrared (MIR)-pump visible reflectivity probe subcycle measurements.
figure 2

a Polarized reflectivity spectra of K-tetracyanoquinodimethane (TCNQ) at 294 K. The black and blue solid lines are for the electric field of light E parallel and perpendicular to the a axis (E//a and E ⊥ a), respectively. The red and blue shades show the spectra of MIR-pump and visible-probe pulses, respectively. The inset in the right panel illustrates the Mott-gap transition (the orange arrow) and intramolecular transition (IMT) (the blue arrow). The inset in the left panel illustrates the atomic motions of modes 1 and 2. SOMO and HOMO represent the singly and highest occupied molecular orbitals, respectively. b Schematic of the experimental setup. c The intensity envelope of the ultrashort visible probe pulse.

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MIR pump ultrashort visible reflectivity probe subcycle measurements on the intramolecular transition band

Figure 2b illustrates a schematic of the MIR pump subcycle reflection probe spectroscopy, which is almost identical to that used in a previous study, in which Floquet states concerning the intramolecular excited state were detected28. In the present study, we focus on the electronic-state control by generating Floquet states of the ground state, in which the nonmagnetic states are mixed with the original spin singlet states. The electric-field waveform and Fourier power spectrum of the MIR pulse are shown in Figs. 3a and 2a, respectively. This pulse has a central frequency of 1069 cm−1, exciting mode 1 strongly and mode 2 weakly. Figure 2c shows a temporal profile of the ultrashort visible probe pulse. This pulse has a temporal width δtr of 6.6 fs (E ⊥ a), which is sufficiently shorter than the period of the MIR pulse, ~30 fs, enabling subcycle spectroscopy. Its spectrum shown in Fig. 2a (the blue shade) covers the IMT of TCNQ−, which facilitates the detection of changes in the electron and spin densities of each molecule via its reflectivity change, ΔR(t)/R, where t is the delay time of the probe pulse relative to the MIR-pump pulse. A bandpass filter with a bandwidth of ~35 meV and a central photon energy of 2.07 eV was inserted in front of the detector to measure ΔR(t)/R at the IMT peak. Technical details of the experiments can be found in the Methods section and Supplementary Note 1. The selection of the probe energy is detailed in Supplementary Note 2. All measurements were performed at 294 K.

Fig. 3: Reflectivity changes in the intramolecular transition band induced by the phase-locked mid-infrared (MIR) pump pulse.
figure 3

a Electric-field waveform, EMIR(t), of the MIR pulse. b Time characteristics of the reflectivity change ΔR(t)/R at 2.07 eV at 294 K (the thin solid lines). The thick solid lines show the low-frequency components below 10 THz, ΔRLF(t)/R. The orange, green and blue solid lines are for the MIR pulse with the maximum electric-field amplitude, EMIR, of 2.1, 4.1 and 6.1 MV cm−1, respectively. c Imaginary part of the dielectric constant (ε2) spectrum for the electric field of light E parallel to the a axis (E//a) at 294 K. d Fourier power spectrum, IHF, of the high-frequency components ΔRHF(t)/R in the temporal range from 200 fs to 2950 fs. e Raman spectrum, IRaman, for \(z\left({xx}\right)\bar{z}\) configuration at 294 K. x and z correspond to the a-axis and the normal to the ab-plane, respectively. f EMIR-dependence of amplitudes of the high-frequency components AHF of 2Ω1-oscillation. g EMIR-dependence of max|ΔRLF(t)/R| around the time origin. Broken lines in f, g are proportional to (EMIR)2. The error bars are smaller than the sizes of data points.

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Figure 3b shows the time evolution of the reflectivity changes, ΔR(t)/R, for the MIR pulse with the maximum electric-field amplitude, EMIR, of 2.1, 4.1 and 6.1 MV cm−1. ΔR(t)/R exhibits high-frequency oscillations with a period of ~14 fs, which is almost half the MIR-light period. The thick lines show the low-frequency component below 10 THz, ΔRLF(t)/R, which was extracted using a Fourier filter. In ΔRLF(t)/R, low-frequency oscillations with a period of ~200 fs or more and a long-lived decrease in the reflectivity were observed. The high and low frequency oscillations are expected to be related to the out-of-phase ag-mode vibration and lattice-mode vibrations due to the destabilization of the spin-Peierls phase, respectively.

First, to clarify the origin of the high-frequency oscillations, we extracted the high-frequency components ΔRHF(t)/R above 20 THz from ΔR(t)/R for EMIR = 6.1 MV cm−1, using a Fourier filter. The extracted profile of ΔR(t)/R is shown by the open circles in Fig. 4b. The Fourier power spectrum of ΔRHF(t)/R, IHF, is shown in Fig. 3d, in which a strong peak at ∼2370 cm−1 and weak peaks at ∼2210 and ∼2530 cm−1 were identified. The spectral shapes of IHF for EMIR = 2.1 MV cm−1 and 4.1 MV cm−1 are almost identical with that for EMIR = 6.1 MV cm−1. To elucidate the origins of these oscillations, we show the ε2 spectra of modes 1,2 obtained from the R spectrum using the Kramers-Kronig transform in Fig. 3c and the Raman spectrum in the \(z\left({xx}\right)\bar{z}\) configuration in Fig. 3e (see the Methods section for the details of the steady-state optical spectroscopy measurements). The horizontal scale in Fig. 3c is half of that in Figs. 3d and 3e. x and z correspond to the a-axis and normal to the ab-plane, respectively. The peak frequencies of ∼2370 cm−1 and ∼2530 cm−1 in IHF almost coincide with 2Ω1 = 2356 cm−1 and Ω1 + Ω2 = 2508 cm−1, respectively, where Ω1 = 1178 cm−1 and Ω2 = 1330 cm−1 are the frequencies of mode 1 and mode 2, respectively (Fig. 3c). Therefore, these oscillations correspond to the charge modulation in each dimer by ag modes via EMV coupling (Fig. 1a). The modulation of the SOMO energy ϵs in each molecule can be written as \({\epsilon }_{{{{{{\rm{s}}}}}}}\propto \left[{g}_{1}{Q}_{1}\left(t\right)+{g}_{2}{Q}_{2}\left(t\right)\right]\), where Qi(t) and gi (i = 1,2) show the normal coordinate and EMV-coupling constant of each mode, respectively40. gi is a parameter that characterizes how much the SOMO energy changes with the intramolecular vibration Qi(t) and is defined by \({g}_{i}=\sqrt{\frac{\hslash }{{\varOmega }_{i}}}\frac{\partial {\epsilon }_{{{{{{\rm{s}}}}}}}}{\partial {Q}_{i}}\). Since K-TCNQ has inversion symmetry, the reflectivity change is proportional to \({\left[{g}_{1}{Q}_{1}\left(t\right)+{g}_{2}{Q}_{2}\left(t\right)\right]}^{2}\), which should include oscillatory components with the frequencies of 2Ω1, 2Ω2, Ω1 + Ω2, Ω1 − Ω2. Since mode 2 with the frequency Ω2 was not strongly excited as compared to mode 1 with the frequency Ω1 in the experiment as mentioned above, the oscillation of (Ω1 + Ω2) is much weaker than that of 2Ω1, and the oscillation of 2Ω2 is not observed. Q1(t) and Q2(t) are proportional to EMIR. Therefore, the amplitudes of the observed oscillations, AHF, are expected to be proportional to (EMIR)2. In fact, the magnitudes of AHF of the oscillation with the frequency of 2Ω1 evaluated from the Fourier power spectra exhibits a (EMIR)2 dependence as shown in Fig. 3f.

Fig. 4: Fitting analyses of high- and low- frequency components of reflectivity changes.
figure 4

a The square of the electric-field waveform EMIR(t) of the mid-infrared (MIR) pulse with the maximum electric-field amplitude, EMIR, of 6.1 MV cm−1. b Time characteristics of the high-frequency component ΔRHF(t)/R (open circles). The red line shows the fitting curves. The purple and pink solid lines represent the components of the fitting curve corresponding to HPF{F(t)} and HPF{G(t)} in Eq. (1), respectively. HPF is an operator that extracts high-frequency components. F(t) and G(t) are functions defined by Eq. (2) and Eq. (3), respectively. c Time characteristics of the low-frequency components ΔRLF(t)/R(open circles) and the fitting curves (red line). The blue, orange and green solid lines represent the components of the fitting curve corresponding to the first, the third, and the second terms (LPF{b0[F(t)]}, oscillation A, and oscillation B) in Eq. (6), respectively. LPF shows an operator that extracts a low-frequency component.

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On the other hand, the oscillation at 2210 cm−1 corresponds to no peak in the ε2 spectrum, but to the peak (~2200 cm−1) seen in the Raman spectrum in Fig. 3e. Therefore, this oscillation is attributable to the Raman mode excited by a two-photon process23. In this mode, all the molecules vibrate in phase and no intermolecular charge transfers are induced. Furthermore, the MIR electric field, EMIR(t), is expected to induce charge modulation directly in non-resonant and coherent manner. The reflectivity change due to this modulation should occur during the presence of the pump pulse and be proportional to EMIR(t)2.

Considering these facts, we performed a fitting analysis of the high-frequency component above 20 THz (ΔRHF(t)/R) using the following equations, in which the weak 2530 cm−1 oscillation was neglected.

$$\frac{\Delta {R}_{{{{{{\rm{HF}}}}}}}\left(t\right)}{R}={{{{{\rm{HPF}}}}}}\left\{F\left(t\right)+G \, (t)\right\}$$
(1)
$$F\left(t\right)={\left\{{a}_{0}{E}_{{{{{{\rm{MIR}}}}}}}\left(t\right)+{a}_{1}[{E}_{{{{{{\rm{MIR}}}}}}}\left(t\right)\otimes {f}_{1}\left(t\right)]\right\}}^{2}$$
(2)
$$G\left(t\right)={{a}_{3}}^{2}{\left[{E}_{{{{{{\rm{MIR}}}}}}}\left(t\right)\right]}^{2}\otimes {f}_{3}\left(t\right)$$
(3)
$${f}_{i}\left(t\right)=\exp \left(-\frac{t}{{\tau }_{i}}\right)\sin \left({\omega }_{i}t+{\phi }_{i}\right)\quad\left(i=1,3\right)$$
(4)
$$g\left(t\right)\otimes {f}_{i}\left(t\right)={\int }_{\!\!\!\!-\infty }^{t}g\left(\tau \right){f}_{i}\left(t-\tau \right)d\tau$$
(5)

Here, HPF in Eq. (1) is an operator that extracts high-frequency components. a0EMIR(t) on the right-hand side of Eq. (2) represents the direct charge modulation by the MIR electric field EMIR(t). The next term, a1[EMIR(t) ⊗ f1(t)], represents the charge modulation due to the ag-mode vibration (mode 1) driven by the MIR electric field EMIR(t) via the EMV coupling. f1(t) in Eq. (2) is a damped oscillator for mode 1. ω1, ϕ1, and τ1 are the frequency, initial phase, and decay time of the mode-1 vibration.  ⊗  shows a convolution integral, the definition of which is shown in Eq. (5), where g(t) shows a driving force of oscillator fi(t). a0 and a1 are the parameters determining the magnitude of each term. The time dependence of the ag-mode vibration of each molecule in a dimer is expressed using the convolution integral of f1(t) with EMIR(t) as shown in Eq. (2). The reflectivity change due to the direct charge modulation by the MIR electric field and the charge modulation by the out-of-phase ag-mode vibration in each dimer is expressed by the high-frequency component of square of {a0EMIR(t) + a1[EMIR(t) ⊗ f1(t)]}, as shown in Eq. (2). G(t) in Eq. (3) expresses the reflectivity change due to the Raman-active ag mode excited by the two-photon absorption process of the MIR pulse. This Raman-active ag mode is represented by a damped oscillator f3(t) with the frequency of ω3, initial phase of ϕ3, and decay time of τ3 (Eq. (4)), which is driven by the square of EMIR(t), [EMIR(t)]2. As a result, the high-frequency oscillation on the reflectivity change due to this mechanism is expressed by HPF{a32[EMIR(t)]2 ⊗ f3(t)}. a3 is the parameter determining the magnitude of this term, which has the same dimension as a0 and a1.

The red line in Fig. 4a shows the temporal profile of [EMIR(t)]2. ΔRHF(t)/R for EMIR = 6.1 MV cm−1 in Fig. 4b (the open circles) is well reproduced using Eqs. (1–5) as shown by the red line in Fig. 4b (see Supplementary Note 3 for the experimental and fitting curves in the wider temporal region). Each term in Eq. (1) is shown in the lower part. The used parameter values in this fitting are listed in Table 1. The obtained frequency values, ω1 and ω3, for oscillators f1(t) and f3(t) are 1184 cm−1 and 2211 cm−1, which are almost in agreement with the frequencies of IR-active ag mode (mode 1), Ω1 = 1178 cm−1, and Raman-active ag mode, ΩRaman = 2207 cm−1, respectively. The latter is assigned to the ag mode of the CN-stretching vibrations in TCNQ molecules50. The decay time τ1 (1405 fs) of mode 1 is considerably shorter than the decay time τ3 (4863 fs) of the Raman-active CN-stretching mode. It is probably because mode 1 is coupled to intermolecular charge transfers via the EMV coupling, but the Raman-active CN-stretching mode is not. F(t) in Eq. (2) generates spin-density oscillation as well as charge-density one within each dimer and possibly decreases the spin-Peierls dimerization, which would be reflected in the low-frequency component below 10 THz, ΔRLF(t)/R, as mentioned earlier. In fact, as shown in Fig. 3g, maximum reflectivity change, max|ΔRLF(t)/R|, is proportional to (EMIR)2 similarly to the 2Ω1-oscillation amplitude AHF (Fig. 3f).

Table 1 Fitting parameters in Eqs. (2–4) used in the analysis of the time characteristic of the high-frequency components ΔRHF(t)/R.
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Now, we explain the analysis of the low-frequency oscillations and discuss the feature of the destabilization of the spin-Peierls phase and reduction of dimeric molecular displacements extracted from the analysis. The time characteristic of ΔRLF(t)/R (EMIR = 6.1 MV cm−1) and its Fourier power spectrum are represented using open circles in Fig. 4c and Fig. 5a, respectively. In Fig. 5a, two oscillations A and B with the frequencies of ∼150 cm−1 and ∼110 cm−1, respectively, are observed. For comparison, the polarized Raman spectrum is shown in Fig. 5c. Oscillation A does not correspond to any Raman modes but is ascribed to the differential-frequency generation of two high-frequency oscillations, modes 1 and 2, with a frequency of Ω2 − Ω1 = 152 cm−1. Oscillation B is attributed to the Raman mode represented by the solid triangle. Density functional theory (DFT) calculations revealed that the mode with 113.5 cm−1 was associated with dimerization, as illustrated in the upper part in Fig. 5d (see Supplementary Note 4 for the details of DFT calculations). These results suggest that the modulation of the spin density by the MIR pulse excitation reduces the dimeric molecular displacements, which drive oscillation B via the displacive excitation of coherent phonon mechanism51. This also suggests that the decrease in reflectivity, that is, the background component in ΔRLF(t)/R is owing to a reduction in the average dimeric molecular displacements.

Fig. 5: Low-frequency oscillatory components driven by destabilization of the spin-Peierls phase.
figure 5

a Fourier power spectrum of the oscillatory component of the time characteristic of the low-frequency component ΔRLF(t)/R (open circles). The orange and green solid lines show the Fourier power spectra of oscillation A and B obtained by the fitting procedure, respectively. b Fourier power spectrum of the oscillatory component of time characteristic of the reflectivity change ΔR(t)/R at 0.71 eV. c Raman spectrum, IRaman, for \(z\left({xx}\right)\bar{z}\) configuration at 294 K. d Schematic of the molecular vibrations with ∼113.5, 50.4, and 20.7 cm−1 obtained by the density functional theory (DFT) calculation. e Schematic of destabilization of the spin-Peierls (SP) phase by charge and spin density modulations induced by a mid-infrared (MIR) pulse. ∆ρ represents partial charge transfers. Green arrows show the coherent oscillation associated with the release of the dimerization (∼113.5 cm−1).

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To confirm this interpretation, we performed a fitting analysis of ΔRLF(t)/R using the following equations Eqs. (6, 7).

$$\frac{\Delta {R}_{{{{{{\rm{LF}}}}}}}\left(t\right)}{R}= \,{{{{{\rm{LPF}}}}}}\left\{{b}_{0}\left[F\left(t\right)\right]+{b}_{1}\left[F\left(t\right)\otimes {f}_{4}\left(t\right)\right] \right.\\ +\left.{b}_{2}\left[{E}_{{{{{{\rm{MIR}}}}}}}\left(t\right)\otimes {f}_{1}\left(t\right)\right]\left[{E}_{{{{{{\rm{MIR}}}}}}}\left(t\right)\otimes {f}_{2}\left(t\right)\right]\right\}$$
(6)
$${f}_{i}\left(t\right)=\exp \left(-\frac{t}{{\tau }_{i}}\right)\sin \left({\omega }_{i}t+{\phi }_{i}\right) \quad \left(i=1,2,4\right)$$
(7)

LPF in Eq. (6) shows an operator that extracts a low-frequency component. F(t) represents the total charge modulations within each dimer by the MIR electric field as expressed in Eq. (2) and is the driving force for the release of the dimerization. The first term in Eq. (6) shows the averaged decrease in the dimeric molecular displacements. This term is considered to depend on the amplitude of the charge modulation and therefore proportional to the envelope of HPF{F(t)}, which can be expressed by LPF[F(t)]. The second term in Eq. (6) represents the coherent oscillation of the dimeric mode (oscillation B), which is also driven by LPF[F(t)]. Assuming that this dimeric mode is expressed by the damped oscillator, f4(t), in Eq. (7), this oscillation can be expressed by {LPF[F(t)]} ⊗ f4(t), which is equal to LPF[F(t) ⊗ f4(t)]. The third term in Eq. (6) represents oscillation A, which is the beating produced by the differential frequency of two ag-mode vibrations, mode 1 and 2. This component should be proportional to LPF{[EMIR(t) ⊗ f1(t)][EMIR(t) ⊗ f2(t)]}. b0, b1, and b2 in Eq. (6) are the parameter determining the magnitude of each term.

Using Eqs. (6, 7), the time characteristic of ΔRLF(t)/R experimentally obtained in Fig. 4c (the open circles) was almost reproduced as shown by the red line in the same figure. Three components in Eq. (6), are shown in the lower part. The used parameter values in this fitting are listed in Table 2. In this fitting procedure, the parameter values of the damped oscillator f1(t) are set to the same as those listed in Table 1 determined by the fitting analysis of ΔRHF(t)/R, except for the decay time τ1 in the [EMIR(t) ⊗ f1(t)]2 term of F(t) in Eq. (6). In general, the decay time of a coherent oscillation, τ, estimated from reflectivity changes is affected by two factors: the decay time of actual amplitude of the vibration, τ0, and the decoherence of the oscillation. Because of the latter factor, the relation of τ0 > τ is expected. In our case, it is reasonable to consider that the suppression of the dimerization is determined not by τ including the effect of the decoherence but by the decay time of actual amplitude of the vibration, τ0. Therefore, we set the decay time of oscillator f1(t) in the [EMIR(t) ⊗ f1(t)]2 term of F(t) in Eq. (2) as a fitting parameter, τ0. On the other hand, the decay time of oscillator f1(t) in the LPF{[EMIR(t) ⊗ f1(t)][EMIR(t) ⊗ f2(t)]} term should be equal to τ1 since the oscillation from this term, that is, oscillation A should include the effect of the decoherence of high-frequency oscillations due to oscillators f1(t) and f2(t). τ0 obtained by the fitting analysis of ΔRLF(t)/R is 2500 fs, which is longer than τ1 = 1405 fs in Table 1 as expected.

Table 2 Fitting parameters in Eqs. (6, 7) used in the analysis of the time characteristic of the low-frequency components ΔRLF(t)/R.
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The Fourier power spectra of the second and third terms in Eq. (6) are represented by the colored solid lines and shades in Fig. 5a, which almost reproduce the Fourier power spectra of ΔRLF(t)/R (open circles). The frequency ω4 of oscillation B is 112 cm−1, which is in good agreement with the calculated frequency (113.5 cm−1) of the dimerization mode shown in the upper part of Fig. 5d. The success of the fitting of the long-lived decrease in ΔRLF(t)/R (the red line in Fig. 4c) with LPF{b0[F(t)]} (the blue line in the same figure) demonstrates that the square of the total charge modulation expressed by F(t), gives rise to the destabilization of the spin-Peierls phase. This result also excludes the possibility that the decrease in the dimeric molecular displacements is caused by a heating effect. In addition, the time characteristic of oscillation B shown by the green curve in Fig. 4c is of a cosine-type, indicating the displacive excitation of coherent phonon mechanism of its generation as pointed out above. This fact supports the validity of our interpretation again. Thus, we can conclude that the out-of-phase ag mode vibration excited by the MIR pulse destabilize the spin-Peierls phase.

The mechanism of destabilization of the spin-Peierls phase by MIR pulse excitation can be explained using a concept of Floquet states as follows. As suggested in the introduction, the resonant excitation of the IR-active ag mode using an MIR pulse leads to a partial charge transfer, Δρ, within each dimer synchronized with the ag mode (left part of Fig. 5e). These processes hybridize the nonmagnetic dimer states expressed by |↑↓, 00〉 and |00, ↑↓〉 with the original singlet-dimer state expressed by |↑0, 0↓〉. In these expressions, the left (right) part shows the electron spin in the left (right) molecule, and the up-spin, down-spin, and spinless states are represented as ↑0, 0↓, and 00, respectively. This hybridized state is a type of Floquet state. In the nonmagnetic states |↑↓, 00〉 and |00, ↑↓〉, the spin-Peierls mechanism does not work, so dimeric molecular displacements should decrease and oscillate coherently (the right part of Fig. 5e). The degree of hybridization, i.e., the coefficients of |↑↓, 00〉 and |00, ↑↓〉 in the wavefunction of the vibrationally excited Floquet states are proportional to Δρ (∝ EMIR), and the density of the nonmagnetic states is proportional to (Δρ)2. The descriptions of this formalism are reported in Supplementary Note 5. In the experiments, max|ΔRLF(t)/R| represented the decrease in dimerization and was proportional to (EMIR)2 as shown in Fig. 3g. The Floquet state produced by such periodic modulation of the spin density should be maintained as long as the intramolecular vibration, that is, the high-frequency oscillation (mode 1) persists in a coherent manner. As seen in Supplementary Fig. 3, the coherent intramolecular vibration continues up to at least 1.5 ps. This is the reason why the decrease in dimerization reflected by the decrease of the reflectivity (the negative background component in ΔRLF(t)/R) was sustained for up to a few picoseconds as seen in Fig. 4c.

MIR pump near-infrared reflectivity probe measurements on the Mott-gap transition band

To obtain more detailed information about the melting of the spin-Peierls phase, we measured the reflectivity change of the Mott-gap transition, using the same MIR-pulse excitation. The Mott-gap transition shows the peak structure at ~1 eV in the reflectivity spectrum in Figs. 2a and 6d, which is known to redshift with the decrease in dimerization8,46. Therefore, from the analysis of the transient reflectivity change of this peak, we will be able to evaluate quantitatively the decrease in dimerization. Figure 6a illustrates a schematic of the MIR pump near-IR probe reflection spectroscopy. This was not a subcycle measurement because we used near-IR probe pulses with a temporal width of ~90 fs. Figure 6b shows the time characteristic of ΔR(t)/R at 0.71 eV for an excitation by an MIR pulse with the central frequency of 1060 cm−1 and EMIR = 6.0 MV cm−1, which are almost the same as those used in the subcycle measurements. Around the time origin, a pulsed response appears in ΔR(t)/R. Given that the magnitude of ΔR(0)/R is proportional to (EMIR)2 (not shown), it is ascribed to the effect of the direct charge modulation, as expressed by the first term in Eq. (1). ΔR(t)/R at t > 0.15 ps exhibits coherent oscillations and a long-lived positive component, which resembles ΔRLF(t)/R (Fig. 4c).

Fig. 6: Reflectivity changes in the Mott-gap transition band in the near-infrared (NIR) region induced by the mid-infrared (MIR)-pump pulse.
figure 6

a Schematic of the experimental setup. b Time characteristic of the reflectivity (R) change ΔR(t)/R at 0.71 eV at 294 K for the MIR pulse with the maximum electric-field amplitude, EMIR, of 6.0 MV cm−1 (the black solid line). The red solid line represents five times ΔR(t)/R. c Time characteristic of the oscillatory component, ΔROSC(t)/R, (open circles). The red line shows the fitting curve. Time characteristics of oscillatory components B, C, and D determined by the fitting procedure are shown by the green, blue, and purple solid lines, respectively. d The R spectrum for the electric field of light E parallel to the a axis (E//a) (the black solid line) due to the Mott-gap transition band and ΔR(t) spectra at the delay time of the probe pulse relative to the MIR-pump pulse, t = 1 ps, 2 ps, and 5 ps (the red triangles, the blue circles and green squares, respectively). The error bars are smaller than the sizes of data points. The red broken line shows the simulation curve.

Full size image

First, we discuss the oscillatory component ΔROSC(t)/R extracted from ΔR(t)/R at 0.71 eV, which is shown by the open circles in Fig. 6c. Fourier power spectrum of ΔROSC(t)/R is presented in Fig. 5b, in which four modes are identified. The higher two oscillations at ~150 cm−1 and 110 cm−1 correspond well to oscillations A and B observed in ΔR(t)/R by the visible probe measurement shown in Fig. 5a, respectively. We labeled the two lower-frequency oscillations at ~50 cm−1 and 20 cm−1 as C and D, respectively. To determine the frequencies of these oscillatory components more quantitatively, we analyzed the time characteristic of ΔROSC(t)/R in the temporal region from 0.5 ps to 5.5 ps using the following formula.

$$\frac{\Delta {R}_{{{{{{\rm{OSC}}}}}}}\left(t\right)}{R}=\mathop{\sum}\limits_{i={{{{{\rm{B}}}}}},{{{{{\rm{C}}}}}},{{{{{\rm{D}}}}}}}{C}_{i}\left[h\left(t\right)\otimes {f}_{i}\left(t\right)\right]$$
(8)
$${f}_{i}\left(t\right)=\exp \left(-\frac{t}{{\tau }_{i}}\right)\sin \left({\omega }_{i}t+{\phi }_{i}\right) \quad \left(i={{{{{\rm{B}}}}}},{{{{{\rm{C}}}}}},{{{{{\rm{D}}}}}}\right)$$
(9)

In the MIR pump near-IR probe measurements, the temporal widths of pump and probe pulses are both 90 fs, and the time resolution is estimated to be 127 fs. h(t) in Eq. (8) is a response function in the measurement system and is expressed by a Gaussian profile of exp[−(t/76.4 fs)2], the full width half maximum of which is equal to 127 fs. We assumed three damped oscillations (i = B, C, and D) for the oscillations and neglected the weak oscillation A. τi, ωi, and φi are the decay time, frequency, and initial phase of each oscillation, respectively.

By the fitting procedure, the time characteristic of ΔROSC(t)/R was well reproduced as shown by the red line in Fig. 6c. Each oscillatory component is shown in the lower part. The used parameter values in this fitting are listed in Table 3. Frequencies of oscillations B, C, and D are 110 cm−1, 49.3 cm−1, and 20.3 cm−1, respectively. According to the DFT calculation, the mode with 50.4 cm−1 is a shear-type mode, in which molecules are displaced parallel to the molecular plane as shown in the middle part in Fig. 5d. The mode with 20.7 cm−1 is another dimerization mode in which molecules rotate around the long axis of TCNQ− as illustrated in the bottom part in the same figure. Since those modes are also related to the dimerization, they can be interpreted as driven by the release of the dimerization. In fact, the magnitudes of the initial phases of those oscillations, φB, φC, and φD, are almost equal to π/2 or −π/2 rad, suggesting that those oscillations are also of the cosine type similarly to the coherent oscillation B due to mode 1. These oscillations are not observed in ΔRLF(t)/R obtained by the visible probe measurements because their intensities are weak.

Table 3 Fitting parameters in Eqs. (8, 9) used in the analysis of the time characteristic of the oscillatory component ΔROSC(t)/R.
Full size table

Here, we analyze the spectral changes of the Mott-gap transition and evaluate quantitatively the decrease in dimerization. We plotted in Fig. 6d the ΔR(t) spectra at t = 1ps, 2 ps, and 5 ps after the pulsed response disappeared together with the original R spectrum (the black solid line). ΔR(t) is negative above 0.85 eV and positive below this value. To analyze these spectra, we assumed that the original R spectrum consisted of two Lorentz oscillators, as previously reported44, and changed the energy and intensity of the lower oscillator corresponding to the Mott-gap transition to reproduce the ΔR(t) spectra. Assuming a redshift and an intensity decrease of the Mott-gap transition, the ΔR(t) spectra are approximately reproduced, as shown by the red broken line in Fig. 6d. From the magnitude of the redshift, the decrease in dimeric molecular displacements was estimated to be ∼10% of the original magnitude. The decrease in the Mott-gap transition intensity was attributed to the decrease in the intradimer transfer integrals. Details of the analysis of the ΔR(t) spectra are provided in Supplementary Note 6.

Finally, we compare the destabilization of the spin-Peierls phase in K-TCNQ by the vibrational excitation studied here with that by the electronic excitation beyond the gap using a 1.55-eV pulse previously reported8,46. In the electronic excitation with the 1.55-eV pulse, it was revealed that the spin-Peierls phase became unstable by photogenerated spinless holons and doublons fragmenting the one-dimensional antiferromagnetic spin chains. This mechanism of destabilization of the spin-Peierls phase is essentially different from that by the charge-spin modulation by the MIR excitation reported here. It is therefore interesting to compare the efficiency of the decrease in the dimeric molecular displacements by the photoexcitation and MIR excitations. In fact, we evaluated the low-energy shift of the Mott gap transition from the change of the reflectivity spectrum due to the 1.55-eV excitation and estimated the magnitude of the decrease in the dimeric molecular displacements as in the case of MIR excitation. The results show that for the 1.55-eV excitation with the excitation photon density of 0.095 photon per TCNQ, the decrease in the dimeric molecular displacements is ~50%. Furthermore, for each of the 1.55-eV and MIR excitations, we evaluated the total amount of light energy absorbed in the region from the crystal surface to the penetration depth (148 nm) of the probe pulse at 0.775 eV, the reflectivity change at which characterizes the low-energy shift of Mott gap transition, and compared the decreases in the dimeric molecular displacements per unit energy. The result revealed that the energy efficiency of the decrease in the dimeric molecular displacements was approximately three times higher for the MIR excitation than for the 1.55-eV excitation. This comparison demonstrates that the generation of the charge-spin modulated Floquet state by the MIR excitation is effective for the electronic state control. Supplementary Note 7 details the analysis of the reflectivity change by the 1.55-eV excitation and the comparison of the efficiency of the decrease in the dimeric molecular displacements by the MIR and 1.55-eV excitations.

Conclusion

In summary, we demonstrated that the spin-density modulation owing to the intermolecular charge transfer induced by the ag-mode excitation caused destabilization of the spin-Peierls phase. This phase control using the periodic spin-density modulation can be regarded as a typical example of Floquet engineering. The MIR pump visible subcycle reflection probe and near-IR reflection probe measurements revealed that the time-periodic spin-density modulation by the ag-mode excitation induced the hybridization of the nonmagnetic dimer states with the original singlet-dimer states and resulted in the destabilization of the spin-Peierls phase. The resultant decrease in dimerization was accompanied by the multiple coherent molecular oscillations corresponding to the release of dimeric molecular displacements. The coupling between intramolecular vibrations and electronic systems has been observed in many molecular solids. Therefore, by applying the method proposed here using electron and spin-density modulations induced by intramolecular vibrational excitations to other molecular solids, it may be possible to generate charge-spin modulated Floquet states and drive various types of efficient phase transitions.

Methods

Sample preparations

Single crystals of K-TCNQ were grown from KI and TCNQ by the diffusion method52. A typical size of ab plane of used single crystals is 5 mm × 0.5 mm, on which reflection measurements are performed. Their typical thickness is 0.5 mm.

Steady-state optical spectroscopy measurements

The polarized reflectivity spectra were measured using a specially designed spectrometer with a 25-cm-grating monochromator in the visible and near-IR region (0.5-5.0 eV) and a Fourier-transform infrared spectrometer in the MIR region (0.08-1.2 eV). Both of these spectrometers were equipped with optical microscopes. The complex dielectric constant \(\widetilde{\varepsilon }(\omega )\) spectra were calculated from the R spectra using the Kramers–Kronig transformation. The polarized Raman spectra were measured by using a Raman spectrometer equipped with a He-Ne laser (1.96 eV) and an optical microscope. The obtained scattering intensities were corrected using a Bose factor.

MIR pump ultrashort visible reflectivity probe subcycle spectroscopy

The schematic diagram of the MIR pump ultrashort visible probe subcycle spectroscopy is reported in Supplementary Note 1. In this measurement, a Ti: sapphire regenerative amplifier with the central photon energy of 1.55 eV, temporal width of ~35 fs, maximum pulse energy of 7.5 mJ, and repetition rate of 1 kHz is used as a light source. From the output from the regenerative amplifier, two pulses with 4.0 mJ and 1.0 mJ are picked up. The former is introduced to a twin-optical parametric amplifier (OPA). In the twin-OPA, the pulse is further divided into two pulses, which are input to two OPAs, OPA1 and OPA2. A part of the pulse excites a sapphire plate to generate a white-light pulse, which is used as a seed pulse in OPA1 and OPA2 in common. The pulses input to OPA1 and OPA2 are used for the amplification of the seed pulse in each OPA. The near-IR idler pulses output from OPA1 and OPA2 are guided onto a 1-mm thick GaSe crystal, and an MIR pulse is generated from the GaSe crystal by a difference frequency generation (DFG) process53. The MIR pulse thus obtained is divided into two pulses. One is used for a pump pulse to excite a sample and the other is used to measure electric-field waveform of the pulse itself during the measurement of transient reflectivity changes of the sample. To stabilize the carrier envelope phase of the MIR pulse, the feedback control of the optical path length through OPA2 is performed so that two optical path lengths through OPA1 and OPA2 are equal. In addition, another feedback control is performed using the delay line of the probe pulse so that the optical path length difference of the pump and probe pulses are unchanged with time54. The other output from the regenerative amplifier is input to a home-made noncollinear OPA (NOPA) to generate ultrashort visible pulses55. A typical spectrum of an output pulse from NOPA is shown in the blue shade in Fig. 2a, the central photon energy of which is 2.0 eV. The temporal width of the pulse was evaluated using a frequency-resolved optical gating (FROG) method56.

A part of the pulse is used as a sampling pulse for an electro-optical sampling to measure the electric-field waveform of the MIR pulse. In the electro-optical sampling, LiGaS2 with the thickness of 20μm is used as a nonlinear optical crystal to give rise to a polarization rotation of the sampling pulse proportional to the MIR electric field. A typical electric-field waveform and its Fourier power spectrum of the MIR pulse are shown in Fig. 3a and Fig. 2a (the red shade), respectively. The magnitude of the electric-field amplitude is calculated from the electric-field waveform, EMIR(t), the beam diameter, and the fluence of the MIR pulse57.

MIR-pump near-IR reflectivity probe spectroscopy

In the MIR pump near-IR probe reflection spectroscopy, another regenerative amplifier with the central photon energy of 1.55 eV, temporal width of ~90 fs, maximum pulse energy of 4.7 mJ, and repetition rate of 1 kHz is used as the light source (see Supplementary Note 1). From the output of the regenerative amplifier, two pulses with 1.8 mJ and 0.7 mJ are input to OPA3 and OPA4, respectively. An MIR pump pulse is generated from the signal and idler pulses output from OPA3 via the DFG process in GaSe. This MIR pulse is tuned to have the same spectrum as that used for the subcycle spectroscopy measurement. Near-IR probe pulses with the photon energy of 0.5 eV-1.1 eV are generated from OPA4. These near-IR pulses have temporal widths of ~90 fs. Therefore, this is a non-subcycle measurement.