Raman and fluorescence contributions to the resonant inelastic soft x-ray scattering on ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ heterostructures

We present a detailed study of the Ti $3d$ carriers at the interface of ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ heterostructures by high-resolution resonant inelastic soft x-ray scattering (RIXS), with special focus on the roles of overlayer thickness and oxygen vacancies. Our measurements show the existence of interfacial Ti $3d$ electrons already below the critical thickness for conductivity. The (total) interface charge carrier density increases up to a ${\mathrm{LaAlO}}_3$ overlayer thickness of 6 unit cells before it levels out. Furthermore, we observe strong Ti $3d$ charge carrier doping by oxygen vacancies. The RIXS data combined with photoelectron spectroscopy and transport measurements indicate the simultaneous presence of localized and itinerant charge carriers. At variance with previous interpretations, we show that in our excitation energy dependent RIXS measurements the amounts of localized and itinerant Ti $3d$ electrons in the ground state do not scale with the intensities of the Raman and fluorescence peaks, respectively. Rather, we attribute the observation of either Raman components or fluorescence signal to the specific nature of the intermediate state reached in the RIXS excitation process.

Figure 1

(a) Sketch of the experimental geometry for XAS and RIXS measurements. Samples were aligned with the sample normal ([001] axis) lying in the scattering plane. The incident angle of the photons was set to ${20}^{\circ }$ from the sample surface while the scattering angle was kept at ${90}^{\circ }$. The polarization vector of the incoming light was within the scattering plane ($p$ polarization). (b) X-ray absorption spectrum at the Ti $L_3$ (Ti $2p_{3/2}$) edge of a 6-uc LAO/STO heterostructure measured in total electron yield mode. The used photon energies for RIXS measurements are marked by labels $a\text{−}o$. (c)–(e) Basic RIXS processes using photons tuned to, e.g., the $e_g$ resonance. The electron depicted in blue is involved in the deexcitation process. (c) Only elastic scattering occurs for Ti ions in a $3d^0$ configuration (${\mathrm{Ti}}^{4+}$). (d, e) Beside elastic scattering (d) also inelastic scattering (e) is possible for Ti ions in a $3d^1$ configuration (${\mathrm{Ti}}^{3+}$), ending in an excited state with an electron in the $e_g$-manifold and observable as energy loss peak in the RIXS spectra.

Figure 2

Series of RIXS spectra. The labels $a\text{−}l$ and $a\text{−}o$ in (a) and (b) correspond to the excitation energies marked in the XAS spectrum in Fig. 1. (a) Series of RIXS spectra of a bare STO sample excited across the Ti $L$ edge. The spectra are normalized by acquisition time. (b) Series of RIXS spectra of a 6-uc LAO/STO heterostructure excited across the Ti $L$ edge. The spectra are normalized by acquisition time. The black and the orange dashed lines are guides to the eye marking the energies of the Raman and the fluorescence spectral features, respectively.

Figure 3

(a) RIXS spectra measured at the $e_g$ resonance of a bare STO sample and LAO/STO heterostructures with various overlayer thicknesses. The spectra are normalized to the $3d^1\underline{L}$ charge transfer excitations. (b) Low-energy region of the RIXS spectra in Fig. 3. (c) Spectral weight of the structure around 2.3 eV in Figs. 3 and 3 from a fitting analysis plotted against the film thickness.

Figure 4

(a) RIXS spectra of bare STO and LAO/STO heterostructures with varying LAO overlayer thickness measured 1 eV below the $e_g$ resonance. The spectra are normalized to the $3d^1\underline{L}$ charge transfer excitations. (b) Low-energy loss region of the spectra in Fig. 4. (c) Fit analysis of the off-resonance RIXS spectrum of the 6 uc LAO/STO sample using seven Gaussian peaks. (d) Inelastic spectral weight of the $dd$ excitations and the fluorescence feature obtained from the fitting of the RIXS spectra in Figs. 4 and 4, plotted as function of LAO overlayer thickness.

Figure 5

(a) Series of RIXS spectra for samples with varying oxygen vacancy concentration normalized to the $3d^1\underline{L}$ emission. PO, MP, and LP refer to post-growth oxygen annealing, growth in medium and in low oxygen pressure (see Sec. 2). (b) Intensities of the $dd$ excitations and fluorescence signal (multiplied by a factor of 2) obtained by fitting of the RIXS spectra. Both increase in parallel with the oxygen vacancy concentration.

Figure 6

(a) HAXPES Ti $2p$ spectra for the PO, MP, and LP samples recorded at an emission angle of ${35}^{\circ }$ off normal emission. (b) Comparison of the ${\mathrm{Ti}}^{3+}/{\mathrm{Ti}}^{4+}$ ratio obtained from fitting the Ti $2p$ spectra and the total RIXS intensity (sum of $dd$ excitations and fluorescence feature). Note that there is no scaling associated with the abscissa except that the $V_O$ concentration is increasing from the left to the right. (c) Temperature-dependent sheet resistance of the PO, MP, and LP samples.

Figure 7

Schematic drawing of two possible RIXS processes with different intermediate states. (a) The excited electron stays localized in the $e_g$ states. After the decay process the final state is $3d_{e_g}^1$ ($dd$ excitation, Raman signal). (b) The excited electron gets immediately delocalized which results in x-ray fluorescence. Here the final state is $3d^0$ (fluorescence signal). Our results can be explained by a superposition of these two different channels in the intermediate state.