Spectral and spatial distribution of polarization at the LaAlO${}_3$/SrTiO${}_3$ interface

The polarization induced at the LaAlO${}_3$/SrTiO${}_3$ interface has been explored by optical second harmonic generation (SHG) spectroscopy. Our data reveal that an orbital reconstruction of the SrTiO${}_3$ surface occurs when three epitaxial monolayers of LaAlO${}_3$ are deposited on top of it. The reconstruction manifests as a spectral modification of a Ti${}^{4+}(3d)$ state at the LaAlO${}_3$/SrTiO${}_3$ interface which is accompanied by a displacement of the Ti${}^{4+}$ ions in adjacent SrTiO${}_3$ monolayers in order to compensate for the polarization discontinuity induced at the interface. According to the SHG experiment, the carriers transferred to the interface are trapped because in spite of the orbital reconstruction, the interface remains insulating. The onset of conductivity with the formation of a two-dimensional electron liquid appears to be a subordinate effect related to a minority of carriers and occurs upon further increase of the LaAlO${}_3$ coverage.

Figure 1

SHG spectra of the LAO/STO interface for varying thickness of the LAO films (counted in the number of monolayers $n$) and different polarization combinations (notation as in Table ). The same relative scale for the SHG intensity is used in all plots. The SHG energy is $2\hslash \omega$ with $\omega$ as frequency of the incoming light. Vertical arrows indicate the reconstruction occurring at the critical thickness $n=3$, where a pronounced sample-to-sample spread in the SHG yield is observed, with the extremes being labeled $3+$ and $3-$. The insets show the relative change of the SHG yield compared to the value at $n=0$, integrated on the whole spectrum.

Figure 2

Bulk and surface contributions to the SHG spectrum. Data points: Exemplary SHG spectrum at $n=6$ for the $\mathit{pp}$ configuration. Line: theoretical bulk-like SHG signal derived from ellipsometry measurements (see text). Inset: The difference between data and fit reveals the surface-related state at 3.6 eV. The line is a guide to the eye.

Figure 3

(a) Experimental scheme and polarization geometry. (b) Normalized SHG signal in dependence of the polarization $\alpha$ of the incident fundamental light for fixed output polarizations ($s$ red, $p$ black, $d$ blue) of the SHG light. (c) The $\left|{\chi }_{\mathit{zzz}}\right|$ and $\left|{\chi }_{\mathit{zxx}}\right|+\left|{\chi }_{\mathit{xxz}}\right|$ moduli vs $n$ at 3.6 eV. Each data set has been normalized to the $n=0$ values for a better comparison, since $\left|{\chi }_{\mathit{zzz}}\right|$ is larger by a factor 10. The data points were derived from polarization-dependent SHG data as in (b). Note that (c) shows susceptibility data ($\propto \chi$) at a single photon energy (the peak of the surface state) while Fig. 1 shows spectrally integrated intensity data ($\propto {\chi }^2$). In the former the transition centered at $n=3$ is more pronounced.

Figure 4

Analysis of the $\mathit{pp}$ contribution to SHG. Spectral dependence of $\left|{\chi }_{\mathit{zzz}}\right|$ for samples with $n⩾3$ (upper panel) and $n⩽3$ (lower panel). For comparison, the upper and lower inset shows the $\left|{\chi }_{\mathit{xxz}}\right|$ and $\left|{\chi }_{\mathit{zxx}}\right|$ spectra, respectively.