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Full oxide heterostructure combining a high-Tc diluted ferromagnet with a high-mobility conductor

We report on the growth of heterostructures composed of layers of the high-Curie temperature ferromagnet Co-doped (La,Sr)TiO3 (Co-LSTO) with high-mobility SrTiO3 (STO) substrates processed at low oxygen pressure. While perpendicular spin-dependent transport measurements in STO//Co-LSTO/LAO/Co tunnel junctions demonstrate the existence of a large spin polarization in Co-LSTO, planar magnetotransport experiments on STO//Co-LSTO samples evidence electronic mobilities as high as 10000 cm2/Vs at T = 10 K. At high enough applied fields and low enough temperatures (H<60 kOe, T<4 K) Shubnikov-de Haas oscillations are also observed. We present an extensive analysis of these quantum oscillations and relate them with the electronic properties of STO, for which we find large scattering rates up to ~ 10 ps. Thus, this work opens up the possibility to inject a spin-polarized current from a high-Curie temperature diluted oxide into an isostructural system with high-mobility and a large spin diffusion length.


I. INTRODUCTION
The early years of spintonics have focused on the giant magnetoresistance (GMR) of magnetic metallic multilayers 1 , and the tunnel magnetoresistance of magnetic tunnel junctions combining metallic ferromagnets and insulating barriers 2 . Both have led to interesting devices such as magnetoresistive read heads, sensors and an incoming new generation of non volatile magnetic random access memories (MRAMs).
Further developments in spintronics 3 now aim at combining ferromagnets with semiconductors in order to, for instance, modulate spin-polarized transport by a gate voltage. This functionality opens exciting perspectives, but is prohibited in fully metallic structures because of the large carrier density (n ≈ 10 22 cm −3 ). Unfortunately, at the interface between a ferromagnetic metal (FM) and a semiconductor (SC) spin-flip events (inversely proportional to the resistivity ρ times the spin diffusion length l sf ) lead to an almost complete loss of the spin polarization inside the metallic ferromagnet due to the difference in the resistivities between the two materials 4,5 . Such a loss is not observed in metallic multilayers such as Co/Cu, due to the similarity of their ρ×l sf products, and an efficient spin injection can occur in Cu. It has been suggested that introducing a spin-dependent resistance at the FM/SC interface can solve this problem of "conductivity mismatch" 5,6 . Yet, one of the best solutions would be to realize heterostructures combining highly spin-polarized ferromagnets and non-magnetic materials with similar resistivities, to enable efficient spin injection (in the ohmic regime), and low carrier density, to enable gate voltage effects.
Most efforts in this direction have focused on semiconductor structures using II-VI or III-V diluted magnetic semiconductors (BeZnMnSe 7 or (Ga,Mn)As 8 ) as spinpolarized injectors. Since the Curie temperature (T C ) of (Ga,Mn)As is lower than about 170K 9 , such devices are limited to low-temperature operation.
Oxide materials have not been considered so far but should be interesting candidates since high-T C ferromagnetism has been reported in diluted magnetic oxide systems (DMOS) like Co-doped TiO 2 10 and ZnO 11 for instance. In addition, high-T C ferromagnetism was recently found in La-and Co-doped SrTiO 3 thin films 12,13 . In this paper we present results on structures combining (La, Sr)Ti 1−x Co x O 3 (Co-LSTO) and SrTiO 3 (STO). The archetypical perovskite STO is widely used as an insulating and diamagnetic substrate for thin film growth. Remarkably, its transport properties can be drastically modified by doping with Nb 14 , La 15 or by creating oxygen vacancies, and a transition towards a metallic state occurs for carrier densities as low as ≈ 10 17 cm −3 (14,16).
Here, we report the properties of ferromagnetic Co-LSTO thin films grown on STO (001) substrates at low oxygen pressure (7×10 −7 ≤ P O2 ≤ 5×10 −6 mbar). In these conditions, the Co-LSTO films are ferromagnetic with a large intrinsic spin-polarization and the STO substrates are conductive. Both materials have lowtemperature resistivities in the mΩ·cm range and in STO, we find mobilities of up to 10 4 cm 2 /Vs. Accordingly, Shubnikov-de Haas (SdH) oscillations are observed and their analysis reveal that carriers have long scattering rates of τ ≈ 10 −11 s, suggesting a spin-diffusion length exceeding 1 µm. We argue that this observation, together with the low carrier density in STO and the large spinpolarization of Co-LSTO, opens the way for the realization of full oxide spin field effect transistors (spin-FET).

II. EXPERIMENTAL
Co-LSTO and LSTO epitaxial thin films were grown on 10 mm × 10 mm × 0.5 mm STO(001) or LAO(001) (LAO : LaAlO 3 ) substrates by pulsed laser deposition (PLD) 13 from (La,Sr)Ti 1−x Co x O 3 targets with x = 0.02 and x = 0 (see Table I for a summary of the sample description). The La/Sr ratio was about 2:1. The deposition oxygen pressure (P O2 ) was varied from 7×10 −7 mbar to 10 −4 mbar. For current-perpendicular-to-plane (CPP, Fig. 1(a)) transport measurements in Co-LSTObased magnetic tunnel junctions (MTJs), a 2.8 nm LAO layer was grown in the same conditions on the Co-LSTO films. The Co-LSTO/LAO bilayers were then covered by a Co/CoO/Au stack, processed into tunnel junctions 17 and measured in standard 4-wire DC configuration. The magnetic properties of thin films were measured with an alternating gradient force magnetometer (AGFM) at room temperature. Current-in-plane (CIP, Fig. 1(b)) magnetotransport measurements were performed on Co-LSTO and LSTO single films in Hall geometry, with an AC set-up (22 Hz) and in magnetic fields up to B = 16 teslas and temperatures down to T=1.5K. Each sample had a pair of current, voltage and Hall contacts, to which 30 µm diameter platinum wires were attached with silver paint. The Hall resistance R xy was measured at fixed temperatures and in field sweepings from maximum negative to maximum positive value, in order to eliminate the possible mixing of magnetoresistive components (R xy = [R xy (B) − R xy (−B)]/2). The Hall resistance was linear with the magnetic field for all samples. The mobility was determined as µ = L/w(R xy /R xx B), where L is the distance between the voltage contacts, w is the width of the specimen and R xx is the CIP-resistance. For the measured samples, L varied between 5 and 6 mm, and w = 2 mm.

III. MAGNETOMETRY AND CPP MEASUREMENTS: FERROMAGNETISM AND SPIN POLARIZATION OF CO-LSTO
The inset of Fig. 2 shows that Co-LSTO films are ferromagnetic at room temperature, with a maximum saturation magnetization (M S ) of about 5 emu/cm 3 obtained for films grown at the lowest pressures (P O2 ≤ 5×10 −6 mbar). We have probed the spin polarization of the Co-LSTO layers by measuring the magnetotransport properties (in CPP geometry) of Co-LSTO/LAO/Co MTJs. experiments with, in particular, the analysis of the peculiar TMR bias dependence and the determination of the spin polarization (-80%) are presented elsewhere 18 .
Our resistance and mobility data can therefore be summarized as follows. The large values of ℜ and µ appear only when Co-LSTO films are grown on STO substrates at low oxygen pressure (samples ♯1 − ♯4). Indeed, this conductive behavior, together with a high-   We note that it is remarkable that the conditions necessary to grow the DMOS with a large spin-polarization generate this high-mobility state in the STO. The thickness over which the high-mobility state is created in STO is discussed later. Magnetic field and temperature dependence of the CIP resistance R xx for sample ♯2 is shown in Fig. 6. The magnetic field H was applied perpendicularly to the sample plane. A large positive perpendicular magnetoresistance ing oscillations (at T ≤ 4 K and µH ≥ 6 T) that are due to the Shubnikov-de Haas (SdH) effect. We emphasize that we have observed SdH oscillations in all other high-mobility samples. Oscillations with the same period are also observed when the field is applied parallel to the sample plane in the longitudinal configuration (not shown). Such observation evidences that the highmobility region is 3D-like and is not an interface effect. Quantum transport effects like SdH oscillations are usu- ally observed in systems with high mobilities. This is the case of semi-metals like Bi 20 or semiconductors like GaAs 21 , but SdH oscillations have been very seldom observed in oxide materials 22,23,24 .
In order to isolate the SdH oscillations, first a background positive magnetoresistance R bkgnd was determined by fitting the experimental data R xx to a loworder polynomial (cf. inset of Fig. 6). The oscillating part ∆R SdH of the magnetoresistance was then obtained as ∆R SdH = R xx − R bkgnd . Fig. 7 shows that ∆R SdH scales with mobility µ in the same way as does the perpendicular magnetoresistance PMR. The origin of the large values of the PMR is presumably related to the perturbation of the electronic orbitals by the applied field and, thus, they are more significant when the mean free path, i. e. the mobility, is larger. Our results indicate that both SdH amplitudes and PMR originate from similar physical mechanisms. Fig. 8 presents the oscillations of ∆R SdH as a function of 1/B and temperature. We analyzed these SdH oscillations in our samples using the conventional Lifshitz-Kosevich expression 25 . The amplitude of the oscillation is given as: where ∆R SdH is the amplitude of the SdH-oscillating part of the resistance, and F =hA/2πe (A is the extremal orbit area in k-space perpendicular to the applied field) is expressed in teslas. The oscillation amplitude is damped due to the smearing of the Fermi surface orbit by temperature (R T ), scattering (R D ) and spin-splitting effects (R S ) : where m H is the effective mass, T D =h/(2πk B τ ) is the Dingle temperature and τ is the scattering rate; where g ef f is the effective Landé factor. A Fast Fourier Transform (FFT) method has been used to obtain the power spectra of the measured resistance values. This analysis indicates a primary frequency of F ≈ 24 − 35 T, depending on sample (Fig. 9). The data also suggest the presence of higher-frequency components; however, their amplitude is much lower, and therefore they will be neglected in the following discussion. From the frequency F we can infer the crosssectional area A of the closed electronic orbits contributing to the SdH oscillations. Experimental data support a conduction band of STO consisting of ellipsoids of revolution having the long axis along the <100> crystalline axes, and minima at the Γ-points 16,26,27 . Taking into account this k-space geometry and the value of k F , we can estimate the carrier density as n ≈ 1.0 × 10 18 − 1.9 × 10 18 cm −3 (see Table II and section VIII). We observe that the mobility increases with decreasing n (cf. inset of Fig.  9), in agreement with previous reported works 14 . This may be explained by assuming that oxygen vacancies act as carrier donors, being simultaneously scattering centers.
In comparison, the carrier density of sample ♯5 (Co-LSTO on LAO) deduced from Hall experiments is n ≈ 9×10 21 cm −3 . We recall that in this case the Hall experiments allow the extraction of the electronic properties of the film, since the substrate is an insulator. The measured carrier density is consistent with about 0.6 carrier per formula unit, which is in a good agreement with what is expected from the film composition, assuming the presence of some oxygen vacancies. For the high-mobility samples (♯1 − ♯4), the effective mass (m H ) of the carriers in STO was estimated by analyzing the temperature dependence of the SdH oscillations amplitude and plotting ln (∆R SdH /T ) vs. temperature. This expression is accurate within an error < 2% and can be deduced from Eq. (1), assuming that T/B ≥ 0.14/(m H /m e ) (KT −1 ). We have checked this condition after the extraction of m H . Our analysis yields the values of m H between 0.94 − 1.2m e (cf. Table II). The Dingle temperature T D was obtained from the slope of the plot of ln (∆R SdH B 1/2 sinh(α(m H /m e )T /B)) versus 1/B at T = 1.75 K. Due to the limited number of oscillations in the explored range of field values, this analysis turned out to be quite difficult. Nevertheless, values of T D = 0.3 − 1 K were obtained, corresponding to scattering rates τ D = 4 − 12 × 10 −12 s. The values of τ D correspond to the scattering rates of the closed electronic orbits around the extremal cross sections of the Fermi surface. Due to the cubic symmetry of STO, we can estimate the scattering rate τ = µmH e at low temperature, assuming that the effective mass is isotropic and equal to m H . Using the values of µ and m H (table II) we get τ = 1.5 − 6 × 10 −12 , in good agreement with the values of τ D .
Knowing the carrier densities and mobilities, we can calculate the resistivity through ρ xx = 1/(neµ). We find increasing values in the range ρ xx = 0.6 − 1.5 mΩ cm, for decreasing mobilities within the range 2250 -10500 cm 2 /Vs (see Table II). These values of ρ xx are consistent with those from the literature, for similar mobility values 14 .
The values of ρ xx and n allow us to estimate the order of magnitude of the thickness t STO of the high mobility region inside the STO. From ρ xx = (wt STO )R xx /L, with L ≈ 5 − 6 mm and w ≈ 2 mm, we infer t STO ≈ 300 -900 µm. We can also estimate t STO from the measured Hall constant R H = 1/ne = R xy t STO /B, and assuming the values of the carrier densities extracted from the SdH analysis (Table II) we find again t STO ≈ 300 -900 µm. In other words, the high mobility system is not an interfacial interface effect, but it is extended to a sizable part of the STO substrate. This is also supported by the observation of SdH oscillations when the magnetic field is applied in the film plane in the longitudinal configuration (see section V). An additional support for this conclusion comes from the estimation of the spread of the oxygen vacancy diffusion in STO, by using the diffusion constants determined experimentally from optical experiments 28 . Even in the less favorable case (considering trapping effects due to impurities inside the STO, and at pressures P O2 ≈ 10 −2 mbar, i. e. around four orders of magnitude higher than our growth conditions), the determined diffusion constants were D ≈ 10 −4 cm 2 /s at T ≈ 700 o C; with this value, the diffusion of O-vacancies during the deposition time t dep ≈ 10 2 − 10 3 s can be estimated to be l Ovac ≈ (D × t dep ) 1/2 ≈ 1 mm. Thus, the oxygen vacancies can diffuse across the STO substrate, which is consistent with the t STO ≈ 300 -900 µm we found from transport data.

VI. PERSPECTIVES
The resistivity of the Co-LSTO films can be calculated from the resistance of the LAO//Co-LSTO and high-P O2 STO//Co-LSTO samples and the Co-LSTO film thickness. This yields 0.9 mΩ·cm and 1.15 mΩ·cm at low temperature, respectively, see Table III. Thus, the lowtemperature resistivities of the Co-LSTO films and the oxygen-deficient STO substrates are in the mΩ·cm range. Due to the high mobility of the latter, it is tempting to consider the possibility of spin-injection from Co-LSTO into STO, as in the Co/Cu case. More precisely, in this case the spin-polarization of the injected current is given by 5 P = β/(1 + r N /r F ) = β/[1 + (ρ N l N sf /ρ F l F sf )] (5) with β being related to the spin-up resistivity ρ ↑ and spin-down resistivity ρ ↓ channels in the ferromagnet by β = (ρ ↑ − ρ ↓ )/(ρ ↑ + ρ ↓ ). ρ F , ρ N and l F sf , l N sf are the resistivities and the spin diffusion length in the ferromagnet and the non-magnetic material, respectively. In the present case, we know ρ N /ρ F ≈ 1 and β should be close to -1 as the spin-polarization of Co-LSTO is -80% 18 . In conventional metals, l sf is usually much longer than the mean free path λ. Here λ ST O ≥ 100 nm and λ Co−LST O ≈ 1 nm but the spin diffusion lengths are unknown for virtually all oxide materials.
Since oxygen-deficient STO thin films with mobilities and resistivities comparable to those reported for single crystals have already been fabricated 29,30 , Co-LSTO/STO superlattices could exhibit a significant CPP GMR and systematic GMR studies should allow measuring l sf in both materials.
It must be pointed out that the efficient spin-injection from Co-LSTO into STO may be limited to the lowest temperatures due to the steep increase of resistivity of STO (cf. Fig. 3). However, if the r N /r F ratio turns out to be too large to allow an efficient spin-injection, the latter could be increased by inserting for instance, an ultrathin tunnel barrier of LAO 5 . Our TMR measurements indeed demonstrate that in the low oxygen pressure conditions required to obtain ferromagnetic Co-LSTO and high-mobility STO, LAO retains its insulating properties.
Finally, we would like to mention that several groups have fabricated FETs using STO as the channel material, with gains reaching 100 at room temperature 31 . Remarkably, the field effect proves efficient for a wide range of carrier density, from the undoped 31 to the metallic state (n ≈ 10 18 cm −3 ) 30 and even in the low-temperature superconducting phase 32 . If the field effect can modify the spin-diffusion length (in addition to the carrier density), or enables the tuning of spin-flip mechanisms (in analogy to the principle of the Datta and Das transistor 33 ), full oxide spin-FET using STO channels and Co-LSTO as spin injector and detector could be built in the near future.

VII. CONCLUSION
In conclusion, we have demonstrated the feasibility of growing a full oxide structure combining a highly spin polarized diluted magnetic system Co-LSTO and highmobility (up to ≈ 10 4 cm 2 /Vs) STO, by using low oxygen pressure growth conditions. At low temperatures and high magnetic fields, we have observed Shubnikovde Haas oscillations in the resistance of the STO. Careful analysis of this behavior for several samples has allowed us to extract valuable information on the electronic properties of the high-mobility STO. Besides the very large mobility, we have found that the metallic state of STO occurs for carriers densities as low as ∼ 10 18 cm −3 , with large scattering rates up to ≈ 10 −11 s. The combined properties of the two materials -i. e. the large spinpolarization of Co-LSTO and the long mean free path of STO -makes them interesting to realize spin-injection devices like spin FET, the low carrier density of STO enabling external control by gate voltage. Several studies have recently demonstrated the potential of Ti perovskites for oxide electronics 34,35,36 . We are convinced that our findings extend this potential to oxide spintronics.

VIII. ANNEX: ESTIMATION OF THE CARRIER DENSITY FROM SDH OSCILLATIONS
The Fermi surface of STO is composed of three ellipsoids of revolution centered at Γ-points with the long axis k F,max along <100> crystallographic axes and the short k F,min axes transverse to them 16,26,27 . The ratio between the longitudinal (m l ) and transverse (m t ) masses have been determined experimentally as m l /m t ≈ 4 16,26 . Recalling that ∂ 2 E(k)/∂k 2 ∝ 1/m, we can infer that k F,max /k F,min ≈ 4.
Let us assume that a field H z is applied along the [001] direction. Then the extremal electronic closed orbits corresponding to the 2 spheroids directed along x-and yaxis are ellipsoidal with cross sections equal to π · k F,min · k F,max , whereas the cross sections of the ellipsoid along the z-direction is circular with an area π · k 2 F,min . In addition, since k F,max /k F,min ≈ 4 there are about 4 more electrons around the ellipsoidal closed orbits than those orbiting the circular orbits. Taking into account these facts, we assume that the main frequency peak of the ∆R SdH oscillations comes from electrons orbiting the ellipsoidal cross sections, and, thus, A = π · k F,min · k F,max . As the total volume in the k-space occupied by the 3 ellipsoids is V k = 3 × 4π 3 k 2 F,min k F,max , we can estimate the carrier concentration as n = 3 × k 2 F,min kF,max 3π 2 .