In their comment to our paper1 on the observation of anomalous acoustic phonon dispersion in SrTiO3 (STO), Devos et al.2 present results obtained by stimulated Brillouin scattering on the very same system (STO(001) capped with Al) over an extended probe wavelength range. By using a different setup employing distinct probe wavelengths (λpr) from a tunable Ti:sapphire oscillator in the 370–510 nm range, they found a substantial disagreement with our data around 440 nm for the frequency of oscillation (f) of the differential reflectivity, which is related to the sound speed (vs) by the formula: , where n is the refractive index of STO. On the other hand Devos et al. found a nice agreement with the expected behaviour for f in case of linear acoustic phonon dispersion, which corresponds to a constant sound speed.
Stimulated by this comment, we built up a new broadband picosecond acoustics (PA) setup to extend our measurement range towards lower photon wavelengths. To this purpose, we replaced the sapphire plate, generating the white-light continuum (WLC) used as a probe beam, with a CaF2 plate, slowly moved in the focus to avoid photodegradation; this shifted the WLC cut-off from 440 nm (for sapphire) down to ≈330 nm (for CaF2). Noteworthy, in this new setup, we employed a self calibrated spectrometer, whose accuracy on each wavelength is lower than 1 nm, thus avoiding any possible artefact coming from manual calibration with interferometric filters, as in our original setup.
The frequency of oscillation f is shown in Figure 1, where we compare the new data (green thick curve) with those from our original paper (red thin curve) and with the expected frequency for a constant sound speed of 7900 m/s (dashed black line). The agreement between the new and old data is good at large wavelengths but a clear deviation appears below 480 nm. Noteworthy the new experimental oscillation frequencies are perfectly superposed with those expected for a constant sound velocity in STO, corresponding to a linearly dispersive behaviour, down to 355 nm.
Frequency of oscillation of the differential reflectivity as a function of the probe wavelength: (red thin line) previously published data, (green thick line) new data, (dashed black line) theoretical curve for constant sound speed.
Frequency of oscillation of the differential reflectivity as a function of the probe wavelength: (red thin line) previously published data, (green thick line) new data, (dashed black line) theoretical curve for constant sound speed.
These data clearly demonstrate that our original measurements were not accurate in the low wavelength range, most probably due to an incorrect manual calibration of the spectrometer in this range.
To summarize, having extended the wavelength range of the probe pulse and improved the accuracy of our spectrometer, we can conclude that there is no anomalous acoustic phonon dispersion from 75 to 130 GHz along the (001) direction of STO, i.e. up to phonon wave vectors of about 100 rad/µm. The sound speed of STO appears to be constant at 7900 m/s in this frequency range, in agreement with the fact that the phonon wave vectors probed in this experiment are very close to the center of the Brillouin zone.
These results show that broadband PA can be used to measure sound speed and attenuation in a broad frequency range, providing that a good accuracy in the spectrometer calibration is achieved.
