Orbital Reconstruction and the Two-Dimensional Electron Gas at the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ Interface

In 2004, Ohtomo and Hwang discovered that an electron gas is created at the interface between insulating ${\mathrm{LaAlO}}_3$ and ${\mathrm{SrTiO}}_3$ compounds. Here we show that the generation of a conducting electron gas is related to an orbital reconstruction occurring at the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface. Our results are based on extensive investigations of the electronic properties and of the orbital structure of the interface using x-ray absorption spectroscopy. In particular, we find that the degeneracy of the Ti $3d$ states is fully removed and that the Ti $3d_{xy}$ levels become the first available states for conducting electrons.

Figure 1

(a) A sketch of the XAS process for $2p\to 3d$ transitions. The available, empty $3d$ ${\mathrm{Ti}}^{4+}$ states are depicted for cubic (middle) and tetragonal (right) crystal fields. (b) Total electron yield XAS spectra (normalized to the peak $a_1$), acquired with $E\parallel ab$ ($I_{ab}$) on a ${\mathrm{TiO}}_2$-terminated ${\mathrm{SrTiO}}_3$ single crystal (black circles). The blue circles show reference XAS spectra taken on a ${\mathrm{LaTiO}}_3$ single crystal, and the red continuous line is the result of the atomic multiplet simulation for STO [13]. (c) Experimental total electron yield XAS spectrum of a conducting 4 uc LAO/STO interface (black circles) compared to calculated XAS spectra (continuous lines) of STO covered by one monolayer of ${\mathrm{La}}_x{\mathrm{Sr}}_{1-x}{\mathrm{TiO}}_{3-d}$ with $x=1$ (red line), $x=0.2$ (blue line), and $x=0.1$ (black line).

Figure 2

(a) Total electron yield linear dichroism acquired at 300 K on STO (gray line), Nb-STO (green line), and LAO/STO as a function of the LAO thickness (black lines, Augsburg samples grown at $8\times {10}^{-5}\mathrm{mbar}$; blue line, Twente 4 uc sample grown at $2\times {10}^{-3}\mathrm{mbar}$). The calculated linear dichroism reproducing the data on bare STO or Nb-STO is shown as a red line. (b) Comparison between the calculated linear dichroism of ${\mathrm{Ti}}^{4+}$ (red line) and ${\mathrm{Ti}}^{3+}$ (green line) and the data on 4 uc STO/LAO (black line). The splitting between in-plane and out-of-plane $t_{2g}$ and $e_g$ levels is assumed to be the same for the ${\mathrm{Ti}}^{3+}$ and ${\mathrm{Ti}}^{4+}$ cases. (c) Comparison between $I_{ab}$ (black line) and $I_c$ (red line) experimental TEY spectra on 4 uc LAO/STO (open circles) and calculated ones for a bilayer assuming a ${\mathrm{Ti}}^{4+}$ configuration which reproduces the dichroism (continuous lines). The region between $a_1$ and $b_1$ peaks is better visible in the inset. For clarity, the curves in (a) and (b) are plotted with regular, artificial $y$ offsets.

Figure 3

The integral of the absolute dichroism (open triangles, Augsburg samples and STO; blue circle, Twente sample; green circle, Nb-STO sample) and the position of the $b_1$ peaks from the $I_{ab}$ (filled squares) and $I_c$ (filled diamonds) spectra as a function of the number of ${\mathrm{LaAlO}}_3$ layers. In the figure, the left scale refers to the dichroism data, while the right scale relates to the shift of the $b_1$ peaks. The inset shows the region of the TEY XAS spectra around the peak $b_1$ for STO (red circles), Nb-STO (green circles), and LAO/STO. Red triangles in the inset mark the position of the peak.