Comparison of coherent phonon generation by electronic and ionic Raman scattering in ${\mathrm{LaAlO}}_3$

In ionic Raman scattering, infrared-active phonons mediate a scattering process that results in the creation or destruction of a Raman-active phonon. This mechanism relies on nonlinear interactions between phonons and has in recent years been associated with a variety of emergent lattice-driven phenomena in complex transition-metal oxides, but the underlying mechanism is often obscured by the presence of multiple coupled order parameters in play. Here, we use time-resolved spectroscopy to compare coherent phonons generated by ionic Raman scattering with those created by more conventional electronic Raman scattering on the nonmagnetic and non-strongly-correlated wide-band-gap insulator ${\mathrm{LaAlO}}_3$. We find that the oscillatory amplitude of the low-frequency Raman-active $E_g$ mode exhibits a sharp peak when we tune our pump frequency into resonance with the high-frequency infrared-active $E_u$ mode, consistent with first-principles calculations. Our results suggest that ionic Raman scattering can strongly dominate electronic Raman scattering in wide-band-gap insulating materials. We also see evidence of competing scattering channels at fluences above $28\mathrm{mJ}/{\mathrm{cm}}^2$ that alter the measured amplitude of the coherent phonon response.

Figure 1

(a) Temporal evolution of the pump field according to Fourier-filtered electro-optic sampling (see text for details). The inset shows the power spectral density. The yellow-shaded area is the support of the Fourier filter for the temporal evolution. (b) Time dependence of the ellipticity change $S$ for various pump fluences. The data are shown together with fits (black lines, see text). The curves are offset for clarity. The inset shows how the amplitude $A$ changes with fluence $F$. Both panels share the delay-time axis and the pump pulse displayed in (a) corresponds to a fluence of $29.9\mathrm{mJ}/{\mathrm{cm}}^2$.

Figure 2

Fluence dependence of the oscillations at different pump frequencies. (a) Scaling of the $E_g$ mode amplitude $A$ with the fluence calculated using Eq. (1) for various pump spectra including linear fits up to the fluence $F_{\mathrm{c}}$ (dashed vertical line). (b) Different normalized pump spectra featuring Gaussian fits (black lines). The colors of the spectra in (b) correspond to the data points and fits shown in (a).

Figure 3

Spatially resolved maps of a selected area of the sample. (a) Optical microscope image showing stripes oriented along the [0 1 0] direction (indicated by the arrow), (b) amplitude $A$ on logarithmic color scale, and (c) phase $\varphi$ on a linear color scale, extracted from fits of transient data taken at each point to Eq. (2).

Figure 4

Fluence-corrected scalings $a_{\mathrm{corr}}\left({\nu }_{\mathrm{p}}\right)$ (points, left axis) of the $E_g$-phonon amplitude and calculation values of the phonon-amplitude responses (lines, right axis) on logarithmic scales. For $a_{\mathrm{corr}}$, the ${\nu }_{\mathrm{p}}$ values are set according to the center of mass of the excitation spectrum, of which the horizontal error bars indicate the FWHM. We show the calculated frequency-dependent amplitudes of both the Raman-active $E_g$ mode $Q_{\mathrm{R},0}$ and the infrared-active $E_u$ mode $Q_{\mathrm{IR},0}$.

Figure 5

Outline of the experimental setup. The pump path is shown in blue, while the probe path is shown in orange. The inset shows an illustration of the probe beam interacting with the pump beam inside the material.

Figure 6

Normalized reflectivity changes for pump wavelength 800 nm (375 THz) and probe wavelength 400 nm, as described in the text. The solid curve shows a fit according to Eq. (2), with parameters $A=0.13\pm 0.04\%,B=-0.0002\pm 0.0009\%,\nu =0.95\pm 0.02\mathrm{THz},\varphi =1.5\pm 0.3\mathrm{rad},{\tau }_{\mathrm{R}}=0.8\pm 68\mathrm{ps},{\tau }_{\gamma }=1.5\pm 0.2\mathrm{ps}$. The parameters $B$ and ${\tau }_{\mathrm{R}}$ have large relative uncertainties since there is no significant background offset.

Figure 7

Calculated values of the $d$ component of the frequency-dependent Raman tensor [see Eqs. (B1) and (B2)] over a broad spectral range up to the band gap.