Controlling Kondo-like Scattering at the SrTiO3-based Interfaces

The observation of magnetic interaction at the interface between nonmagnetic oxides has attracted much attention in recent years. In this report, we show that the Kondo-like scattering at the SrTiO3-based conducting interface is enhanced by increasing the lattice mismatch and growth oxygen pressure PO2. For the 26-unit-cell LaAlO3/SrTiO3 (LAO/STO) interface with lattice mismatch being 3.0%, the Kondo-like scattering is observed when PO2 is beyond 1 mTorr. By contrast, when the lattice mismatch is reduced to 1.0% at the (La0.3Sr0.7)(Al0.65Ta0.35)O3/SrTiO3 (LSAT/STO) interface, the metallic state is always preserved up to PO2 of 100 mTorr. The data from Hall measurement and X-ray absorption near edge structure (XANES) spectroscopy reveal that the larger amount of localized Ti3+ ions are formed at the LAO/STO interface compared to LSAT/STO. Those localized Ti3+ ions with unpaired electrons can be spin-polarized to scatter mobile electrons, responsible for the Kondo-like scattering observed at the LAO/STO interface.

In this paper, we present results from temperature-dependent and magnetic-field-dependent transport as well as X-ray absorption near edge structure (XANES) studies obtained for the LAO/STO and LSAT/STO interfaces. LAO and LSAT film are grown with various oxygen partial pressures P O2 (0.05-5 mTorr). Our data show that when P O2 is beyond 1 mTorr, the 26 unit cells (uc) LAO/STO interface begins to exhibit Kondo-like scattering, characterized by the resistance upturn (around 40 K) followed by the resistance saturation with negative isotropic magneto-resistance at low temperatures. In contrast, the LSAT/STO interfaces can always maintain the low-temperature metallicity when P O2 is increased up to 100 mTorr. The XANES studies performed at Ti L 32 -edge show that the Ti 3+ /Ti 4+ ratio is larger at the LAO/STO interface, compared to the LSAT/STO interface. The Ti 3+ /Ti 4+ ratio obtained from XANES should be regarded as a total number of electrons that occupy the Ti 3d orbitals, including the itinerant and localized electrons. Considering the similar itinerant carrier density for LAO/STO and LSAT/STO interfaces, the larger amount of localized Ti 3+ ions the LAO/STO interface can be spin-polarized and scatter the mobile electrons, leading to the observed Kondo-like features.

Results
Temperature-dependent transport property. The data illustrating temperature-dependent sheet resistance R S (T) for 26 uc LAO/STO and LSAT/STO interfaces with different P O2 are shown in Fig. 1. For the LAO/STO interface in Fig. 1(a), the low-temperature metallic state (dR S /dT > 0) is preserved in the samples with P O2 below 1 mTorr, suggesting a normal 2DEG is established at the interface. When P O2 is above 1 mTorr, the LAO/STO interfaces show a clear upturn of sheet resistance (dR S /dT < 0) below 40 K, and R S becomes gradually saturated (dR S /dT ≈ 0) under further cooling. These features are different from a normal 2DEG with the low-temperature metallic state. However, for the 26 uc LSAT/STO interface in Fig. 1(b), the metallic state of 2DEG can be always maintained down to 2 K when P O2 is changing from 0.05-50 mTorr. Only a slight resistance upturn at ~15 K can be observed when P O2 is increased to 100 mTorr. Hence, when increasing the P O2 , the metallic state is less favored at the interface with the lager lattice mismatch.
Usually, the upturn of sheet resistance is caused by either carrier scattering with low carrier mobility μ S , or carrier localization with low carrier density n S . In Fig. 2(a), all the LAO/STO interfaces show the decreasing n S from 100 to 2 K, probably due to the localization of the oxygen-vacancy-induced carriers as reported in the SrTiO 3-δ 30,31 . However, carrier localization alone cannot explain resistance upturns in Fig. 1(a). All the samples studied here, exhibit a similar low-temperature n S (2-3 × 10 13 cm −2 at 2 K) independent on P O2 , and it is in contradiction with the resistance upturn, which has been observed only for the sample with high P O2 . On the other hand, for carrier mobility μ S in Fig. 2(b), the LAO/STO interfaces with high P O2 (1 and 5 mTorr) show the decreasing μ S below 40 K on cooling, while the increasing μ S during cooling is observed at the interfaces with low P O2 (0.05-0.5 mTorr). This data is consistent with the appearance of resistance upturn (metallic state) at the high-P O2 (low-P O2 ) interface. So, the upturns of R S (T) must be ascribed to the carrier scattering, instead of carrier localization.  2(c) presents the n S as a functional of temperature at the LSAT/STO interfaces. As can be seen the trend is similar to that of the LAO/STO samples. In particular, if compared with the LAO/STO interface, the LSAT/ STO interfaces prepared at P O2 = 0.05− 0.5 mTorr exhibit a larger decrease of carrier density at low temperature, indicating the low P O2 could create more oxygen vacancies at the LSAT/STO interface than at the LAO/STO. The carrier mobility μ S of all the LSAT/STO samples is increasing under cooling, as shown in Fig. 2(d). At the interface with a small lattice mismatch, e.g. LSAT/STO, μ S is always higher as compared to the interface with a large lattice mismatch, e.g. LAO/STO. Moreover, even though the carrier density n S at 2 K is almost independent of P O2 , the carrier mobility μ S at 2 K is very sensitive to P O2 at both LAO/STO and LSAT/STO samples. As shown in Fig. 2(e), when P O2 is increased from 0.05-5 mTorr, μ S at 2 K is reduced by factor of 300 for the LAO/STO (from 1,000 to 3 cm 2 V −1 s −1 ) and 15 for the LSAT/STO (from 23,000 to 1,500 cm 2 V −1 s −1 ) interface, respectively. For the low-P O2 interfaces, the high carrier mobility might be due to the oxygen vacancy formation in the STO bulk. Comparison of the LAO/STO and LSAT/STO interfaces properties at different P O2 , reveals that: 1) the resistance upturn is caused by carrier scattering with low μ S , and 2) μ S is more sensitive to P O2 at the interface with a larger lattice mismatch. Fig. 3, the low-temperature (T = 2 K) magneto-resistance, defined by MR = [R(H)-R(0)]/R(0), is shown for the LAO/STO and LSAT/STO interfaces with different P O2 . The positive MR is observed in all the samples except the LAO/STO sample with P O2 = 5 mTorr. The LSAT/STO interface always exhibits the larger positive MR than LAO/STO interface with the same P O2 . For both interfaces, the magnitude of positive MR is consistently reduced with increasing P O2 value. The positive MR is induced by the Lorentz-force-driven helical path for mobile carriers 32 , and it can be enhanced by increasing μ S 33,34 . This is consistent with our observation that the larger positive MR appears at the higher mobility interface, of which the lattice mismatch is smaller and P O2 is lower. However, the negative MR at the LAO/STO sample with P O2 = 5 mTorr  is out of this picture, since the Lorentz force alone cannot induce the negative MR. The strong spin-orbit coupling may induce the large negative MR 35 , but it does not correlate with the R S (T) data for the LAO/STO interface with P O2 = 5 mTorr. Two reasonable mechanisms can be proposed to explain the upturn in R S (T) and negative MR-one is the spin-related Kondo scattering 5,15,36 , and the other is orbital-related weak anti-localization [37][38][39] .

Magnetotransport property. In
In order to distinguish these two different mechanisms, the MR curves with different field orientations are shown in Fig. 4(a) for the LAO/STO interface with P O2 = 5 mTorr. The sample exhibits no observable difference in MR curves with changing the field orientation, and MR (H = 9 T) is always negative. This isotropic and negative MR confirms the spin-related Kondo-like scattering for the resistance upturn 5,15,36 . On the other hand, the metallic LSAT/STO interface exhibits the clear anisotropic MR, as shown in Fig. 4(b). The positive MR is gradually suppressed by increasing the angle θ between the sample normal and field direction. Moreover, the negative MR appears when the in-plane field (θ = 90°) is applied. The angular-dependent MR, which is defined by AMR = [R(θ )-R(90°)]/R(90°) in Fig. 4(c), clearly presents the isotropic MR at the 5 mTorr LAO/STO interface, medium anisotropic MR at the 0.05 mTorr LAO/STO and 5 mTorr LSAT/STO interface, and strong anisotropic MR at the 0.05 mTorr LSAT/STO interface. This suggests the AMR can be enhanced by lowering P O2 and reducing lattice mismatch.

X-Ray absorption near edge structure (XANES).
In order to clarify the origin of the Kondo-like scattering at the LAO/STO interface, Ti L 32 -edge XANES spectra are compared in Fig. 5(a) for TiO 2 -terminated STO substrate (t-STO, reference for substrate), Ti 2 O 3 (reference for Ti 3+ ), 10 uc LAO/STO and LSAT/STO interfaces with P O2 = 5 mTorr. The XANES is a powerful tool to examine the low-density Ti 3+ ions under a strong Ti 4+ background 40 . As can be seen, the LAO/STO interface exhibits a higher intensity around Ti 3+ states (see reference Ti 2 O 3 spectrum) peaks denoted by red dash line as compared with LSAT/STO. Moreover, a linear combination fit analysis based on t-STO and Ti 2 O 3 reference spectra revealed a Ti 3+ /Ti 4+ ratio in a range of ~10% for the LAO/STO interface. In contrast, linear combination fit analysis for the LSAT/STO sample results in a negligible Ti 3+ /Ti 4+ ratio of about 1% which is below the uncertainty range of XANES. Here we want to stress that Ti 3+ /Ti 4+ ratio obtained from XANES should be proportional to the total number of electrons that occupy the Ti 3d orbitals, including the mobile 2DEG and the localized Ti 3+ ions. Given that both interfaces show similar n S (3− 4 × 10 13 cm −2 from Hall measurement) of mobile 2DEG at room temperature, the larger amount of localized Ti 3+ ions is expected at the LAO/STO interface. One localized Ti 3+ ion can provide one unpaired electron, which can be spin-polarized and provide the local magnetic moment to scatter the mobile 2DEG at low temperatures, leading to the Kondo-like scattering at the LAO/STO interface.

Discussions
Our transport data demonstrate that the Kondo-like scattering is induced at the LAO/STO interface with high P O2 , but not at the LSAT/STO interface. The XANES analysis and Hall measurement identify a large amount of localized Ti 3+ ions at the LAO/STO interface, where the itinerant 2DEG can be scattered by the localized Ti 3+ ions with local magnetic moments to show the Kondo-like effect. However, there are still two questions needed to be addressed in our discussion. The first is why there are more localized Ti 3+ ions at the LAO/STO interface; the second is why P O2 can influence the Kondo-like scattering.
For the first question, the different lattice mismatch at the LAO/STO and LSAT/STO interfaces is emphasized. As well documented, most of the localized electrons are located near the interface, where the interface disorders can lift the mobility edge for Anderson localization [41][42][43][44] . However, the interface disorders such as cation antisite defect 20 and oxygen vacancies 21-23 that may induce local magnetic moment should be at the same level for both interfaces, because the LAO/STO and LSAT/STO interfaces were fabricated under the same condition including laser energy, growth temperature and oxygen pressure. By contrast, the interface lattice distortion, especially for the STO layer that is close to the interface, must be much larger at the LAO/STO interface than the LSAT/STO interface due to the larger lattice mismatch and symmetry breaking at the LAO/STO interface. Such lattice distortions including the tetragonal-like TiO 6 deformation 25 and octahedral tilting 27,45 would narrow the Ti 3d band, resulting in electron localization and magnetic interface 27,28 . Hence, when increasing the lattice mismatch from LSAT/STO to LAO/STO interface, the larger structural distortion is expected to produce more localized Ti 3+ ions and stronger Kondo-like scattering. Regarding the influence of P O2 , calculations have shown that the Kondo effect is observable with low density of oxygen vacancy (high P O2 ), if the oxygen vacancy interacting with Ti 3d orbitals it can induce local magnetic moments 19,21,22 . Here, we argue that P O2 can also tune the location of itinerant electrons, resulting in a stronger Kondo-like scattering for the higher P O2 . When P O2 is low, not only the interface but also the bulk region of the STO substrate become conducting due to the oxygen vacancy. In this case, the conductive bulk region of STO could weaken the confinement potential of the interface electrons, so the itinerant electrons can travel away from the interface where the localized Ti 3+ ions are located [41][42][43][44] , leading to a weaker magnetic scattering. Therefore, the mobile electrons are spatially separated from the localized Ti 3+ as shown in Fig. 5(b), and the spin-relate Kondo-like scattering from localized Ti 3+ is very weak. When P O2 is increasing, the propagation depth of mobile carriers in the STO substrate is greatly reduced 46 . In other words, by increasing P O2 the mobile electrons are pushed to the interface with a better confinement 47 . So, as schematically shown in Fig. 5(c), the itinerant electrons are much closer to the localized Ti 3+ ions and the stronger interaction between itinerant carriers and localized Ti 3+ are expected. It leads to the Kondo-like features, including resistance upturn and saturation, low carrier mobility, and isotropic negative MR, which are observed at the sample with increasing P O2 . This model can also explain the AMR behavior at the metallic interface as shown in Fig. 4(b). By applying an in-plane magnetic field, the Lorentz force will drive the mobile carriers along the 2DEG normal to interact with the localized Ti 3+ close to the interface. So, when the magnetic field is changed from out-of-plane to in-plane (θ from 0°-90°), the spin-relate scattering arising from the localized Ti 3+ begins to take effect to suppress the positive MR and eventually show the negative in-plane MR.

Conclusions
In summary, the crucial roles of lattice mismatch and growth oxygen pressure in Kondo-like effect has been demonstrated by comparing LAO/STO and LSAT/STO interfaces. For the LAO/STO interface with 3.0% lattice mismatch, the Kondo-like effect appears in the 26 uc sample when P O2 is above 1 mTorr. For the LSAT/STO interface with 1.0% lattice mismatch, the metallic state is always preserved up to P O2 of 100 mTorr. From the XANES and Hall measurement, a larger amount of the localized Ti 3+ is identified at the LAO/STO interface compared to the LSAT/STO interface. Those localized Ti 3+ ions can be spin-polarized and scatter the mobile electrons, leading to the observed Kondo-like features. Our results demonstrate that the Kondo-like effect at the SrTiO 3 -based interface can be dually-controlled by lattice mismatch and P O2 , paving the path for engineering the interface magnetism at the functional oxide heterostructures.

Methods
Sample fabrication. 26 unit cells (uc) of LAO and LSAT layers were deposited onto a TiO 2 -terminated STO (001) substrates by pulsed laser deposition using a KrF laser (λ = 248 nm). The LAO and LSAT single crystal targets are used for deposition. During the deposition, the laser repetition is kept at 1 Hz, laser fluence at 1.8 J/cm 2 , growth temperature at 760 °C, and P O2 varies from 0.05-100 mTorr. The deposition is monitored by in-situ reflection high energy electron diffraction (RHEED), from which the growth rate of 22-24 seconds per unit cell can be seen.

Magnetotransport measurements.
The Hall bar is patterned on samples for measuring the transport property. The length of bridge is 160 μm, and the width is 50 μm. The transport property measurements were conducted in Physical Property Measurement System (Quantum Design, PPMS). X-Ray absorption near edge structure (XANES) measurements. The XANES data have been recorded for the 10 uc LAO/STO and LSAT/STO interface with P O2 = 5 mTorr. The thickness is chosen at 10 uc to guarantee the access to the interface during XANES measurements at the Ti L 32 -edge. The XANES spectra were collected at the SINS beam-line at the Singapore Synchrotron Light Source (SSLS). To avoid possible contamination and surface modification, experiments were performed in UHV chamber with a background pressure of about 2× 10 −10 mbar. All XANES spectra presented here were recorded ex-situ and at X-ray incident angle of 90° using total electron yield (TEY) mode.