Strong laser polarization control of coherent phonon excitation in van der Waals material Fe3GeTe2

Optical manipulation of coherent phonon frequency in two-dimensional (2D) materials could advance the development of ultrafast phononics in atomic-thin platforms. However, conventional approaches for such control are limited to doping, strain, structural or thermal engineering. Here, we report the experimental observation of strong laser-polarization control of coherent phonon frequency through time-resolved pump-probe spectroscopic study of van der Waals (vdW) materials Fe3GeTe2. When the polarization of the pumping laser with tilted incidence is swept between in-plane and out-of-plane orientations, the frequencies of excited phonons can be monotonically tuned by as large as 3% (~100 GHz). Our first-principles calculations suggest the strong planar and vertical inter-atomic interaction asymmetry in layered materials accounts for the observed polarization-dependent phonon frequencies, as in-plane/out-of-plane polarization modifies the restoring force of the lattice vibration differently. Our work provides insightful understanding of the coherent phonon dynamics in layered vdW materials and opens up new avenues to optically manipulating coherent phonons.


INTRODUCTION
Coherent phonon is the quantized in-phase lattice vibration in solids. It is a fundamental medium to explore various quantum systems, including quantum dots 1,2 , superconducting qubits [3][4][5] , and integrated photonic devices [6][7][8][9] . Coherent phonon could easily reach terahertz (THz) regime and become the basis for paradigm shift in various fields including high-frequency electronics 10,11 , information technology 12,13 , and medical diagnostics 14 . THz phonons could potentially reduce the footprint of phononic devices, improve spatial resolution of imaging techniques, and boost the speed of acousto-electronic/optical devices by several orders of magnitude compared to traditional ultrasonics in MHz frequencies.
Underlying all the aforementioned prospects, the ability to control coherent phonon frequency has far-reaching significance 15 , especially in the emergent two-dimensional (2D) materials where the atomic layer thickness allows highly designable and manipulable inter-atomic interactions for phonon control. However, the phonon frequency control in 2D materials has thus far only been realized via doping, strain, structural and thermal engineering. For example, the phonon frequency can be controlled over 500 GHz in graphene by doping 16,17 . The softening of phonon with increased strain has been observed in MoS 2 18,19 , and the phonon modes E 1 2g and A 1g in MoS 2 can be also shifted by adjusting the thickness (i.e., layer number) 20,21 or by changing the temperature 22,23 . These approaches are either slow or irreversible.
In layered vdW materials, the atoms are bound with strong covalent bonds inside each constituent layer, while the adjacent layers are held together by weak vdW force. This unique structural feature generates strongly anisotropic physical properties. Hence, anisotropic electron, phonon and magnon coupling as well as their transport properties may be achieved in vdW materials. For example, the manipulation of thermal conductivity may be realized by exploring the phonon transport across a vdW interface [24][25][26][27] . The interaction between coherent phonons and charge carriers could lead to new paths for the generation of microwave frequencies, as the cases that have been explored for nanoelectromechanical systems in the MHz-GHz frequency regime 28 , for piezoelectric heterostructures in the sub-THz regime 29 , and for semiconductor devices such as Schottky diodes 11,30 as well as tunneling devices 10 . Because of strong elastic anisotropy and phonon quantization, layered vdW materials could be ideal platforms for phonon nanoscopy 31 and nondestructive imaging for molecules and cells coupled to vdW layers.
Therefore, understanding and manipulation of phonon frequency become increasingly attractive in vdW materials including graphene, transition metal dichalchogenides (e.g., MoS 2 and WS 2 ), metal chalcogenides (e.g., InSe and GaSe), hexagonal boron nitride (h-BN), to name a few 32 . However, although structural and temperature/thermal engineering of phonon frequency have been achieved in vdW materials, these approaches are not suitable for high speed/frequency microscopic phononic applications. It is desirable to have non-thermal and swift control of phonon frequency in layered vdW materials. So far vdW materials have shown a wide variety of fascinating physical phenomena. Take Fe 3 GeTe 2 as an example, it has shown 2D itinerant ferromagnetism [33][34][35][36] , topological nodal lines 37 , tunneling spin-valve behavior 38 , heavy fermion states 39 , manipulable magnetic domains 40,41 , and strong electron correlation effects 42 . However, the nonthermal control of coherent phonon frequency has not been accomplished in vdW materials to the best of our knowledge.
Here, we apply time-resolved pump-probe technique to generate and study coherent phonons in exfoliated vdW Fe 3 GeTe 2 flakes. The experimental results and theoretical calculations confirm that the observed oscillation in reflectivity is attributed to the A 1g phonon mode (~3.5 THz). In order to take advantage of the heavily asymmetric in-plane and out-of-plane interactions in vdW layer, we launch the pump laser beam at a large angle (70°) with respect to the normal to the vdW layer which enables out-ofplane electric field component during excitation. Surprisingly, we observe around 3% phonon frequency modulation (~100 GHz) for the phonon mode generated by in-plane and out-of-plane polarized pump pulses. The phenomenon is reproducible in multiple flakes. The power dependent measurements are also carried out with fixed laser polarization and no obvious frequency modulation is observed which indicates a non-thermal origin of such phonon frequency control. We attribute the observed phonon frequency modulation to the modulation of restoring force of the lattice vibration in Fe 3 GeTe 2 based on the orientation of laser polarization. Our findings contribute to the understanding of coherent phonon dynamics in vdW materials and the development of high speed phononic devices.

Morphology and polarization dependent transient reflectivity of Fe 3 GeTe 2 flake
The morphology of the exfoliated Fe 3 GeTe 2 flake is mapped out by Atomic Force Microscope (AFM) as shown in Fig. 1(a) (The AFM image for the other sample is shown in the supporting information). The size is about 4 × 5 um 2 , while the thickness is around 35 nm (about 44 layers), see inset of Fig. 1(a). The timeresolved pump-probe reflectivity measurements have been applied to vdW materials 43,44 . The setup splits the femtosecond pulsed laser beam (800 nm) from a Ti-Sapphire oscillator into two beams. One is used as pump beam and the other is called probe beam. Both beams are focused on the sample at the same spot. We use the femtosecond laser pulse (50 fs) in the pump beam to generate excitations and monitor the reflectivity of probe beam by varying the time of the probe pulse arriving the sample spot. In the conventional time-resolved pump-probe reflectivity measurements, the pump beam is incident perpendicular to the sample surface, which limits the orientation of pump pulse electric field only in the sample plane. In our experiments, we enable the outof-plane electric field component in the pump pulses by tilting the incident pump beam to investigate the effect of the electric field orientation on the coherent phonon excitation and relaxation in the transient reflectivity spectra. As shown in Fig. 1(b), the pump beam is sent into the sample about at 70°angle with respect to the normal to the sample surface. We define the S-polarization as 0°(in blue) and P-polarization as 90°(in green). Thus 0°p olarization has only in-plane electric field component while 90°p olarization can exert significant out-of-plane electric field to the sample. See Supplementary Fig. 1 in the supplementary information for further description about the experimental setup.
The transient reflectivity spectra are plotted in Fig. 1(c) as a function of pump laser polarization (probe is S-polarized throughout the experiments). All the measurements were conducted under ambient temperature. The spectra in Fig. 1(c) start with strong fluctuations around delay time t = 0 which represent the initial excitation of hot carriers when the pump pulse just arrives the sample followed by superposition of a periodical oscillation signal and exponential decay signal. The oscillation signal is attributed to the coherent phonon excitation in the sample 45 . The large exponential decay background is due to the hot carrier relaxation through lattice. Intriguingly, as the pump polarization is rotated from 0°(in-plane) to 90°(out-of-plane), we notice a small shift in the oscillation peak/valley positions which indicates a slightly altered coherent phonon frequency as a function of pump polarizations (see the dashed line in Fig. 1(c)). To further confirm it, we did numerical fittings to each transient reflectivity spectrum. The transient reflectivity signal can be approximated mathematically by a summation of exponential decay function and a damping oscillation function: where A c and τ c are the amplitude and relaxation time for hot carrier excitation corresponding to the large decay background in the signal. A p , τ p and f p are amplitude, lifetime, and frequency of the coherent phonon, respectively and φ is the oscillation phase angle. The extracted coherent phonon frequency as a function of pump laser polarization given by Eq. (1) is plotted in Fig. 1(d). It turns out that the frequency of the coherent phonon is indeed modulated by the laser polarization. The phonon frequency monotonically increases when the pump polarization is varied from in-plane (0°) to out-of-plane direction (90°). The modulation of phonon frequency by the orientation of the pump polarization by~3% (100 GHz) is remarkable since the thermal control of similar phonon frequency change would require a temperature change of~360 K 44 . Furthermore, our result shows the ability to continuously control the phonon frequency which has interesting potential applications for high frequency phononic circuit/devices. Figure 2(a) displays a fit of transient reflectivity data under pump polarization 0°to Eq. (1). The coherent phonon frequency is extracted as 3.42 ± 0.02 THz. The fit to transient reflectivity data under 90°pump polarization in Fig. 2(b) gives a coherent phonon frequency of 3.53 ± 0.02 THz. There is very good agreement between the numerical fitting curves (red solid lines) and the experimental data in both cases. The obtained phonon frequency shift is about 3% (~100 GHz) for the two different pump polarization configurations, which is consistent with the observation in Fig. 1(c) and (d). We further plot the simulated phonon oscillations in transient reflectivity without the decaying background as shown in Fig. 2(c). It is obvious that the mismatch of oscillation peak and valley positions becomes more and more significant upon increasing the delay time, which indicates that the coherent phonon frequency is different in the two pump polarization configurations. This is exactly what happens when we use phonon frequency numerically extracted from 90°pump polarization configurations to fit the 0°data as shown in Fig. 2(d). We see that the discrepancy between the numerical fit (red solid line) and experimental data (blue solid line) becomes larger and larger in the longer time domain (e.g., 1-3 ps). Such laser polarization control of coherent phonon frequency is repeatable on different samples in our experiments (see Supplementary Fig. 2 in the supplementary information). The coherent phonon frequency is always higher (by about 3%) in the pump polarization 90°configuration than the 0°configuration. In other words, when the pump polarization is in the sample plane, the excited coherent phonon frequency is relatively low, while it increases about 100 GHz when the pump polarization becomes out of sample plane. These results and AFM images of additional samples can be found in the supporting information. In addition, to prove that the observed frequency modulation by laser polarization is indeed because of 2D vdW material (with the in-plane/out-of-plane) structural anisotropy, we also did the same pump polarization dependent transient reflectivity experiments with the same pump and probe incident configuration on a 2 nm CoFeB thin film sample, and the spectra are shown in the supporting information ( Supplementary Fig. 3   spectrum on substrate ( Supplementary Fig. 4 in the supplementary information) shows no oscillatory signal, which confirms that the transient reflectivity signal from substrate does not contribute to the coherent phonon oscillation signal.

First-principles calculations
To understand the observed laser polarization control of coherent phonon frequency in Fe 3 GeTe 2 , we calculated the phonon band structures of bulk Fe 3 GeTe 2 by density functional theory (DFT). The phonon dispersion of Fe 3 GeTe 2 can be observed in Fig. 3(a). The high symmetry path is Γ-M-K-Γ, the longitudinal acoustic (LA) and transverse acoustic (TA) branches correspond to vibrations within the plane, and the other mode (ZA) corresponds to out-of-plane vibration. It is worth mentioning that there is no imaginary frequency near the Γ point, which indicates that the structure is thermodynamically stable.
The crystal structure of Fe 3 GeTe 2 is p63/MMC space group [see Fig. 3(b)] with the A 1g mechanical representations. The Fe and Ge atoms located at 4e and 4 f Wyckoff positions compose the A 1g Raman active modes. To be specific, 4 Fe atoms at the 4e Wyckoff position vibrate in the out-of-plane direction, which is the same for 4 Te atoms at the 4 f Wyckoff position [see Fig. 3(b)]. We also calculated the vibration eigenvector of the Raman active A 1g mode. The phonon frequency of this A 1g vibrational mode is 3.86 THz, which is labeled as a red star in the phonon dispersion in Fig. 3(a). Note that the phonon frequency obtained in our experiments is around 3.50 THz, which is a little off from the calculated value. The discrepancy can be attributed to (1) the firstprinciples calculations are carried out at absolute zero temperature, but as the temperature increases, the phonon frequency normally decreases due to lattice expansion 44,46 , and (2) sample size effect: the first-principles calculations are carried out for bulk crystal, while experiments are conducted on nano-films or finite thickness. Raman spectroscopy is an important experimental method to characterize solid phonon physics, which reflects the magnitude of the quantized energy of lattice vibration. The vibrational frequency of the A 1g mode obtained by Raman spectroscopy in Fe 3 GeTe 2 flakes at room temperature and with similar sample size is in great agreement with our experimental observations 46 . The origin of the phonon is lattice vibration in which the interactions between atoms (restoring forces) essentially determine the vibration frequencies. It has been reported that, in 2D materials (e.g., MoS 2 ), the frequency of A 1 g phonon mode shows redshift with a decreasing number of layers which is attributed to the weakening of the restoring forces acting upon vibrations while the E 2g phonon mode blueshifts [47][48][49][50] . It is known that the vibration of atoms in A 1g phonon mode is out-of-plane (refer to monolayer plane) while that of E 2g phonon mode is inplane. The opposite response of phonon frequency for A 1 g and E 2 g mode in 2D materials may root in the heavily asymmetric inplane/out-of-plane inter-atomic interactions and suggests the possibility to control the phonon frequency by instantaneous modification of restoring forces, e.g., through laser polarization.
To obtain further insight into the phenomenon, we calculated the electronic charge distribution for different atoms in Fe 3 GeTe 2 lattice as shown in Fig. 4(a). It can be shown that electron distributions around Fe, Ge, and Te atoms show different levels of overlap between each other which qualitatively represent the interaction between neighboring atoms. A comparison of the electronic charge distribution overlap along in-plane orientation (a and b axes) and out-of-plane orientation (c-axis) shows that the electron distribution overlap between Fe-Fe and Te-Ge-Te along the out-of-plane orientation is much stronger than that along the in-plane orientation. This agrees with the fact that the highly symmetric in-plane/out-of-plane interactions exist in Fe 3 GeTe 2 lattice and potentially can be selectively excited by the laser pulse with different polarization orientations. It has been reported that the ultrafast laser pulses can induce transient superconductivity up to room temperature in YBa 2 Cu 3 O 6+x 51,52 . Later femtosecond X-ray diffraction experiments showed that the ultrafast lattice excitation induces modification in the Cu-O 2 intra-bilayer and inter-bilayer distances, accompanied by anisotropic changes in the in-plane O-Cu-O bond buckling 53 . In 2D materials, the coherent light-matter interaction that can control the symmetry breaking in WS 2 54,55 , WSe 2 56,57 , and symmetry switching in ZrTe 5 58 has been observed 59 . The ultrafast phase transition in 2D VSe 2 has also been reported and attributed to electron-lattice interaction 60 . Most recently, Afanasiev et.al., has demonstrated non-thermal lattice control through mid-infrared electric field pulses driven phonons to manipulate the magnetic interactions in DyFeO 3 61 . Moreover, the photoinduced magnetic anisotropy in two-dimensional van der Waals (vdW) antiferromagnet NiPS 3 shows the control of the magnon amplitude by pump laser polarization 62 . In our case, the polarization of femtosecond laser pulse essentially represents the direction of few-cycle oscillating electric field with super high frequency. In our experimental configuration, the pump laser is incident with large tilted angle which provides maneuverable inplane and out-of-plane polarization/electric field components. It is possible that the laser pulses with different polarizations are Y. Gong et al. coupled to the anisotropic electron-lattice interaction in Fe 3 GeTe 2 asymmetrically (in-plane/out-of-plane) and modify the restoring force for A 1g phonon mode, which in turn induce the phonon frequency modulation.
Laser power dependent transient reflectivity of Fe3GeTe2 flake In addition, we conducted pump power dependent transient reflectivity measurements with a fixed pump polarization (90°) to further understand the origin of the observed coherent phonon frequency control. Based on previous reports 44 , the phonon frequency varies slightly with temperature which may be due to the thermal expansion of the lattice. Thus, one of the hypotheses for the phonon frequency modulation is based on the thermal origin in which the absorption of pump pulse energy under two orthogonal pump polarizations is significantly different causing substantial local temperature difference, in turn changing the phonon frequency. In transient reflectivity experiments, pump laser power is usually proportional to the local temperature on the sample surface. If the thermal effect is the major contribution, the pump laser power should also be able to tune the phonon frequency. Figure 4(b) shows the transient reflectivity spectra under 90°pump polarization at different pump laser powers. Under low pump laser power (e.g., 10 mW), the coherent phonon excitation is very weak so the oscillations in the spectrum are rough even after averaging over 40 times. Under high pump laser power (e.g., 124 mW), the oscillations are clear, but the lifetime is very short compared to those measured under intermediate pump laser powers (e.g., 33 mW and 107 mW). This is attributed to the thermal effect induced phonon scattering that significantly shortens the coherent phonon lifetime, which indicates comparatively high local temperature in a 5 μm size flake when compared to, for example, 33 mW case. However, the oscillation peak and valley positions for all four spectra match with each other very well, which shows almost no frequency modulation by pump power within our achievable range. Hence, the thermal effect is unlikely the major contribution to the observed pump polarization control of coherent phonon frequency.

DISCUSSION
In summary, we report an efficient control of coherent phonons in Fe 3 GeTe 2 by changing laser polarizations. Unlike the conventional time-resolved pump-probe experiments, our pump laser beam used a very large angle of incidence (70°) with respect to the sample plane which enables out-of-plane electric field component when rotating the laser polarizations. A wide-range phonon frequency modulation by about 3% (100 GHz) was observed. Our firstprinciples calculations reveal asymmetric in-plane and out-of-plane inter-atomic interactions in Fe 3 GeTe 2 allow the laser pulse with different polarization orientations to couple to the anisotropic electron-lattice interactions and modify the vibration stiffness/ restoring force of A 1g phonon mode asymmetrically. Moreover, the pump power dependent transient reflectivity results show no obvious coherent phonon frequency modulation confirming a nonthermal origin for such manipulation. Our findings not only provide the fundamental understanding of the coherent phonon dynamics in layered materials but also exhibit the significance of phonon frequency modulations for the development of high frequency phononic devices.

Sample preparation
The bulk Fe 3 GeTe 2 single crystals were synthesized by chemical vapor transport method, and Fe 3 GeTe 2 flakes were mechanically exfoliated and deposited on 260 nm-thick-SiO 2 /Si chips.

Transient reflectivity measurements
The transient reflectivity results were collected by time-resolved pumpprobe spectroscopy. The pump beam was modulated by a mechanical chopper at 1.5 kHz. The probe beam was sent into an objective (perpendicular to the sample surface) to be focused onto micrometersize samples. The probe reflectivity as a function of time delay between pump and probe pulses was collected by the same objective and read by a balanced detector. The transient reflectivity change was eventually determined and output by a lock-in amplifier.

Density functional theory
Our first-principles calculations are based on DFT using the projector augmented wave method as implemented in the Vienna ab initio simulation package [63][64][65] . The second-order interatomic force constants were calculated by the finite displacement method and the phonon dispersion was then obtained by using the Phonopy package.

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