Phonon-related monochromatic THz radiation and its magneto-modulation in 2D ferromagnetic Cr2Ge2Te6

Searching multiple types of terahertz (THz) irradiation source is crucial for the THz technology. Here, by utilizing a two-dimensional (2D) ferromagnetic Cr2Ge2Te6 crystal, we firstly demonstrate a magneto-tunable monochromatic THz irradiation source. With a low-photonic-energy broadband THz pump, a strong THz irradiation with frequency ~0.9 THz and bandwidth ~0.25 THz can be generated and its conversion efficiency could even reach 2.1% at 160 K. Moreover, it is intriguing to find that such monochromatic THz irradiation can be efficiently modulated by the magnetic field below 160 K. According to both experimental and theoretical analyses, the emergent THz irradiation is identified as the emission from the phonon-polariton and its temperature and magnetic field dependent behaviors confirmed the large spin-lattice coupling in this 2D ferromagnetic crystal. These observations provide a new route for the creation of tunable monochromatic THz source which may have great practical interests in future applications in photonic and spintronic devices.


Introduction
Terahertz (THz) radiation source plays a crucial role in relevant research and applications. After decades of intensive cultivation, the playground of THz sources has been widely developed in many materials, such as semiconductors, 1 nonlinear electrooptic crystals, 2 surface plasma, 3,4 metamaterials, 5 ferro-/non-magnetic heterojunctions, 6 etc. Recently, with extraordinary electrical and optical properties, 2D van der Waals (vdWs) materials has been also used for the novel THz irradiation source developing. 7 For instance, Xu et.al. reported the THz surface emission based on the competition between surface optical rectification and photocurrent surge in layered MoS2. 8 Under the excitation of strong infrared pulses, Ma et.al. proposed a new THz emitter based on observed the THz phonons and experimentally realized quasi-monochromatic THz radiations. 24,25 2D vdWs materials are natural superlattice structures with weak inter-layered interactions that hundreds of times weaker than intra-layered cases. 26 Moreover, layered 2D vdWs materials possess not only high anisotropy but also rich variety of inter-layered breathing phonon modes in THz range. 27,28 This feature holds a great potential for the monochromatic THz radiations from the phonons in 2D vdWs materials. Its main advantage, in comparison to fermionic (electron) cases, the phonon related radiations in principle would be 'zero-threshold' and high efficiency with high quality factors due to the its bosonic quasi-/particles nature that is independent of their population and possess relatively long lifetimes. [29][30][31][32][33] Surprisingly, little attention has been devoted to the study of 2D vdWs bosonic THz wave and no cogenetic phonon-based monochromatic THz radiation has been published yet.
Here, by choosing ferromagnet Cr2Ge2Te6 as a model system, we firstly demonstrate a 2D phonon-based monochromatic THz radiation. It was found that a strong THz irradiation with frequency ~0.9 THz and bandwidth ~0.25 THz can be generated with a low-photonic-energy broadband THz pump. The conversion efficiency varies with temperature and can even reach 2.1% at 160 K. Moreover, it is intriguing to find that the external magnetic field (B) could efficiently modulate such monochromatic THz irradiation especially when B is parallel to the ab-plane of the 2D Cr2Ge2Te6 crystal. After carefully experimental and theoretical examining, the emergent THz irradiation is identified as the emission from the phonon-polariton in this 2D ferromagnetic crystal. Our findings suggest that the use of 2D materials may provide a variable source for bosonic-related monochromatic THz radiation.

Results
Fig. 1 | Terahertz responses of Cr 2 Ge 2 Te 6 crystal. a, Schematic diagram of the transmission measurement configuration. b, Time-resolved THz spectra transmitted thorough the sample at some critical temperatures. c, Frequency-domain THz spectra corresponds to temperatures of 300 K (red curve) and 120 K (blue curve). The black curve is the reference THz signal through the pinhole of the sample holder without any sample. The inset is the close-up view of the red dashed frame area at 120 K.
To create a phonon-based THz emitter, appropriate materials are important. In addition to intensively studied metamaterial and graphene, 2D vdWs magnetic materials are another ideal material for this purpose because their exotic properties and their strong spin-phonon coupling are expected to give effective responses to external magnetic fields. 34 Cr2Ge2Te6 is one of the prototypes. It undergoes a paramagneticferromagnetic transition at TC = 68 K. 35 The THz transmission response of Cr2Ge2Te6 single crystal was measured by means of THz-TDS system as schematically shown in Fig. 1a. The measurements were taken from room temperature to 10 K with an Oxford Spectromag He-bath cryostat (see details in Method part). After penetrating through the sample, the time-resolved THz signals were collected and the typical results are depicted in Fig. 1b. In the time domains of transmitted THz wave obtained at 300 K, there is a main wave which has the same shape as the incident THz wave with lower intensity due to the absorption of Cr2Ge2Te6 crystal. With temperature decreasing, the intensity of the main wave increases at first and then drops below 160 K ( Supplementary Information Fig. S1). Apart from the main wave, it is intriguing to find that there are additional oscillations superimposed on the rear portion of the main waveforms (black arrow in Fig. 1b). Such THz oscillations emerges at 225 K and exists until the lowest temperature of 10 K we measured. Its amplitude slightly varies with temperature and reaches the maximum at 120 K.
There are two possible origins for these additional oscillations. One is Fabry-Pérot effect that arises from multiple reflections between internal interfaces of the sample, another is electromagnetic (EM) radiations. The loss functions for both experimental results and theoretical predictions of Fabry-Pérot effect were calculated. 36 As shown in the supplementary Fig. S2, the experimental result is significantly different from the theoretical feature of the Fabry-Pérot effect. Especially, the loss function of these oscillations corresponds to the THz response around 0.9 THz and could even be negative, which indicates negative loss after penetrating the sample. In order to further explore the additional oscillations, the fast-Fourier-transformation from TDS results was done and the corresponding typical frequency domain spectra (FDS) results are depicted in Fig. 1c. By comparing the results of 300 K (red curve) and 120 K (blue curve), it is found that the additional oscillations yield a certain frequency around 0.9 THz. Especially, at 120 K, the amplitude of output THz wave at ~0.9 THz is almost 2.7 times of 300 K case and even higher than the free-space pinhole reference (black curve), as shown in the inset of Fig. 1c. Considering both the negative loss function and large output THz wave at ~0.9 THz, it is reasonable to conclude that the additional oscillations are emergent THz radiation. Furthermore, by calculating the FDS of transmittance variation (Delta T) of specific temperature with reference to the case of 300 K that without radiation emerged ( Supplementary Information Fig. S3), it is found that the additional oscillation is monochromatic and its center frequency, monochromaticity, and amplitude are strongly dependent on temperature. Figure 2a presents the temperature dependence of the center frequency (fc) and full-width at half-maximum (FWHM) of the THz radiation. At first glance, the most important common performance is that the temperature dependence of fc and FWHM separate the temperature coordinate into three regions with boundaries of 160 K and TC. While the striking contrast is that their dependences are totally opposite. Specifically, for the case of fc, when temperature drops from 220 K to 160 K, it first dramatically increases from 0.80 to 0.87 THz. While in the following region from 160 K to TC, it turns to increase in a slowing trend from 0.87 to 0.90 THz. Afterwards, at temperatures lower than TC, the frequency is further hardened to 0.93 THz. However, for the FWHM that indicates the monochromatism of the radiations, its temperature dependence in these three regions corresponds to the narrowing from 0.46 to 0.35 THz rapidly (220 K to 160 K), the approximate plateau form from 0.35 to 0.32 THz (160 K to TC), and a further narrowing to 0.25 THz below TC, respectively.
As a rule of thumb, the conversion efficiency (ψ) is a critical characteristic. 37 Here, the radiation performance is evaluated with the parameter of , where Iab and Ir are intensity of absorbed pump pulse and generated THz radiation, EO is the P-P amplitude of the first oscillation waveforms, Ei and Et are P-PM of the incident and transmitted THz waveforms, respectively.
Corresponding results are shown as hexagonal symbols in Fig. 2b. The ψ also shows the same temperature regions as fc and FWHM. From 220 K to 160 K, the ψ starts to emerge and first be dramatically enhanced to ~2.1%, which is higher than the cases of fermionic cases, such as photoconductive and nonlinear optical rectification (usually lower than 0.1%). [38][39][40] Whereas in the region below 160 K, the increasing trend then gradually transforms into a declining one. Peculiarly, for temperatures below TC, it is dramatically attenuated and finally reaches ~0.86% at 10 K. All in all, the temperature dependence of ψ possesses the same features and originations as the case of P-PM, in which transformations below 160 K and TC could attribute to the enhanced THz absorption arising from the formation of magnetic correlations. [41][42][43] However, the emergency temperature (225 K) of the THz radiation is far away from the Curie temperature (TC ~68 K) and also above the spin fluctuation temperature (~160 K). 43,44 Moreover, the THz radiation frequency (~0.9 THz/3.7 meV) of Cr2Ge2Te6 crystal is quite larger than its spin excitation gap (~0.28 meV). 45 These two factors imply that the observed THz radiation is not entirely spin related.
Previous studies on semiconductor-based THz sources indicate that the THz radiations are usually assisted by intrinsic phonons in these materials. 46  TP and form a new bosonic quasi-particle, i.e., so called phonon-polariton (P-Polariton). 52,53 After that, these photon pumping induced bosonic P-Polariton could in turn generate far-field EM radiation with frequency close to the original LO phonon as schematically illustrated by process (2) and (3) in Fig. 3b. 21,54 Due to the energy of this bosonic P-Polariton generated THz radiation is carried in the piezoelectricity vibrations, it is reasonable to consider it as a highly efficient bosonic laser-like process. 29,55 Beyond that, according to the further calculations ( Supplementary Information Fig. S5), it was found that the c constant dependent evolution of phonon frequency is consistent with both the experimental results of fc shown in Fig. 2a and the previous reports of spin-phonon interactions. 34 According to the above discussion and the tensor symmetry of 3 structure, it can be predicted that, for a certain THz-Pump field, the electric displacement and corresponding THz radiation should possess a 6-fold in-plane symmetry (see Part Ⅵ of the Supplementary Information). In order to confirm this issue, the in-plane anisotropic dependence of the THz radiation amplitude was investigated by tuning the in-plane azimuth of the sample. As shown in Fig. S6b, it exhibits a cycle of π/3 that matches well with the 6-fold symmetry of the P-Polariton as predicted. In addition, the THz excitation amplitude dependence of the radiation amplitude was also investigated by inserting two THz polarizers after the low-temperature-grown GaAs photoconductive antenna (LT-GaAs-PCA). As shown in Fig. S6d, the radiation and excitation amplitudes are linearly correlated and there is no saturation and threshold observed, which is also in good consistent with the feature of bosonic lasing reported before. 30 These features not only indicate that the radiation effect could be further improved by enhancing the stimulation intensity, but also means that the stimulated irradiation source in Cr2Ge2Te6 is extremely sensitive to the weak THz field (~kV/cm). This is in good accordance with the extremely high sensitivity of Cr2Ge2Te6 to external low-intensity photonic field. 56 Unlike other THz sources based on 2D materials, 8  Different from other 2D semiconductors, Cr2Ge2Te6 holds ferromagnetism. Except electron and phonon, spin is non-negligible degree and it has been demonstrated that there exist strong spin-phonon coupling in Cr2Ge2Te6 and its isostructural Cr2Si2Te6 materials. 34,57,58 As presented in Fig. 2, it is found that not only the c-axis lattice constant but also the amplitude, frequency, and FWHM of the emergent THz emission have abnormal near around the TC of Cr2Ge2Te6 crystal, which also imply the subtle interplays between the phonon-involved THz radiation and spin orders.
Hence, it is reasonable to expected that the THz radiation could also be tuned by external magnetic field (B).
The effect of B on the THz radiations was investigated by the THz-TDS system with a superconductor magnet. The system stability under high magnetic field was verified beforehand (see supplementary Fig. S7a). At low temperatures, there is significant variation of the THz response could be observed when B is applied (see supplementary The magnetic field dependence of Delta RB obtained at corresponding fc and different temperatures were summarized in the Fig. 4a-f. For B//c-axis, the Delta RB is negligible above TC and it is also small (< -5%) below TC. When B//ab-plane, the Delta RB starts to emerge around 160 K and increases with decreasing of the temperature. Notably, at 10 K, the Delta RB in ab-plane could reach the maximum around -20% (with B = 5 T), which is greater than the case of c-axis (~-3%). Such anisotropic feature of the magnetic field modulation effect on Delta RB can be clearly observed in Fig. 4g, in which the temperature dependent Delta RB under B = 5 T is plotted. By applying an external magnetic field, the spin state of the Cr2Ge2Te6 crystal can be modified for both longrange order (below TC) and short-range order (TC <T<160 K). 43,44 As one of the possible mechanism, the magnetic field induced the spin-flips scattering could suppress the electron-phonon interactions as well as the dipole active phonon involved P-Polariton. 59,60 Accordingly, with such large spin-phonon coupling in this 2D ferromagnetic material, the switching of spin state by B would bring the modulation of phonon-related THz emission. Moreover, the spontaneous spin orientation of Cr2Ge2Te6 is along c-axis. And then, from viewpoint of spin modulation, the magnetic field effect is significant when B//ab-plane, which is consistent with our observations shown in Fig. 4. The magneto modulation effect provides another proof for its P-Polariton-related radiation mechanism. All these features not only offer another degree of freedom for the regulation of THz radiation in practical applications, but also provide a convincing evidence for the correlation between the THz radiation, phonons, and spin orders.

Summary
In summary, benefiting from the coherent LO layer-breathing mode, a magnetotunable monochromatic THz radiation was demonstrated in a 2D vdWs ferromagnet Cr2Ge2Te6. After pumping by a broadband THz wave, a strong monochromatic THz irradiation can be generated. The frequency, FWHM, and the intensity of the emergent THz radiation vary with the temperature and its conversion efficiency could even reach 2.1% at 160 K. Our experimental and theoretical analyses indicate that the emergent THz irradiation is from the pump induced phonon-polariton in this 2D vdWs material. Moreover, due to the existing strong spin-phonon coupling, it is interesting to find that such monochromatic THz irradiation can be efficiently modulated by the magnetic field below 160 K. In addition to the general fermionic cases, our findings suggest that the use of 2D vdWs ferromagnet might provide a viable source for the realization of bosonic THz source with tunable and monochromatic features, which may have great practical interests in future applications in photonic and spintronic devices.

Methods
The Cr2Ge2Te6 single crystals are prepared with the self-flux technique, following the procedure described in ref. [61,62]. The effective size of the sample is ~6×4×0.2 mm. The terahertz data was collected with home-built terahertz time domain spectroscopy system (THz-TDS) has been introduced in detail in ref. [63]. The sample is assembled on the sample holder of Oxford Instruments Spectromag He-bath cryostat, with which one could realize test environments of temperature from 10 to 300 K and magnetic field up to 7 Tesla. After propagating through these fused silica windows of the cryostat, the coverage of the THz spectral is from 0.1 to 1.5 THz. The temperature dependent X-ray diffraction (XRD) was measured with the XRD setup using highintensity graphite monochromatized Cu Kα radiation system (Rigaku corporation, Japan). Then, the influence of cooling process on the copper base is excluded and finally obtain the accurate temperature dependent evolution of the lattice constant. According to the time-resolved spectra of the transmitted THz signals, the peak-topeak amplitude of the main waveforms (P-PM) could be easily picked out. Its temperature dependence is depicted in Fig. S1. The evolution of the P-PM divided the temperature coordinate into three regions with the boundaries of 160 K and TC. To be specific, for the main waveforms in time domain, as the temperature drops from 300 K, the P-PM was significantly enhanced until 160 K. Afterwards, along with the temperature further dropped in the range of 160 to 120 K, the upward trend of the P-PM slows down and reaches the maximum. Peculiarly, the P-PM enhancement of 120 K with respect to the 300 K case could reach ~40%. At last, the trend eventually develops into a steep declining one below TC and reaches the minimum at 10 K. According to previous studies on THz responses of semiconductor materials, the enhancement of transmittance at temperature above 160 K could attribute to the attenuated transition of intrinsic carriers among intra-band levels. 1,2 As to the temperature below 160 K, magnetic correlations start to appear and ensuing spin-electron interactions come into play, which dramatically give rise to an absorption in THz range. [3][4][5] As a result, during the cooling process, the competition of these two mechanisms would subsequently bring about the transition and decline of the P-PM amplitude.  According to the inter-layered lattice constant derived from XRD results, the crystal 11 structure of Cr2Ge2Te6 is elongated along c-axis. 9 Consequently, the unit cell of In this part, the in-plane anisotropy and incident THz amplitude dependence of the radiation effect is investigated by performing the in-plane azimuth dependence. For the case of variating azimuth of the sample, due to the degenerated crystal point group of 3, it's sufficient to choose three azimuth angles within the symmetry period (2π/3) to verify the in-plane anisotropy. As shown in Fig. S6a