Introduction

During the last years magnetic kagome metals have emerged as an interesting class of materials due to their unusual properties. In terms of electronic structure, a simple tight-binding model constructed on the kagome lattice is well known to result in dispersionless flat bands and Dirac cones1. Thus, unconventional (localized) carriers due to the correlation effects together with topological states are expected for these materials. Combining such features with magnetism makes magnetic kagome metals suitable to host different types of exotic phenomena, and in this regard, the family of kagome FeSn-binary compounds (FeSn, Fe3Sn, Fe3Sn2) presents several promising candidates. For Fe3Sn2, both the linearly dispersing bands and the flat bands were previously observed experimentally2,3, and recently it attracted great attention after discoveries of massive Dirac fermions2, large anomalous Hall effect4, skyrmion bubbles at room temperature5 and tunable spin textures using an external magnetic field6.

Fe3Sn2 is a layered rhombohedral material belonging to the \(R\bar{3}m\) space group, with hexagonal lattice parameters a = b = 5.3 Å and c = 19.8 Å7. Its crystalline structure is composed of Fe3Sn kagome bilayers, where the Fe kagome network is stabilized with Sn1 atoms and sandwiched between honeycomb Sn2 layers [Fig. 1b, c]. Furthermore, Fe3Sn2 presents an in-plane lattice distortion known as breathing kagome2. Here the length of Fe–Fe bonds varies slightly, generating triangles with two different sizes in the kagome plane, as highlighted in Fig. 1c. Regarding the magnetic structure, Fe3Sn2 is a ferromagnetic material with high ordering temperature, TC ~ 640 K7,8,9. The magnetic moments first align in the out-of-plane direction, and by cooling the system down, the spins realign to the in-plane direction. This process happens in a broad temperature range, around 150 K, and its signatures were observed with several different experimental techniques, such as Mössbauer9,10, neutron diffraction7, electronic transport11, and infrared spectroscopy12. This magnetic transition is also reflected in some of the optical pump-probe results in the present work, which will be discussed in more detail later.

Fig. 1: Optical pump-probe experiment on Fe3Sn2.
figure 1

a Basic schematic of the optical pump-probe experiment in the reflectivity configuration. b Crystal structure of Fe3Sn2, with Fe3Sn1 kagome bilayers and honeycomb Sn2 layers. Sn1 atoms from the trigonal kagome layer and Sn2 atoms from the honeycomb lattice are distinguished using different colors to facilitate the view. c Fe–kagome network centered by the Sn1 atoms and the breathing kagome bonds demonstrated with triangles of different colors. d Optical pump–probe trace of Fe3Sn2 at 300 K with the fluence of 1.6 mJ cm−2. Black dots are experimental data, and the red solid line is the exponential fit according to Eq. (1). Blue dots are the result of subtracting the exponential fit from the experimental data, isolating the oscillatory part of the signal. Inset shows the Fourier transform of the coherent oscillations, with a resonance frequency of about 2.40 THz, corresponding to one of the A1g totally symmetric phonon modes of Fe3Sn2.

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It has been shown that the observed properties of Fe3Sn2 are closely related to the peculiarities of its lattice and magnetic structure2,13. The fingerprints of the non-trivial carrier dynamics have been identified in optical studies12, whereas the interplay of the topological orders with magnetism and strongly correlated electrons is yet to be clarified. The tunability of different contributions is highly desirable, also for possible future applications of Fe3Sn2.

Here, we present an ultrafast optical pump–probe spectroscopy investigation on Fe3Sn2, as shown schematically in Fig. 1a. This method has been extensively used to study the dynamics of non-equilibrium charge carriers and coherent phonons in solids14,15,16,17,18, and it is well suited to study metallic systems19,20,21,22, where different contributions can be identified. So far, the ultrafast dynamics of kagome metals have not been widely explored. There is one report on the magnetic compound GdMn6Sn623 where a low amplitude coherent phonon was observed. The charge-density-wave (CDW) compounds, on the other hand, received a bit more attention with a few reports on CsV3Sb524,25,26 and a recent study on ScV6Sn627, where the ultrafast response of the unusual CDW state has been probed. In this letter, we report the temperature- and fluence-dependent transient reflectivity measurements of Fe3Sn2. Our results reveal strong coherent phonon oscillations in Fe3Sn2, with intriguing similarities to the CDW case, even though no CDW has been reported in Fe3Sn2 as a ferromagnetic Kagome metal. Thus, indicating the electron-phonon coupling as the possible mechanism related to the unconventional carriers in kagome metals.

Results

Figure 1d presents the general behavior of our transient reflectivity measurements. Here, reflectivity change (ΔR/R) is given as a function of the pump-probe time delay at 300 K with pump fluence of 1.6 mJ cm−2. The best fit for all pump-probe traces was achieved with the following equation:

$$\Delta {{{{R}}}}/{{{{R}}}}={y}_{0}+{c}_{1}\exp (-t/{\tau }_{1})+{c}_{2}\exp (-t/{\tau }_{2}),$$
(1)

where c1 and c2 are constants, y0 is an offset parameter and τ1 and τ2 are relaxation times. The time scales of the relaxations are: τ1 in the order of ~1 ps and τ2 in the order of a few tens of picoseconds, both processes will be discussed with more detail as a function of temperature and excitation fluence. The offset term, y0, can be understood as a much longer thermal relaxation, and due to experimental limitations, it had to be approximated as a constant. Another interesting feature is that around the first ~8 ps after pump-probe temporal overlap, the decaying signal is modulated by pronounced oscillations. This is the coherent optical phonon induced by the ultrashort pump pulse that will also be further analyzed as a function of temperature and fluence.

Relaxations

The temperature dependence of the transient reflectivity, the obtained relaxation times, and the offset constant y0 are given in Fig. 2a–d, whereas Fig. 2e depicts c1 and c2, the constants representing the amplitude of the τ1 and τ2 according to Eq. (1), respectively. Figure 2f–j demonstrates the fluence dependence of the same parameters. We limited the time delay to 8 ps, longer time delays can be found in Supplementary Fig. 1.

Fig. 2: Temperature- and fluence-dependence results from the transient reflectivity experiment.
figure 2

a Temperature-dependent optical pump-probe traces of Fe3Sn2 using 0.92 mJ cm−2. The curves at different temperatures are separated by a 0.5 × 10−3 offset. b–e present the Eq. (1) parameters τ1, τ2, y0, c1, and c2, respectively. Fluence-dependent experimental data at 10 K are shown in (f). Panels g–j are τ1, τ2, y0, c1, and c2 as a function of pump fluence. The purple solid line in g is fit for τ1 using the two-temperature model at 300 K. Fluence dependence results for τ1 at all temperatures are quite similar, so for better visualization, the data and the fits at 170 and 10 K were added to the Supplementary Fig. 8. Omitted error bars in panels e, i and j are due to the uncertainty being smaller than the actual points. In panel h the error bars were omitted for better visualization, only the biggest one, at 300 K and 0.35 mJ cm−2 is shown. In all panels, error bars represent the confidence interval of the exponential fitting procedure.

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Due to the metallic nature of Fe3Sn211, τ1, and y0 can be explained using the phenomenological two-temperature model (TTM) for metals19,20,28, where τ1 is the relaxation of the hot electrons, and y0 reflects the dissipation of the residual lattice heating. As given in Fig. 2b, τ1 is temperature independent, lying around 1.1 ps. y0, on the other hand, increases with increasing temperature up to around 175 K, and then it saturates for higher temperatures, indicating that cooling down the sample removes the excess heat and brings the system to equilibrium faster [Fig. 2d]. The fluence dependencies of τ1 and y0 also corroborate this explanation, as seen in Fig. 2g and i, respectively. By simply taking into account the electron/lattice temperature and the electron–phonon coupling, the increase of τ1 with fluence can be nicely reproduced by the TTM model [purple solid line in Fig. 2g]. A similar change has also been observed at 10 K and 170 K (see Supplementary Note 2 and Supplementary Fig. 8 for details about the TTM and the analysis for 10 K and 170 K).

Coming to the τ2, the dynamics behind this process indicate a departure from a simple Drude metal. Considering that the spectra are dominated by the coherent phonon oscillations and the excess heat of the system generates a background, τ2 is more reliably extracted at low temperatures, where y0 vanishes. The τ2 value is weakly temperature dependent [Fig. 2c] changing from 30 ps to ~25 ps with decreasing temperature. At high temperatures, we did not observe any fluence dependence [Fig. 2h]. With the decreasing temperature at lower fluences, a small decrease is present, and it goes into the saturation limit at higher pump fluences.

Previous optical studies12 indicated that Fe3Sn2 is not a simple metal. Its optical conductivity shows two distinct intraband contributions. A sharp Drude contribution is accompanied by a second peak due to the localized carriers (localization peak), which is the common situation on both magnetic and nonmagnetic kagome metals12,29,30,31,32. Considering that the traditional metallic behavior expected for an optical pump-probe experiment is already taken into account by τ1 and y0, we ascribe τ2 to the ultrafast response coming from the localized carriers. Here pumping leads to the delocalization of these unconventional carriers, and we believe to be observing the time scale of the localization process. The amplitude of this process should be proportional to the spectral weight of the localization peak observed in the broadband IR spectroscopy measurements12. Indeed a direct comparison reveals a temperature-independent behavior for both the spectral weight of the localization peak [Fig. S5(e) of Ref. 12] and the amplitude of τ2 [c2 in Fig. 2e].

The temperature-driven dynamics show a different evolution of c1 and c2, as given in Fig. 2e. While with decreasing temperature, c2 does not change, c1 shows a slight increase and saturates below the spin-reorientation temperature. Here the change of the carrier density is probably not related to the change in the Fermi level with temperature, but rather with gapping of certain parts of the Fermi surface upon the reorientation of the spins. With increasing fluence, on the other hand [Fig. 2j], a linear increase is observed for both c1 and c2, which is consistent with the increase of photo-excited carriers at higher fluences.

Phonon mode

Now let us turn to the coherent optical phonon identified in the spectra. These laser-induced oscillations are generated by the lattice atoms vibrating in phase to each other, and measured as a periodic modulation of the optical properties18,33,34. In Supplementary Note 1 the details regarding data analysis for the resonance frequency and amplitude of the mode can be found. Such coherent phonon oscillations are reported for different systems in the literature18,34,35,36,37,38. However, the strength of these oscillations in the current measurements is an interesting finding. Such strong oscillations are usually observed in systems with CDW instabilities and other types of collective order as for example in the case of K0.3MoO339,40, VO241 and the kagome CsV3Sb5−xSnx42 with a coherent phonon that becomes Raman-active only through coupling to the CDW order. Fe3Sn2, however, is not known to host any of such instabilities. Elemental crystal systems without CDW may also present such strong features, like Bi34,43 and Sb18, however, in both cases, there is at least a periodic lattice modulation related to the excited mode. On the other hand, the correlated nature of the kagome metals has been identified by different means, including the observation of the aforementioned localization peak in the optical spectra. Here, the intraband carriers are damped by the back-scattering from the collective modes, which in principle, can have any bosonic excitation as the origin. Our observation of this unusual phonon coupling makes phonons a plausible candidate for this collective mode.

Figure 3a–c depicts the temperature dependence of the obtained phonon parameters, namely the resonance frequency, amplitude, and width. Its frequency, retrieved using a Fourier transform, was found to be around 2.40–2.50 THz, which corresponds to an A1g totally symmetric mode44. As also shown in Fig. 3, this is primarily an Sn mode where the Sn1 atoms from the center of the hexagons in the kagome plane move only in the out-of-plane direction. Thus, it does not affect the Kagome network significantly. The mode is dependent on both temperature and magnetic structure, presenting a clear phonon softening with increasing temperature and anomalies on its amplitude and peak width around the spin reorientation temperature range (~150 K). The shaded area in Fig. 3a–c highlights this temperature range where the magnetic transition takes place. While the spins realign from out-of-plane to in-plane the phonon amplitude shows a plateau-like behavior. The phonon softening and the increase of the amplitude of the phonon oscillations have also been observed with increasing fluence, as shown in Supplementary Fig. 5.

Fig. 3: Coherent phonon evolution with temperature and comparison with DFT optical conductivity calculations.
figure 3

Temperature dependence of a frequency, b amplitude, and c width of the A1g phonon mode in Fe3Sn2. The shaded area in a–c is to highlight the temperature range where the system goes through a spin reorientation. The lines in b are guides to the eyes. d Presents the calculated optical conductivtiy via DFT for the nominal Fe3Sn2 along with the distorted structure under A1g phonon mode. e Depicts the change in optical conductivity under the influence of the phonon mode. The orange circles are the change of the optical conductivity estimated by changing the experimental reflectivity12 by 10−3. The red line in d and e is the pump–probe frequency of 800 nm. f Difference in the optical conductivity with respect to the nominal value for all the A1g modes, with Ph1 being the one measured in our experiments. Bilayer kagome structure has been given on top of f with the representation of the A1g phonon mode demonstrated with the red arrows. Error bars in panel a are smaller then the points, therefore, they were omitted. For b and c, the error bars show the standard deviation considering all the temperature-dependent measurements.

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Phonon softening with temperature and fluence is often attributed to anharmonic terms in the vibrational potential energy45,46. However, other signatures of these anharmonic effects are not observed in our data. For instance, the amplitude does not follow the expected increasing behavior with decreasing temperature and shows a plateau around the spin reorientation temperature. Furthermore, the width does not show a monotonous decrease with decreasing temperature. In fact, it hardly changes. Other evidence against the anharmonic phonon softening is that the decay rate of the phonon does not change significantly with temperature (see Supplementary Fig. 3). To be sure about the behavior of all the phonon parameters, we measured the temperature dependence more than once. Figure 3a–c presents an average from the different data sets.

Along with the evidence against the anharmonic phonon coupling, the absence of Eg phonon modes, the cosine-like character of the oscillations, shown in Supplementary Fig. 4, and the large amplitude of the oscillations when compared to the non-oscillatory decaying signal (also increasing linearly with fluence), are strong indications of displacive excitation of coherent phonons (DECP) as the mechanism behind this coherent phonon generation47. This indicates a strong electron–phonon coupling in Fe3Sn2 in both low and room-temperature regimes, as DECP depends exclusively on this coupling to induce coherent oscillations. The maximum of the non-oscillatory exponential decay increases with fluence, indicating a larger photo-excited carriers density at higher fluences, and then a considerable electronic softening of the lattice is expected37,48. As a consequence, the reduction of the restoring force for the A1g lattice displacement appears naturally with the excitation of a larger number of electrons. Thus, this phenomenon can be understood as solely an electronic softening of the crystal lattice.

Discussion

Such a strong phonon coupling suggests some sort of an incipient lattice distortion in Fe3Sn2. At first glance, the breathing kagome distortion [Fig. 1(c)], where the successive Fe-bonds in kagome network are slightly different, is a reasonable cause. On the other hand, in this case, it is expected that the breathing Eg mode, which directly affects the kagome network, would be the phonon that modulates reflectivity. Considering that the observed A1g mode does not affect this breathing kagome structure, this assumption seems to be unlikely. This, therefore, distinguishes Fe3Sn2 from systems like Bi and Sb, where as discussed earlier, the strong reflectivity modulation can be understood solely in the context of a periodic lattice distortion, raising again the question of why such high coherent phonon amplitude is present in Fe3Sn2.

Another possibility why Fe3Sn2 is special lies in the proclivity of kagome metals for CDW instabilities that have been revealed not only in nonmagnetic compounds like AV3Sb5 and ScV6Sn624,25,49,50, but also in the magnetic kagome metal FeGe51. Our data support growing evidence that even in the absence of a CDW transition, charge carriers in kagome metals can be strongly coupled to specific phonons that, in turn, have a crucial effect on their dynamics.

Finally, we use density-functional-theory (DFT) to elucidate the effect of the A1g phonon mode on the optical conductivity, details of the calculations are given in Supplementary Note 3. We have introduced the atomic displacements due to the phonon mode, as demonstrated in Fig. 3, and calculated the optical conductivity as given in Fig. 3d. The displacement amplitude is taken as 0.1 Å, which is consistent with the estimated atomic displacement (see Supplementary Fig. 10). To demonstrate changes in the optical conductivity, and ensuing changes in the reflectivity, we have plotted in Fig. 3e the difference in optical conductivity with respect to the undistorted structure. The results suggest that at 800 nm [red line in Fig. 3e], the observed 2.5 THz phonon mode has a strong impact on the optical conductivity and can clearly be the reason behind the observed 10−3 change in the reflectivity (the orange circles are the estimates over the experimental reflectivity spectra). The distortion of the structure in two opposite directions nicely leads to a symmetric change of the optical conductivity. For comparison, changes in the optical conductivity induced by all four A1g modes have also been calculated, as shown in Fig. 3f (details about the lattice displacement of the three other modes are presented in Supplementary Fig. 9). Such results suggest that at 800 nm, the most prominent change is due to the observed 2.5 THz A1g mode, and other modes do not alter the optical conductivity significantly. These calculations may also explain why we could measure only a single phonon mode as a reflectivity modulation while the other totally symmetric A1g modes were not observed.

In summary, photo-induced changes in reflectivity of the kagome metal Fe3Sn2 reveal the dynamics of carriers and coherent optical phonons rendering Fe3Sn2 different than conventional metals. We detect three time scales. Two of them, the faster and slower ones, are clearly related to the highly metallic nature of the material and can be well explained using the two-temperature model for conventional metals. Regarding the medium time scale, on the other hand, we believe to be probing the localization time of the unconventional carriers that get delocalized due to laser pumping. Their distinct relaxation time and coupling to short optical pulses allow an independent probe of Drude and localized carriers, as well as the control of localization using ultrafast optical probes. Additionally, strong coherent phonon oscillations have been observed, indicating a strong electron-phonon coupling in Fe3Sn2 even at room temperature. The nature of this phonon mode is attributed to the electronic softening of the crystal lattice due to the large photo-induced carrier density. The spin reorientation of Fe3Sn2 around 150 K does not seem to have a significant effect on the dynamics of charge carriers, although it manifests itself in the temperature dependence of the coherent phonon. In conclusion, our study demonstrates the salient role of phonon dynamics and electron-phonon coupling even in those kagome metals where no CDW instabilities occur.

Methods

Sample details

Single crystals of Fe3Sn2 were grown using the self-flux method as described elsewhere11. The (001)-plane with lateral dimensions of 1000 μm × 800 μm × 200 μm is used for the optical pump–probe transient reflectivity measurements. We used the same as-grow sample as in our previous infrared spectroscopy study12.

Transient reflectivity measurements and data analysis

Temperature- and fluence-dependent optical pump-probe experiments were performed in the reflection geometry. For both pump and probe, we used 60 fs long laser pulses, centered at 800 nm and generated by a Ti:sapphire laser amplifier with 250 kHz repetition rate. The probe spot on the sample surface was around 25 μm (FWHM), while the pump was 35 μm (FWHM). Transient reflectivity was measured up to 150 ps delay time with 1 ps time resolution. Up to around 9 ps delay time, we increased the time resolution to 33 fs to resolve the phonon oscillations.

The overall temperature and fluence dependence of the transient reflectivity does not change drastically and can be fitted solely by employing Eq. (1). By subtracting this fitting from the experimental data, it is possible to isolate the oscillations. The fast Fourier transform (FFT) of these oscillations gives the resonance frequency of the phonon mode that couples to the electronic background. Using a Lorentzian function we fitted the FFT spectrum in order to obtain the amplitude and the width of the phonon mode, as discussed in the main text.

Density functional theory calculations

Density-functional-theory (DFT) calculations of the band structure were performed in the Wien2K52,53 code using the Perdew–Burke–Ernzerhof flavor of the exchange-correlation potential54. We used experimental structural parameters determined by X-ray diffraction measurements. The optic module55 was used for evaluating the optical conductivity. Spin-orbit coupling was included in the calculations of band structure and optical conductivity. Furthermore, ferromagnetic order was taken into account, where the spins on Fe-atoms are aligned along the in-plane direction, which eventually occurs below the spin-reorientation temperature. The DFT-obtained magnetic moment per Fe-atom was 2.18 μB, which is very close to the experimental values11. Self-consistent calculations were converged on the 24 × 24 × 24 k-mesh. Optical conductivity was calculated on the k-mesh with up to 100 × 100 × 100 points within the Brillouin zone.

The phonon calculations were performed in VASP using the same structural parameters and the built-in procedure with frozen atomic displacements of 0.015 Å. Magnetic moments were directed along the c-axis to avoid symmetry lowering.