Two-dimensional electron systems in perovskite oxide heterostructures: Role of the polarity-induced substitutional defects

The discovery of a two-dimensional electron system (2DES) at the interfaces of perovskite oxides such as $\mathrm{LaAl}{\mathrm{O}}_3$ and $\mathrm{SrTi}{\mathrm{O}}_3$ has motivated enormous efforts in engineering interfacial functionalities with this type of oxide heterostructures. However, the fundamental origins of the 2DES are still not understood, e.g., the microscopic mechanisms of coexisting interface conductivity and magnetism. Here we report a comprehensive spectroscopic investigation on the depth profile of 2DES-relevant $\mathrm{Ti}3d$ interface carriers using depth- and element-specific techniques like standing-wave excited photoemission and resonant inelastic scattering. We found that one type of Ti $3d$ interface carriers, which give rise to the 2DES are located within three unit cells from the n-type interface in the $\mathrm{SrTi}{\mathrm{O}}_3$ layer. Unexpectedly, another type of interface carriers, which are polarity-induced Ti-on-Al antisite defects, reside in the first three unit cells of the opposing $\mathrm{LaAl}{\mathrm{O}}_3$ layer (∼10 Å). Our findings provide a microscopic picture of how the localized and mobile Ti $3d$ interface carriers distribute across the interface and suggest that the 2DES and 2D magnetism at the $\mathrm{LaAl}{\mathrm{O}}_3/\mathrm{SrTi}{\mathrm{O}}_3$ interface have disparate explanations as originating from different types of interface carriers.

Figure 1

Depth sensitivity of SW techniques for the LAO/STO superlattice. (a) The superlattice sample, ${\left(\mathrm{LA}{\mathrm{O}}_{\mathrm{n}}/\mathrm{ST}{\mathrm{O}}_{\mathrm{m}}\right)}_{\mathrm{p}}$ ($n=5\mathrm{uc}$, $m=5\mathrm{uc}$, and $p=20$), was used for the SW measurements by varying the x-ray incidence angles θ around the Bragg angle ${\theta }_{\mathrm{B}}$. The photoemission yield distribution of (b) SW-HXPS $\left(hv=3000\mathrm{eV}\right)$ and (c) SW-RXPS $\left(hv=459\mathrm{eV}\right)$. (d) The RIXS yield distribution of SW-RIXS $\left(hv=459.3\mathrm{eV}\right)$. The yield distribution demonstrates the probing depth sensitivity of these techniques. The probing depth for RXPS and HXPS (3λ) is ∼27 and 135 Å, respectively, as indicated in (b) and (c). The probing depth for RIXS (3Λ) is 960 Å [not indicated in (d). According to the probing depths, SW-RXPS is sensitive to the top LAO layer and the first interface, SW-HXPS is sensitive to the top 3 LAO/STO (STO/LAO) interfaces, and SW-RIXS is sensitive to all 20 LAO/STO (STO/LAO) interfaces.

Figure 2

SW photoemission results and the depth distribution of the near Fermi (NF) peak. (a) SW-HXPS results $\left(hv=3000\mathrm{eV}\right)$ (b), (c), (d) SW-RXPS results $\left(hv=459\mathrm{eV}\right)$. (a) The top panel is the fitted core-level spectra of La $3d_{5/2}$ and Sr $2p_{3/2}$ at an off-Bragg angle. The bottom panel shows their experimental (open circle) and best-fit (curve) rocking curves. (b) The top panel is the fitted core-level spectra of La $4d$ and Sr $3d$. The bottom panel shows the experimental and theoretical rocking curves. For the NF peak, its spectrum is shown in c. (c) A valence band spectrum with an inset of the fitted NF peak near the Fermi level. The NF peak is fitted using Voigt function and Fermi-Dirac distribution. (d) The determined depth profile of the NF peak in the top LAO/STO bilayer. The sample depth of zero means the sample surface.

Figure 3

SW-RIXS result and depth distribution of $dd$ excitations. (a) The excitation-energy-dependent RIXS spectra were collected with excitation energies around the $\mathrm{Ti}{L}_3$ XAS edge, ranging from 459.7 to 458.1 eV and marked by color dashed lines in the XAS panel. In the RIXS panel, the black and blue dashed lines are guides to the eyes to show the evolution of the Raman (black) and fluorescence (blue) spectral features, respectively. (b) RIXS spectrum collected using an excitation photon energy of 459.3 eV at an off-Bragg angle for the SW-RIXS measurements. The RIXS spectrum consists of a quasielastic, $d_{xz}/\phantom{d_{xz}{d}_{yz}}{d}_{yz}$, $d_{x^2-y^2}$, $d_{z^2}$, and fluorescence excitations. (c) Experimental (open circle) and best-fit (curve) rocking curves for $d_{xz}/\phantom{d_{xz}{d}_{yz}}{d}_{yz}$, fluorescence, $d_{x^2-y^2}$, and $d_{z^2}$ excitations. The color scheme in this panel adopts that in panel (b). (d) Determined depth profiles of these RIXS excitations in the top five interfaces of LAO/STO heterostructures.

Figure 4

Formation and subband energy levels of a 2DES at a LAO/STO interface. (a) Illustration of the polarity-induced defect mechanism that leads to the 2DES formation. Paired antisite defects (${\mathrm{Ti}}_{\mathrm{Al}}$ in the LAO layer and ${\mathrm{Al}}_{\mathrm{Ti}}$ in the STO layer) form in order to alleviate the polarization-induced field across the LAO/STO interfaces. When the LAO layer is below the critical thickness (3 uc), all electrons transferred from ${\mathrm{Ti}}_{\mathrm{Al}}$ in the LAO layer are trapped by the deep ${\mathrm{Al}}_{\mathrm{Ti}}$ defects in the STO layer, causing no mobile electron. In contrast, with LAO layer thickness over 3 uc, the surface oxygen vacancy defects $\left({\mathrm{V}}_{\mathrm{O}\left(\mathrm{S}\right)}\right)$ start to donate half of the electrons to ${\mathrm{Al}}_{\mathrm{Ti}}$ defects, and the rest to form the 2DES $\left(e^{-}\right)$ in the STO layer. The ${\mathrm{Ti}}_{\mathrm{Al}}$ defects ($\mathrm{T}{\mathrm{i}}^{3+}$) can be probed by RXPS and RIXS. The lower panel is the SW-RXPS-determined depth profile, showing two main Ti $3d$ sources. One source in STO is 2DES in the STO and the other is ${\mathrm{Ti}}_{\mathrm{Al}}$ in the LAO, matching the polarity-induced defect mechanism. (b) The orbital transitions from ground state ($d_{xy}$) to final states ($d_{xz}/\phantom{d_{xz}{d}_{yz}}{d}_{yz}$, $d_{x^2-y^2}$, and $d_{z^2}$) are responsible for the $dd$ RIXS process. The distributions of these $dd$ excitations are affected by the quantum confinement effect.