Raman and fluorescence contributions to resonant inelastic soft x-ray scattering on LaAlO$_3$/SrTiO$_3$ heterostructures

TL;DR

This study uses high-resolution RIXS to analyze Ti 3d carriers at LaAlO3/SrTiO3 interfaces, revealing the roles of overlayer thickness and oxygen vacancies in charge carrier behavior and challenging previous interpretations of spectral features.

Contribution

It provides new insights into the nature of Ti 3d electrons and clarifies the interpretation of RIXS spectral features in complex oxide interfaces.

Findings

Interfacial Ti 3d electrons exist below the conductivity threshold.

Oxygen vacancies significantly dope Ti 3d charge carriers.

Localized and itinerant Ti 3d electrons coexist at the interface.

Abstract

We present a detailed study of the Ti 3$d$ carriers at the interface of LaAlO$_3$/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 3$d$ electrons already below the critical thickness for conductivity and an increase of the total interface charge up to a LaAlO$_3$ overlayer thickness of 6 unit cells before it levels out. By comparing stoichiometric and oxygen deficient samples we observe strong Ti 3$d$ 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. However, it is demonstrated that the relative amount of localized and itinerant Ti $3d$ electrons in the ground state cannot be deduced from the relative intensities of the Raman and fluorescence peaks in excitation energy dependent RIXS measurements, in contrast to previous interpretations. Rather, we attribute the observation of either the Raman or the fluorescence signal to the spatial extension of the intermediate state reached in the RIXS excitation process.

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††preprint: APS/123-QED

I Introduction

Complex transition metal oxides exhibit a broad spectrum of intrinsic functionalities such as high temperature superconductivity, colossal magnetoresistance, ferroelectricity etc. Artificial layered oxide structures made from such materials may even host novel phases not existing in the individual constituents. A prominent example is the formation of a high-mobility two-dimensional electron system (2DES) at the interface between the polar LaAlO3 (LAO) and the TiO2-terminated non-polar SrTiO3 (STO), if the LAO film thickness exceeds three unit cells (uc).Othomo and Hwang (2004); Thiel et al. (2006) The 2DES is formed by Ti $3d$ electrons on the STO side of the interfaceSing et al. (2009) and a number of fascinating properties are reported: it can be controlled by electric field gating,Caviglia et al. (2008) becomes superconducting below 300 mK,Reyren et al. (2007) and – most strikingly – can simultaneously display ferromagnetismLi et al. (2011); Bert et al. (2011); Kalisky et al. (2012), most likely related to the local moments of $3d$ electrons trapped by oxygen vacancies.Popovic et al. (2008); Chan et al. (2009); Elfimov et al. (2002); Pavlenko et al. (2012)

While the exact mechanism for 2DES formation is still under debate, there seems to be a wide consensus that the polar discontinuity at the LAO/STO interface plays a central role. A commonly discussed scenario is the electronic reconstruction,Nakagawa et al. (2006) in which electronic charge is effectively transferred from the surface to the interface at the critical LAO film thickness in order to compensate the electrostatic potential build-up in the LAO. Thus induced extra electrons are confined to the interface, populating the otherwise empty Ti 3$d$ states.Sing et al. (2009) However, cation defects Yu and Zunger (2014) and oxygen vacancies Kalabukhov et al. (2007); Liu et al. (2013) have also been suggested to be the possible origin of the 2DES. Oxygen vacancies are known to act as electron donors in STO, and oxygen vacancy induced conductivity extending deeply into the substrate has indeed been observed for samples grown under low oxygen pressures.Cancellieri et al. (2010) Nonetheless, for heterostructures grown under higher oxygen pressures and/or post-oxidized samples the conductivity remains finite and confined to the interface region.Basletic et al. (2008); Sing et al. (2009) Despite many extensive studies several crucial issues have remained unsolved. For instance, there are serious questions concerning the charge carrier dichotomy responsible for the coexistence of superconductivity and ferromagnetism and the electronic structure of samples below the critical thickness.

Such heterointerfacial materials pose an exciting technical challenge to x-ray and electron spectroscopies since their use is only feasible if a specific interfacial contrast and a large enough probing depth can be accomplished at the same time. So far photoelectron spectroscopy in the soft and hard x-ray regime has been successfully applied to various oxide heterostructures.Sing et al. (2009); Berner et al. (2013); Schütz et al. (2015); Cancellieri et al. (2014) However, the need of sufficiently conductive samples to avoid charging and the limited probing depth preventing measurements on samples with overlayer thicknesses exceeding 10 uc are major disadvantages of the photoemission technique. Resonant inelastic x-ray scattering (RIXS) is appropriate to overcome these problems. As a photon-in/photon-out method it is bulk-sensitive and does not require intense efforts to prepare an atomically clean sample surface. In addition, it allows the measurement of highly insulating samples. Previous studies have established that the RIXS intensity measured at the Ti $L$ (2$p$) edge provides valuable information on the total amount of interfacial Ti 3$d$ electrons in LAO/STO heterostructures.Berner et al. (2010); Zhou et al. (2011) Interestingly, the charge carrier concentrations determined by these early RIXS experiments – combined with data from hard x-ray photoelectron spectroscopy (HAXPES) – were found to be significantly higher than those measured by Hall effect.Berner et al. (2010) This observation has been attributed to the coexistence of itinerant and localized Ti $3d$ electrons, which contribute both to the spectroscopic signals in RIXS and HAXPES whereas Hall measurements are only sensitive to the mobile species.Berner et al. (2010) In their study of LAO/STO superlattices Zhou et al. argued that the Raman and incoherent fluorescence signals in excitation energy dependent RIXS can be used to distinguish between localized and delocalized Ti 3$d$ carriers in the ground state.Zhou et al. (2011)

In this paper, we present the results of a detailed high resolution RIXS study of high quality LAO/STO heterostructures, probed with systematically varying photon energies. In agreement with the earlier superlattice results Zhou et al. (2011) we observe two prominent RIXS peaks involving the interfacial Ti 3$d$ electrons, a localized $dd$-excitation staying at a constant energy loss of around 2.3 eV (Raman-signal) and a fluorescence signal being almost independent of excitation energy. To further elucidate the origin of these two RIXS features we analyze their behavior as function of film thickness and oxygen stoichiometry together with complementary HAXPES and Hall-effect data. Importantly, we find that the Raman vs. fluorescence character of the RIXS peaks reflects the different degree of localization of the intermediate state in the RIXS process but not that of the initial state. We are thus led to conclude that RIXS cannot directly distinguish localized from itinerant Ti 3$d$ carriers in STO-based heterostructures, contrary to earlier suggestions. Zhou et al. (2011)

II Experiment

A series of LAO/STO heterostructures with LAO overlayer thicknesses from 2 to 20 uc were grown by pulsed laser deposition (PLD) on TiO2-terminated STO(001) substrates. Laser ablation of the single crystalline LAO target was achieved with a KrF excimer laser at a fluency of 1.1 J/cm2 and a target-substrate distance of 56 mm. During the film growth the STO substrate was heated up to 780∘C and the oxygen partial pressure was set to 1 x 10*-3* mbar. In order to suppress unwanted oxygen vacancies some samples were treated by a post-oxidation (PO) procedure immediately after the growth (stepwise cooling down from growth temperature to 360∘C in a high oxygen pressure of 500 mbar over a period of 2 hours). Additional samples with a film thickness of 6 uc and intentionally reduced oxygen stoichiometry were grown by skipping the post-growth oxidation step (medium pressure growth = MP). To achieve even higher oxygen vacancy concentrations the oxygen partial pressure during the growth was reduced down to 5 x 10*-7* mbar for other samples (low pressure growth = LP). Reference measurements were performed on commercially available bare STO crystals.

The RIXS and x-ray absorption (XAS) measurements were performed at BL07LSU of SPring-8. A detailed description of the experimental setup can be found in Ref. Harada et al., 2012. All measurements were carried out at room temperature. The experimental geometry for both, RIXS and XAS, is depicted in Fig. 1 (a). The angle of x-ray incidence was kept at 20∘ with respect to the sample surface while the scattering angle was always set to 90∘ with respect to the incoming beam. The x-ray polarization was chosen to lie within the scattering plane ($p$-polarization). By fitting the elastic line of bare STO with a Gaussian the energy resolution was determined to be $\approx$ 90 meV. In order to reduce photon-induced oxygen depletion Walker et al. (2014) the photon spot ($\sim 2\,{\rm\mu m}\times 90\,{\rm\mu m}$) was moved across the sample surface by 10 $\mu$m every 30 minutes. No significant changes were observed in the spectra within this timescale.

A Ti $L_{3}$ edge XAS spectrum of a PO sample with an overlayer thickness of 6 uc measured in total electron yield mode is shown in Fig. 1 (b). The photon energies selected for the RIXS measurements are marked by labels $a$ to $o$. The two peaks centered at energies $a$ and $k$ reflect the cubic crystal-field splitting of the Ti 3$d$ states in the STO substrate and are assigned to transitions from the Ti 2$p$ core level into the 3$d_{t_{2g}}$ and 3$d_{e_{g}}$ states, respectively.

RIXS is a two-step process involving a photoexcitation of a core electron into unoccupied conduction band states and a subsequent decay of the excited state by emitting an x-ray photon. At the Ti $L$ edge, after the excitation of an electron from the Ti 2$p$ to the Ti 3$d$ shell, different radiative decay channels become possible resulting in final states with different electronic configurations. The emitted photon can be elastically scattered where the final state is the same as the original ground state [Figs. 1(c) and (d)]. Alternatively, an inelastic signal is observed when the system remains in an excited final state with, e.g., one electron in an $e_{g}$-state and no electron in the $t_{2g}$ manifold as depicted in Fig. 1(e). However, the latter process can only occur, if there is already one $d$-electron in the initial state. Consequently, such a Raman signal is a measure of the finite 3$d$ electron occupation as has already been shown for other titanates Ulrich et al. (2008); Higuchi et al. (1999) and also for LAO/STO heterostructures Berner et al. (2010) and superlattices.Zhou et al. (2011)

Complementary photoemission experiments have been performed at the HAXPES endstation of beamline P09 at PETRA III (DESY, Hamburg), equipped with a SPECS Phoibos 220 spectrometer. At the used photon energy of 3.5 keV an overall energy resolution of 450 meV was realized. A detailed description of the beamline can be found in Ref. Strempfer et al., 2013.

III Results

III.1 Excitation energy dependence

A series of RIXS spectra of a bare STO substrate as well as a post-oxidized LAO/STO heterostructure with a 6 uc thick film, recorded at photon energies across the Ti $L$ edge and normalized to acquisition time, is displayed in Figs. 2 (a) and (b), respectively. The labels $a$-$o$ correspond to the excitation photon energies marked in the absorption spectrum of Fig. 1 (b). For the bare STO sample the final state can be either $2p^{6}3d^{0}$ or 2p^{6}3d^{1}$$L with $L$ denoting a hole in the ligand O 2$p$ shell. Beside the elastic line and the onset of the 3d^{1}$$L charge transfer excitations at an energy loss of $\approx$ 3.5 eV [the full energy range from 3.5 to 18.0 eV energy loss is depicted in Figs. 3 (a) and 4 (a)], no clear additional signal can be discerned throughout the photon energy series as shown in Fig. 2 (a). In LAO/STO samples above the critical thickness the ground state is partially of type $2p^{6}3d^{1}_{t_{2g}}$ due to the extra electrons in the 3$d$ shell at the conducting interface.

This results in an additional contribution to the RIXS spectra depending on the used excitation energy. In the case of the t2g resonance (label $a$) the excited intermediate state will have the configuration $2p^{5}3d^{2}_{t_{2g}}$. Two different final states are possible either contributing to the elastic line ($2p^{6}3d^{1}_{t_{2g}}$) or to the charge transfer excitations with an energy loss above 3.5 eV as seen in Figs. 3 (a) and 4 (a) and represented by $2p^{6}3d^{2}_{t_{2g}}\underline{L}$).

Increasing the incoming photon energy to the $e$g-resonance (label $k$), $2p^{5}t^{1}_{2g}e^{1}_{g}$ intermediate states can result via an additional decay channel in excited final states of the type $2p^{6}3d^{1}_{e_{g}}$ [see Fig. 1(e)]. Thus, an inelastic signal due to intra-atomic $dd$-excitations from $t_{2g}$ to $e_{g}$ states becomes visible at an energy loss of around 2.3 eV, providing spectroscopic sensitivity to the interfacial Ti 3$d$ carriers [Fig. 2 (b)]. When changing the excitation energy from the $t$2g- towards the $e$g-resonance we can identify two different types of signals overlapping near the $e$g-resonance. While one signal shows a constant Raman-shift of approximately 2.3 eV, the second signal shows fluorescence-like behavior with its energy position being almost independent of the incident photon energy. Similar results have already been obtained by performing excitation energy dependent RIXS on LAO/STO superlattices Zhou et al. (2011) and other oxides like BaTiO3 and BaSO4.Yoshii et al. (2012) In the case of the superlattices, the authors attributed the observation of a Raman-signal to localized charge carriers in the initial state whereas the fluorescence-like signal was assigned to delocalized electrons in the system.Zhou et al. (2011) Contrary to this interpretation, the authors of Ref. Yoshii et al., 2012 assign the observation of Raman-scattering in BaTiO3 and BaSO4 to a process where the excited electron is promoted to an unoccupied state and remains localized at the same atomic site on the timescale of the deexcitation, while the appearance of a fluorescence-like signal is ascribed to the more delocalized character of the state reached by the excited electron in the intermediate state. Thus further detailed experiments are required to clarify the origin of the features seen in the RIXS spetcra of LAO/STO.

III.2 Thickness dependence

To further elucidate the nature of the two RIXS features, we performed detailed RIXS measurements at the $e$g-resonance on post-oxidized (PO) samples with overlayer thicknesses between 2 and 20 uc as well as on bare STO as reference. The results obtained for this series are displayed in Figs. 3 (a) and (b) showing a strong dependence on the LAO thickness. The data are normalized to the intensity of the 3d1$\underline{L}$ charge transfer excitations with energy losses above 3.5 eV which originate mainly from the STO substrate and therefore should be essentially constant for the whole set of samples. To further analyze the spectra, the RIXS signals at a loss energy of about 2.3 eV (see Fig. 3 (b)) have been fitted by Gaussians and the obtained intensities plotted as a function of overlayer thickness in Fig. 3 (c). The absence of any inelastic intensity for bare STO and the subcritical 2 uc sample shows the lack of Ti sites with 3$d^{1}$-configuration (i.e., with extra electrons in the $d$-shell in the initial state). Although the photon-induced generation of oxygen vacancies, i.e., extrinsic electron doping, is minimized by moving the sample continuously during the measurements, spectral weight is clearly visible for the insulating 3 uc sample. Since we do not observe any RIXS signal for the insulating 2 uc sample we consider the observation of an inelastic signal for 3 - 20 uc samples intrinsic to the measured heterostructure. Discrepancies between the present and previous RIXS measurements, which do show finite inelastic spectral weight for the insulating 2 uc heterostructure, likely can be attributed to a small amount of oxygen vacancies. These are caused by the intense synchrotron radiation and become observable if the same sample spot is constantly exposed to the beam as in the previous studyBerner et al. (2010).

The RIXS intensity for the insulating 3 uc sample in the present experiment (see Fig. 3 (b)) can be explained by the presence of $localized$ electrons that are not due to oxygen vacancy doping. This is in line with photoemission spectroscopy measurements showing indications for an incipient insulator-metal transition, as signalled by the appearance of Ti 3$d$ carriers before interface conductivity is observed.Takizawa et al. (2011) Results of x-ray absorption for an insulating 2 uc sample that reveal an orbital reconstruction attributable to interface symmetry breaking and the transfer of localized electrons to interface states, support this scenario.Salluzzo et al. (2013) Our findings are also in line with the critical thickness of 3 uc for ferromagnetism — probably due to the existence of local Ti 3$d$ moments — observed by Kalisky $et$ $al.$ in overlayer thickness dependent scanning SQUID measurements.Kalisky et al. (2012)

The observed RIXS intensity increases continuously with LAO film thickness and saturates at a thickness of 6 uc. In contrast, the mobile charge carrier concentration obtained from Hall measurements shows a sharp step-like behavior at an overlayer thickness of 4 ucThiel et al. (2006). This discrepancy has been attributed in previous experimental and theoretical studies to the presence of delocalized and localized charge carriers where the latter are not observed in transport.Thiel et al. (2006); Popovic et al. (2008); j. Son et al. (2009); Berner et al. (2010)

Since the inelastic signal at the $e$g-resonance is a superposition of two different features as can be recognized from Fig. 2 (b), we focus in the following on measurements using an excitation energy 1 eV below the $e$g-resonance (label $f$), where the Raman- and fluorescence-like components are well separated. The spectra recorded under this condition are depicted in Fig. 4 (a) and (b) for the full set of samples. As selectively shown for the 6 uc sample in Fig. 4 (c), the spectrum in this region contains seven components including the contribution of the charge transfer excitations at energies higher than 3.5 eV. In addition to the elastic line at zero loss energy the fluorescence-like component (green shaded) at 1.45 eV and four distinct $dd$-excitations (purple shaded) can be distinguished owing to the high energy resolution. The latter observation indicates the complete lifting of the Ti 3$d$ degeneracy. By careful fitting of the data with Gaussian line shapes, the energies of the $dd$-transitions on the Ti3+ ions are determined to be 0.17, 0.61, 2.38, and 2.88 eV with an accuracy of $\pm$ 0.10 eV. In a one-particle picture, from these excitation energies the energy separation of the lowest and the highest $t_{2g}$-orbital can be estimated as (0.60 $\pm$ 0.10) eV and the $e$g-splitting as (0.50 $\pm$ 0.10) eV. These values significantly exceed those determined from x-ray absorption for the interface Ti4+-ions.Salluzzo et al. (2009) RIXS measurements of $dd$ excitation energies on LAO/STO superlattices, again representative for the (distorted) Ti*3+O6 octahedra at the interface, yield values for these energy splittings comparable to ours Zhou et al. (2011). The larger values, i.e., the larger crystal-field strength as compared with Ti4+*O6 octahedra, were attributed in this study to an enhanced Coulomb repulsion and covalency between Ti 3$d$ and O 2$p$ states due to the extra occupation with Ti 3$d$ electrons.Zhou et al. (2011)

For a quantitative analysis of the intensities of the inelastic signals and their ratios, the spectra of the whole series of samples have been fitted taking seven Gaussian profiles into account as already explained in Fig. 4 (c). Four represent the crystal-field split $dd$-excitations, one the fluorescence-like feature, and another one the elastic line. The last one models the increasing slope of the 3$d$1$L$ charge transfer excitations setting in at an energy loss of 3.5 eV. The total Raman intensity and the intensity of the fluorescence peak are plotted as a function of film thickness in Fig. 4 (d). As all four $dd$-excitations display the same dependence on LAO thickness within experimental accuracy their intensities have been summed up for clarity and better statistics.

Except for little spectral weight which we ascribe to radiation induced oxygen vacancies, no RIXS intensity is visible for bare STO and the 2 uc LAO/STO sample within the accuracy of our experiment. The total RIXS spectral weight increases for larger overlayer thicknesses and saturates for a film thickness larger than 6 uc. Thereby, the intensity ratio of the fluorescence-like signal and the $dd$-excitations stays essentially constant. The parallel rise in intensity of both signals up to 6 uc in contrast to the step-like increase of the mobile charge carrier concentration at 4 uc as observed in Hall measurements invalidates the attribution of either of the two observed features to $delocalized$ ground state electrons in LAO/STO heterostructures. Also the finite Raman- $and$ fluorescence-like spectral weight for the non-conducting 3 uc sample contradicts such an interpretation. Furthermore, since both structures show essentially the same dependence on film thickness they rather seem to reflect the total charge carrier concentration, including contributions by photogenerated charge carriers, as has been pointed out before for RIXS measurements on the $e_{g}$-resonance where Raman and fluorescence peak overlap.Berner et al. (2010)

III.3 Influence of oxygen vacancies: electron doping

Since oxygen vacancies act as electron donors we also studied 6 uc samples with an intentionally higher amount of oxygen vacancies to further clarify the origin and character of the two observed RIXS excitations. In Fig. 5 (a) the RIXS data — normalized to 3$d$1$L$ charge transfer excitations above 3.5 eV (not shown) — show the increase of the RIXS spectral weight as a function of oxygen vacancy concentration. As obtained from a fitting procedure equivalent to the one used for the thickness dependent series of spectra in Fig. 4 (c), the fluorescence-like component and the integrated spectral weight of the $dd$-excitations rise in the same proportion with the amount of oxygen vacancies [see Fig. 5 (b)]. Since both inelastic features are present in the spectrum for the fully oxidized sample (PO) neither component can be directly correlated to the amount of oxygen vacancies.

Figure 5 (c) shows corresponding HAXPES Ti 2$p$ core-level spectra normalized to the overall integrated intensity. Beside a strong Ti 2$p$3/2 peak due to emission from Ti4+ ions mainly in the STO bulk, a chemically shifted contribution from Ti3+-ions at the interface is visible at smaller binding energies. This signal is a measure for the extra electrons occupying the otherwise empty Ti 3$d$ states and therefore reflects the total amount of charge carriers in the system.Sing et al. (2009) By increasing the amount of oxygen vacancies a strong increase in the total amount of charge carriers is observed in HAXPES represented by the increase of the Ti3+ contribution in the Ti 2$p$ spectrum as shown in the inset of Fig. 5 (c).

Figure 5 (d) displays the total RIXS intensity (sum of the integrated weights of the $dd$-excitations and fluorescence-like features) and the Ti3+/Ti4+ ratio obtained from the fitting of the Ti 2$p$ core-level HAXPES spectra of the three samples. After normalizing the RIXS to the HAXPES data by minimizing the root-mean square deviation of the three data points similar to Ref. Berner et al., 2010, both spectroscopic techniques display qualitative agreement within experimental accuracy. These results suggest that the $total$ RIXS intensity also reflects the $total$ sheet carrier density as the Ti3+ contribution in HAXPES.

According to Ref. Lin and Demkov, 2013, an oxygen vacancy in STO induces a localized level of mainly Ti 3$d$ character that can trap one electron, while the second electron becomes itinerant since double occupancy is forbidden by the strong onsite Coulomb interaction. As both RIXS components, $dd$ excitations and fluorescence, increase in parallel upon doping [see Fig. 5 (b)] one could be misled to assume that one signal originates from localized charge carriers ($dd$-excitations), while the other feature reflects delocalized electrons (fluorescence) which would fit to this 1:1 doping rule. However, we have already ruled out this scenario for the reasons explained above.

As can be seen from resistivity measurements [see Fig. 5 (e)] the effect of oxygen vacancies on the transport properties seems to be considerably smaller when skipping the post growth oxidation procedure (compare PO to MP data) than the effect of reducing the oxygen growth pressure (compare MP to LP data) for our samples. Since the charge carrier mobility at room temperature is essentially constant, it is thus a good measure for the charge carrier concentration that is determined to be 4.6 x 1013 cm*-2* for the PO, 2.4 x 1014 cm*-2* for the MP, and 6.25 x 1016 cm*-2* for the LP sample. Note that a strong increase of the mobile charge carrier concentration is observed for the LP sample since the conducting region is not confined to the interface anymore but comprises the bulk substrate. If we stick to the 1:1 doping rule and assume that we can attribute the two types of RIXS features, $dd$ excitations and fluorescence, to localized and mobile charge carriers in the initial state, respectively, the intensity increase of both RIXS components should be significantly stronger between the MP and LP samples than between the PO and MP samples as expected from the results in Fig. 5 (e). However, this expectation is not confirmed by our RIXS data in Figs. 5 (a) and (b).

Furthermore, the evolution of the $total$ Ti 3$d$ charge carrier concentration obtained from HAXPES and the trend for the mobile charge carriers from resistivity measurements actually suggest that for larger oxygen vacancy concentrations the 1:1 doping rule is no longer valid. This deviation could be explained by the clustering of oxygen vacancies which alters the ratio of localized and delocalized charge carriers as suggested by density functional theory calculations.Jeschke et al. (2015) and should result in a change of the ratio of Raman- $and$ fluorescence-like signal. Again this is not seen in our RIXS data [Figs. 5 (a) and (b)] requires a new interpretation.

IV Discussion

The different behavior of the two components in RIXS of LAO/STO heterostructures upon varying the photon energy across the Ti-$L$ edge point at a different origin of these features. One signal can be ascribed to a Raman process giving rise to a constant energy loss, while the other feature shifts linearly with excitation energy and hence is due to a fluorescence-like channel. A previous assignment of these two features to localized and itinerant Ti 3$d$ charge carriers is clearly disproven by our present data. The observation of both RIXS components for the insulating 3 uc sample and the saturation of both features at an overlayer thickness of 6 uc as well as the inconsistent increase of the Raman- $and$ fluorescence-like intensities compared with the results of transport and HAXPES data upon oxygen vacancy doping call for a different interpretation.

To form such an alternative view it is helpful to analyse the nature of the possible intermediate states in the RIXS experiment after the initial photoexcitation of a core electron into the Ti 3$d$ shell (see Fig. 6). Two type of intermediate states may result. Firstly, the intermediate state can be of the type $2p^{5}3d^{1}t_{2g}3d^{1}e_{g}$ [see Fig. 6 (a)]. In this case, both Ti 3$d$ electrons stay localized at the same atomic site. By deexcitation of one 3$d$ electron, the core hole created in the intial absorption is filled up again under emission of a photon. The energy difference between incoming and emitted photon reflects the associated, electronic $dd$-excitation between the 3$d$ $t_{2g}$- and the $e_{g}$-orbitals and appears in the RIXS spectra as a peak at finite loss energy with respect to the elastic line. In this case, the energy loss is independent of the incoming photon energy.

Secondly, assuming that one Ti 3$d$ electron gets delocalized following the photoexcitation, the intermediate state is of the type $2p^{5}3d^{1}t_{2g}L^{*}$ with $L$∗ denoting an orbital of a neighboring ligand atom with an extra electron [see Fig. 6 (b)]. The probability for this intermediate state is the higher, the more strongly the O 2$p$ ligand orbitals are hybridized with the Ti 3$d$ states. After the radiative decay, the final state is of the type $2p^{6}3d^{0}$ and corresponds to x-ray fluorescence. Here, a 3$d$ valence electron decays radiatively into the $2p$ core hole generated by the preceding photoexcitation of an electron into continuum states above the Fermi level. The energy of the fluorescent x-ray photon in such a transition is independent of the excitation energy and the intensity reflects essentially the occupied $3d^{1}t_{2g}$ density of states.

Taking both decay channels into account, the intermediate state can be generally written as \alpha$$|2$p$53$d$2$>$+\beta$$|2$p$53$d$1$L$∗$>$, where the relative weight of the Raman and fluorescence-like signal is given by |$$\alpha$$|2 and |$$\beta$$|2 (with |$$\alpha$$|2+|$$\beta$$|2=1), respectively, and essentially determined by the hybridization strength of O 2$p$ and Ti 3$d$ orbitals. Therefore, the observation of either the Raman- or the fluorescence-like signal reflects the electronic character of the intermediate states instead of the itinerancy or localized character of the Ti 3$d$ electrons in the ground state.

Our observation and explanation of the two RIXS features due to $dd$ excitations and fluorescence are in full agreement with the experimental RIXS studies on BaTiO3 and BaSO4Yoshii et al. (2012) as well as theoretical studies of the cluster size effect on resonant x-ray emission spectra by Ide and Kotani.Ide and Kotani (1998, 2000) If the cluster-size is small, the excited electron is essentially localized. In larger clusters, intermediate states can occur in which the excited conduction electron is extended in space.

V Summary

We have investigated LAO/STO heterostructures with varying LAO overlayer thickness and oxygen vacancy concentration by means of RIXS at the Ti-$L$ edge. Already for the sample with a 3 uc thick film, i.e., below the critical thickness for conductivity, we have observed finite spectral weight, signalling that localized charge carriers are present in the ground state. This finding is in line with the report on ferromagnetism which has been ascribed to the local moments of trapped electrons. As seen previously, we also have observed two types of contributions to the RIXS spectra, namely due to $dd$ excitations and fluorescence. They behave differently upon the variation of the excitation energy. A detailed analysis for samples with different film thicknesses and oxygen vacancy concentrations in combination with the results of HAXPES and transport experiments, reveals the physical meaning of these two contributions in contrast to previous claims. The appearance of fluorescence in addition to Raman features reflects the probability for the excited electron to escape from the Ti ion in the coherent RIXS process. Thus the RIXS spectra provide information on the intermediate state rather than the ground state properties. Furthermore, by comparing the $total$ RIXS intensity (sum of $dd$-excitations and fluorescence-like signal) and the Ti3+/Ti4+ ratio obtained from HAXPES measurements, we conclude that the $total$ RIXS intensity reflects the $total$ amount of charge carriers (localized $and$ delocalized) present in the system within experimental accuracy.

VI Acknowledgments

Funding by the Deutsche Forschungsgemeinschaft (FOR 1162) is gratefully acknowledged. Experiments at SPring-8 BL07LSU were performed jointly by the Synchrotron Radiation Research Organization and the University of Tokyo (Proposal No. 2012A7429, 2012B7439, 2013A7449). This work was financially supported by a Grants-in-Aid for Young Scientists (23740240) from the Ministry of Education, Culture, Sports, Science and Technology, Japan. We thank Y. Nishitani and Y. Nakata for supporting the experiments.