Jin Hong Lee

Felix Trier

Tom Cornelissen

Daniele Preziosi

Stéphane Fusil

Karim Bouzehouane

Sergio Valencia

Manuel Bibes
email: manuel.bibes@cnrs-thales.fr

Imaging and Harnessing Percolation at the Metal-Insulator Transition of NdNiO 3 Nanogaps

Keywords: metal-insulator transition, phase separation, domain percolation, nanodevice

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Competition between co-existing electronic phases in first-order phase transitions can lead to a sharp change in the resistivity as the material is subjected to small variations in the driving parameter, e.g., the temperature. One example of this phenomenon is the metal-insulator transition (MIT) in perovskite rare-earth nickelates. In such systems, reducing the transport measurement area to dimensions comparable to the domain size of insulating and metallic phases around the MIT should strongly influence the shape of the resistance-temperature curve. Here, we measure the temperature dependence of the local resistance and the nanoscale domain distribution of NdNiO3 areas between Au contacts gapped by 260 down to 40 nm. We find that a sharp resistance drop appears below the bulk MIT temperature at ~105 K, with an amplitude inversely scaling with the nanogap width. By using X-ray photoemission electron microscopy, we directly correlate the resistance drop with the emergence and coalescence of individual metallic domains at the nanogap. Our observation provides a direct insight into percolation at the MIT of rare-earth nickelates.

Percolative electronic transport naturally occurs in heterogeneous media but can also arise in disordered systems or as a result of electronic phase separation in strongly correlated materials 1,[START_REF] Stauffer | Introduction to Percolation Theory[END_REF] . The electronic phase separation typically occurs in systems displaying a first-order metal-insulator transition (MIT) [START_REF] Imada | [END_REF] , as in several classes of transition metal oxides (VO2, 4-10 V2O3 11 or perovskite rareearth nickelates 12 ).

Recently, with an abundant availability of fabrication, lithography and spectroscopy techniques at length scales of nanometers, the MIT behavior of transition metal oxides have been intensively investigated 13 . In the work of Sharoni et al. 14 , multiple resistance drops or jumps within the resistancetemperature (R-T) curve were observed in VO2 nanodevices. The maximal resistance jump size was herein found to scale inversely with device length with so-called avalanche events following a stochastic power law dependence. Another vanadium oxide compound, V2O3, was studied by Wang et al. 15 who found a similar first-order percolation driven MIT in patterned nanodevices. In nanogaps of the phase-separated ferromagnet (La, Pr, Ca)MnO3, G. Singh-Bhalla et al. 16 observed multiple steplike changes of resistance and proposed the presence of possible intrinsic tunnel barriers based on a magnetic-field effect. Kumar et al. 17 reported a stochastic resistance switching process between two coplanar electrodes deposited on a polycrystalline NdNiO3 (NNO) pellet.

Although the previous studies have suggested that the step-like resistance changes could originate from domain distribution based on the R-T characteristic, the direct correlation between domain distribution and resistance change still remains elusive, particularly, in perovskite rare-earth nickelates.

Here, we have analyzed the device-size-dependent R-T curves of NNO nanogaps and then measured their domain evolution by utilizing an X-ray photoemission electron microscope (X-PEEM), thereby correlating the microscopic domain percolation with the macroscopic resistance change.

NNO belongs to perovskite rare-earth nickelates, a family of materials displaying a phase diagram where the MIT temperature can be tuned by the size of a rare-earth cation 18 . The MIT of NNO is first order and accordingly, the material shows a phase separation between a metallic/paramagnetic phase and an insulating/antiferromagnetic phase 19,20 ; the nucleation size of metallic domains inside an insulating matrix domains has been observed to be ~100-300 nm upon warming up across the MIT transition of NNO 20 . Therefore, when the size of NNO nanogaps becomes comparable to the nucleation size of NNO metallic domains, the R-T curve is expected to differ significantly from the bulk one due to the appearance of discernible resistance drops. An optical microscopy image of a NNO nanogap device is shown in Fig. 2(a). Since the Au electrodes are constricted in the center of the nanogap, the measured resistance of the nanogaps mostly originates from the area between the electrodes [see the AFM image in Fig. 2(b)], where the width and length of this area is defined as d (nm) and 2d (nm), respectively. A series of R2pt-T curves (here, R2pt stands for the two-point resistance) from the nanogaps are obtained for d ranging between 40 -260 nm, as shown in Figs. 2(c-j). All curves contain multiple R drops or jumps below the MIT temperature except the device for d = 260 nm that mimics the macroscopic behavior of NNO. In order to capture the delicate relation between d and domain evolution, we have performed two types of analysis. First, the two-exponent phenomenological percolation model 21 is applied by fitting both the insulating-and metallic-phase (I-and M-phase, respectively) regime of R2pt-T heating curves with the equations from the Mott variable range hopping model and the non-Fermi liquid model, respectively, cf. below [also see the fit result in Fig. 3(a)]:

1/4 I-phase 0 1 1 2 2 ( ) exp( / ) exp( / ) G T G G E T G E T      (1)
M-phase 1 2

()

G T A A T  (2)
where I-phase G and M-phase G correspond to the conductance of I-phase and M-phase, and 0,1,2 G , 1,2 E and 1,2

A are fitting parameters. With the two fit curves obtained, the volume fraction of I-phase, i.e., FI-phase, as a function of T [Fig. 3(b)] can be calculated by using the Bruggeman symmetric media equation 22 :

M-phase full I-phase full I-phase M-phase I-phase full ( ){ ( 1) } () () G G G D G FT G G DG      (3)
where full G corresponds to the full heating curve obtained from the experiment, and D is the dimension of our system set to be 2. This two-dimensional approximation seems reasonable since the film thickness is only ~4 nm 23 and the size of M-phase domains is about two orders of magnitude higher 19,20 . In Fig. 3(c), the maximum amplitude of FI-phase drops, i.e., (FI-phaseFI-phase)max is extracted from each R2pt-T heating curve of Figs. 2(c-j), which shows that the shorter the distance between the electrodes becomes, the larger the FI-phase drops are observed. The second analysis exhibits the same trend by comparing the maximum R drop, i.e., (R/R)max, with electrode gap d as shown in Fig. 3(d),.

Only two devices with d = 140 and 150 nm slightly deviate from this trend. This may arise from the local variation of the M-phase nucleation size in these two particular nanogaps. Since the M-phase has a relatively higher Ia compared to the case of the I-phase, the green and yellow pixels between two electrodes correspond to the domain nucleation and evolution of the M-phase.

Accordingly, the blue pixels indicate the I-phase. Far below the MIT temperature [see Fig. 4(a)] the Iphase domains dominate most of the studied area, which matches well with the insulating R2pt-T behavior at the same temperature in Fig. 3 In summary, we have directly correlated the R drops appearing at the MIT of NNO nanogaps with the domain percolation behavior by combining electronic transport measurement and X-PEEM. The comparative analysis between the R2pt-T curve and the X-PEEM images clearly illustrates that the observed R drops below the MIT temperature in the electronic transport measurement of NNO originates from the percolating behavior of the M-phase domains at the nanogaps. Based on our observations, future studies such as visualizing a current-injection-driven or light-pulse-induced domain switching 24 processes in NNO nanogaps will extend our knowledge on the first-order MIT and phase separation. More generally, our finding offers a deeper understanding on the electronic transport in the nanodevices of first-order MIT materials where the domain nucleation is comparable to the size of the devices.

MATERIALS AND METHODS

10-unit-cell-thick NNO films were epitaxially grown by using pulsed laser deposition and monitored with reflection high-energy electron diffraction (RHEED) during the growth of the films.

The detailed growth conditions can be found in previous references 20,25 . Following the NNO film deposition, a PMMA A6 resist soft-mask was prepared with e-beam lithography. To ensure good electrical contact between the Au electrodes and the NNO film, the NNO surface was cleaned by insitu oxygen plasma exposure prior to dc magneton sputtering of 25-nm-thick Au at room temperature.

Subsequently, the residual Au film was removed by lift-off leaving an area between two coplanar Au electrodes of varying size, i.e., d  2d nm 2 . The R-T curves of the prepared NNO nanogaps were obtained by the current pulse measurement in the resistivity module of a Quantum Design Dynacool.

The van der Pauw geometry was used to obtain the resistivity () of the bare NNO films before fabrication of the NNO nanogaps. The two-point resistance of the NNO nanogaps was performed with a temperature sweeping rate of 2 K/min. In order to image the local distribution of metallic (M-phase)

or insulating (I-phase) domains around the NNO nanogaps, the spatially-resolved and temperaturedependent X-PEEM was performed at the UE49 PGM beamline of the BESSY II in the Helmholtz-Zentrum Berlin 26,[START_REF] Kronast | large-scale[END_REF] .

CALIPSOplus under the Grant Agreement 730872 from the EU Framework Programme for Research and Innovation HORIZON 2020.

Figure 1 .

 1 Figure 1. (a) An atomic force microscopy image of an as-grown NNO film. The scale bar represents 1 m. (b) The RHEED intensity and pattern during the growth of film. (c) The resistivity of unpatterned NNO film as a function of temperature.

Figure 2 .

 2 Figure 2. (a) Optical microscopy image of a NNO nanogap device. (b) AFM zoom in of the nanogap area within the white box shown in (a) where the distance between the two Au electrodes (d) is 80 nm. The scale bar represents 100 nm. (c-j) A series of R2pt-T curves with d = 40 -260 nm.

Figure 1 (

 1 Figure 1(a) shows an atomically flat surface of the NNO film. For all devices studied, the films

Figure 3 .

 3 Figure 3. (a) The fit curves of I-phase and M-phase regime in the heating curve of the d = 80 nm case. (b) The extracted fraction of I-phase (FI-phase) from the fit curves in (a). The nanogap-size-dependent (c) FI-phase and (d) R drops.

  (a). As shown in Fig. 4(b), the nucleation and growth of the M-phase domains are observed at 100 K. More importantly, Fig. 4(e) shows that the very first metallic percolation occurs at the nanogap and this result can be related to the starting point of R drops in the R2pt-T heating curve at ~105 K. Figs. 4(c) and (d) show that most of the area in the view becomes metallic after 110 K although the volume fraction of the M-phase still increases between 110 K and 120 K, which may correspond to the beginning of the bulk-like R decrease at ~125 K in the R2pt-T curve.

Figure 4 .

 4 Figure 4. (a-d) The X-PEEM images showing the contrast of normalized Ia/Ib at four different temperatures, i.e., 57, 100, 110 and 120 K. The scale bar in (a) represents 200 nm. (e) The zoomed-in image of the black-dashed box in (b). The red-dashed box indicates the first metallic percolation in between two Au electrodes. The scale bar represents in (e) 100 nm.

ACKNOWLEDGMENTS

This work received support from the ERC Consolidator grant no. 615759 "MINT", the French Research Agency (ANR) as part of the "Investissement d'Avenir" program (LABEX NanoSaclay, ref ANR-10-LABX-0035) through project "AXION", and by the Region Ile-de-France DIM OXYMORE program through project "NEIMO". F.T. acknowledges support by research grant VKR023371 (SPINOX) from VILLUM FONDEN. We thank HZB for the allocation of neutron/synchrotron radiation beamtime. The research leading to this result has been supported by the project


245,000 cells for a gelose surface of 25 cm 2 , against 80,000 cells for a gelose surface of 144 cm 2 in the presented results

M.N. Pons 1,4 , K. Petitcolas 1 , C. Lemaître 1 , Pradalier 2 , H. Guilloteau 3 , C. Merlin 3 Beyond their role, some antibiotics continue to exert an effect below their minimum inhibitory concentration level, where they can act as signaling molecules to modulate various bacterial activities: biofilm formation, exopolymers production, virulence, quorum sensing, cell mobility, and even the dissemination of specific antibiotic resistance genes. This clearly asks the question of the possible effects antibiotics can have once diluted after the disposal of reclaimed wastewater into the aquatic environment or during its reuse. Lately we developed a biosensor approach to identify antibiotics interfering with gene regulation. This approach lies on the use of bacteria genetically modified to express a bioluminescence once the promoter of a relevant function is induced by a modulating antibiotic. Rather than testing arbitrary chosen concentrations, the biosensor is exposed to diffusion gradients of antibiotics in agar plate (as for antibiograms) while luminescence profiles are recorded by CCD camera. With such approach we could detect several antibiotics able to trigger the activation of promoters controlling the mobility functions of "integrative and conjugative elements" (ICEs) such as Tn916 and SXT. An automated image analysis algorithm combined with a modelling of the diffusion process in the agar has been developed to convert the luminescence profile into a concentration profile information, enabling to estimate the level of induction and the range of sub-MIC concentration at which an antibiotic remain effective.

The biosensor strains are first spread onto the agar of a square Petri dish before receiving one to sixteen antibiotics loaded disks deposited in an equispaced manner. The agar plate is incubated at 30°C allowing the antibiotics to diffuse and luminescence and transmitted light images are regularly acquired over time. An automated image processing system has been developed to detect the induction and inhibition zones around each antibiotic loaded disk. For the present experiment two antibiotics were used: ciprofloxacin (CIP) (broad spectrum) and nalidixic acid (NAL) (limited spectrum). Both inhibit the DNA gyrase while CIP inhibits also topoisomerase IV. Commercially available discs (BioRad) were used (30 µg for NAL and 5 µg for CIP). Additional discs were prepared by loading cellulose discs with antibiotic solutions. The MIC values were determined in separate experiments in liquid phase for each antibiotic.

The diffusion of antibiotics in agar is modelled through a finite element computational model based on Fick's second law of diffusion. The simulations are performed using a Computational Fluid Dynamics software (Fluent by ANSYS). The mesh contains ≈ 80,000 cells. It is assumed that the antibiotics deposited in the thin top agar layer exhibit higher diffusivities in this layer than in the bulk solid agar.  First simulation results show that it is possible to estimate the diffusivity of an antibiotic in gelose media. A refinement of the simulation mesh is however necessary, especially for high-MIC antibiotics, to estimate properly sub-inhibitory concentrations. Such refinement is currently tested.

D

  are the antibiotic diffusivity in the top agar and the diffusivity ratio between the top and the bulk agar. Here D top /D bulk = 1000.  Effect of clone and concentration with NAL  Effect of Petri dish with NAL and CIP (same clone)  Effect of concentration on CIP (same clone) MIC (CIP) = 0.015 µg/mL = 4.5310 -5 mole/m 3 MIC (NAL) = 3 µg/mL = 1.2910 -2 mole/m 3 The effect of experimental parameters such as clone and antibiotic type and concentration has been tested. An improvement of the spatial resolution would be useful for antibiotics such as NAL with a high MIC.


Dr Raphaël Aeschlimann

Dr Daniele Preziosi

Prof Philipp Michael Scheiderer

Michael Sing

Dr Sergio Valencia

Jacobo Santamaria

Dr Chen Luo

Dr Hanjo Ryll

Dr Florin Radu

Ralph Claessen

Dr Cinthia Piamonteze

Manuel Bibes
email: manuel.bibes@cnrs-thales.fr

Prof Sing

Ralph Claessen

Prof Jacobo Santamaria

A living-dead magnetic layer at the surface of ferrimagnetic DyTiO3 thin films

Keywords: magnetic oxides, Mott insulators, X-ray absorption spectroscopy, X-ray photoemission spectroscopy

Abstract

When ferromagnetic films become ultrathin, key properties such as the Curie temperature and the saturation magnetization are usually depressed. This effect has been thoroughly investigated in magnetic oxides such as half-metallic manganites, but much less in ferrimagnetic insulating perovskites such as rare-earth titanates RTiO3, despite the appeal of these materials to design correlated two-dimensional electron gases. Here, we report on the magnetic properties of epitaxial DyTiO3 thin films. While films thicker than about 50 nm show a bulk-like response, at low thickness we observe a surprising increase of the saturation magnetization. We model this behavior using a classical model of "dead layer" but we assume that this layer is actually "living", i.e. it responds to the magnetic field with a strong paramagnetic susceptibility.

Through depth-dependent X-ray absorption and photoemission spectroscopy, we show that the "living-dead layer" corresponds to surface regions where magnetic (S=1/2) Ti 3+ ions are replaced by non-magnetic Ti 4+ ions. Element specific hysteresis cycles obtained at the Dy M5 and Ti L3 edges indicate that the surface Ti 4+ ions decouple the Dy 3+ ions, thus unleashing their strong paramagnetic response. Finally, we show how capping the DyTiO3 film with different materials can help increase the Ti 3+ content near the surface and thus recover a better ferrimagnetic behavior.

Among transition-metal perovskites, rare-earth orthorhombic titanates RTiO3, (R=La... Lu or Y) emerge as a particularly interesting family of Mott insulators [1][2][3][4] . The most stable valence state of rare-earths (except for Eu and Ce) is 3+, which imposes a 3+ valence state to the Ti, that is thus in a spin ½ 3d 1 electronic state. A salient feature of RTiO3 compounds is the phase transition from ferrimagnetic to antiferromagnetic (G-type) order when going from small (Lu... Gd) to large rare-earths (Sm... La) [1,3] . This insulating-ferrimagnetic behavior is exceptional among simple perovskites and offers perspectives for engineering novel magnetic states at oxide interfaces [5,6]. . However, the growth of high quality thin films of rare-earth titanates is challenging due to the relatively poor stability of the Ti 3+ valence state [7] . So far, literature on ferrimagnetic titanate thin films is very scarce, aside from a few reports on GdTiO3 [8,9] and YTiO3 [10,11] . Here, we focus on DyTiO3 (DTO), for which thin film growth has never been reported. In the bulk, this compound has a Curie temperature (TC) of 60 K, among the highest in the RTiO3 family, and a non-collinear magnetic order comprising canted Dy moments whose resulting magnetization is antiferromagnetically coupled to that of Ti spins [12,13], , leading to a saturation moment MS = 3.7 µB/f.u. (f.u.: formula unit) [1] . Unlike in the better studied GdTiO3, the magnetic hysteresis cycles of DTO are very square with a strong remanence and a high coercive field [1] , making it more appealing to interfacially imprint a clear magnetic response onto an adjacent oxide layer [6] for instance.

We report on the epitaxial deposition of single-phase epitaxial thin films of DTO using pulsed laser deposition (PLD) in two different growth conditions both corresponding to very low oxygen partial pressures (PO2). We show that while thick films (>50 nm) have almost bulk-like magnetic properties, with a high remanence and a Curie temperature near 60 K, in thinner films a paramagnetic component develops at the expense of the ferromagnetic one. By combining in situ X-ray photoelectron spectroscopy (XPS) and ex situ X-ray absorption spectroscopy (XAS) using several detection modes we could gain insight on the depth dependence of the Ti valence.

Through the correlation between the thickness dependence of the magnetic properties and the depth dependence of Ti oxidation state, we infer how overoxidized Ti ions at the film surface alter the coupling between Dy ions, yielding a peculiar increase of the high-field magnetization in ultrathin DTO films. We present X-ray reflectometry magnetic hysteresis cycles at the Dy M5 and Ti L3 edges that confirm this picture. Finally, we explore the effect of epitaxial capping layers on the Ti valence and the magnetic properties.

Epitaxial thin films of DTO (110)o (o : orthorhombic notation) have been grown on LaAlO3 (001)pc (pc : pseudo-cubic notation) substrates by means of pulsed laser deposition (PLD) in a chamber with a background pressure was in the low 10 -89 mbar range at room temperature and using a multiphase ceramic target ablated by a KrF excimer laser at 2 Hz. The growth of rareearth titanate thin films requires a low PO2 to stabilize the 3+ oxidation of Ti and avoid oxygen interstitials leading to a Ti 4+ state [7][8][9] . We found two suitable growth atmospheres : one under a total pressure of pure oxygen of 410 -7 mbar and one under an argon atmosphere of 110 -3 mbar, both with a substrate temperature of 900°C. The growth was monitored in situ by reflection high-energy electron diffraction (RHEED). For both growth conditions, we observe oscillations of the specular beam intensity (cf insets of Figure 1a andb), indicative of a layerby-layer growth, slightly clearer for growth in pure Ar.

Figure 1a

and 1b shows X-ray diffraction (XRD) 2θ-ω scans for DTO films with a thickness ranging from 5 to 80 nm grown in pure Ar and low PO2, respectively. In addition to the LAO substrate (001)pc reflections, we only observe peaks corresponding to the DTO (110)pc reflections. The out-of-plane lattice constant is between 3.9070.009 Å for all films. For both sets of growth conditions, we thus managed to obtain single phase films of DTO over the full range of thicknesses.

We investigated the magnetic properties of those films through SQUID magnetometry (SQUID: superconducting quantum interference device) after field cooling in 100 Oe. Figure 1c and1d display the field dependence of the magnetization at 10 K for films grown in pure Ar and in low oxygen pressure, respectively. Figure 1e and 1f show the temperature dependence of the magnetization at 100 Oe. Thicker films show a clear hysteresis with a saturation moment at 50 kOe MS=3.5-3.7 µB/f.u., a large remanence and a ferromagnetic transition near 60 K, consistent with the bulk MS and TC [1] . As thickness decreases, TC is gradually reduced for films grown in oxygen whereas it stays more or less constant down to 5 nm for the films grown in pure Ar. In parallel, thickness reduction promotes a puzzling change in the M(H) loops: the loops become less square and more slanted with both remanence and coercivity decreasing, but the high-field magnetization increases up to more than 6 µB/f.u. This behavior is at odds with the situation in ferromagnetic manganites for instance, in which thickness reduction yields a concomitant decrease of both TC and MS, the thinnest films showing no magnetic response [14,15] . These results are summarized in Figure 2. While for both sample series the remanent magnetization monotonically decreases as thickness is reduced (Figures 2a and2c), the saturation magnetization shows an opposite behavior and tends to increase at low thickness (Figures 2b and2d).

In classical itinerant ferromagnets or double-exchange systems such as manganites, the reduction of the saturation magnetization in ultrathin films has been modelled using the socalled "dead-layer" picture that assumes that a fraction of the filmnear the interface with the substrate or at the film surfaceis non-magnetic (i.e. its magnetization is zero). In La2/3Sr1/3MnO3 the dead layer at the interface with an insulating perovskite such as SrTiO3 has a typical thickness of a few nm [14,16,17] . It is believed to originate from changes in the optimal carrier density (due to charge transfer from the adjacent material and/or to the presence of oxygen vacancies) that drive the material's ground state towards neighboring antiferromagnetic and insulating states of the (bulk) phase diagram [16][17][18] .

While our experimental results also suggest that when thickness is reduced the relative contribution of the ferrimagnetic phase of DTO to the overall magnetic response decreases at the expense of another one, they are clearly incompatible with a picture assuming such a non-magnetic dead layer. Instead, we propose that the observed behavior arises from the existence of a non-ferromagnetic "living-dead layer", responding to the field with a strong paramagnetic susceptibility, as suggested by the shape of the M(H) loops in Figure 1c and1d.

To substantiate our claim, we fit the thickness dependence of the remanent and saturation magnetization with this living-dead layer model. Although some dead layer may also be present at the substrate/film interface, we hypothesize that the response is dominated by a dead layer at the film surface. We assume that this layer is paramagnetic and thus has a null magnetization at remanence and a large magnetization at high field. We use a simple bilayer model (a ferrimagnetic layer and a paramagnetic layer):

𝑀 𝑡𝑜𝑡𝑎𝑙 = 𝑚 𝑡𝑜𝑡𝑎𝑙 • 𝑡 = 𝑚 𝑃 • 𝑡 𝑃 + 𝑚 𝐹 • 𝑡 𝐹 𝑚 𝑡𝑜𝑡𝑎𝑙 = (𝑚 𝑃 -𝑚 𝐹 ) • 𝑡 𝑃 𝑡 + 𝑚 𝐹
with t = tF + tP the total film thickness, tF the thickness of the ferrimagnetic layer, tP the thickness of the paramagnetic layer, mF the moment per unit volume of the ferrimagnetic layer and mP the moment per unit volume of the paramagnetic layer. We used the DTO bulk value 3.7 µB/f.u. [1] for mF and focus on the samples grown in pure Ar. Setting mP to the maximum magnetization of the thinnest sample (mP6.5 µB) and using tp as a fitting parameter (model 1) yields a high fit quality, with tp=7-8 nm (Fig. 2a). A dead layer thickness of 5 nm is obtained by fitting the remanent magnetization (Fig. 2a) and assuming here mP=0 µB. For the O2 grown films, the fit of MR (not shown) is not very good, possibly reflecting a progressive reduction of the anisotropy in the ferrimagnetic layer when decreasing thickness. We will come back to these data later on.

We now turn to the origin of this dead layer. To address this issue, we have investigated the valence of the atomic species present in the film using X-ray photoelectron spectroscopy (XPS) and X-ray absorption spectroscopy (XAS) with three detection modes probing the sample over different depths. In Figure 3 we plot the XPS spectra of Ti 2p core levels for two 20 nm films collected at different angles, allowing to vary the probing depth over about 5 nm. Focusing on the spectra for the pure Ar film (Fig. 3a and3b), we notice that each of the Ti 2p1/2 and 2p3/2 peaks comprises two main components: one corresponding to Ti 4+ (shaded in blue) and another to Ti 3+ (shaded in red) at higher and lower binding energies, respectively. A third, minor component, possibly corresponding to Ti 2+ (in green) is also visible [19,20] . At normal emission (Fig. 3a), the 3+/4+ ratio is 80:20 and decreases to 39:61 at 45° emission. The data thus clearly point to a gradient of Ti valence over the sample depth, with a higher concentration of Ti 4+ near the surface [21] . Following Ref. [22] , we estimate that the equivalent thickness of the Ti 4+ surface layer is about 1.3 nm. For the film grown in O2, the XPS spectrum at normal emission (Fig. 3c) suggests a larger proportion of Ti 4+ (3+/4+ ratio is 20:80), in line with the more degraded magnetic response of films grown in O2 in this thickness range.

Further insight into this depth dependence of the Ti valence state is provided by XAS on a 80 nm film. We have acquired spectra using three different detection modes: total electron yield (TEY, probing depth 2-10 nm), total fluorescence yield (TFY, probing depth a few tens of nm) and X-ray excited optical luminescence (XEOL, the whole film thickness is probed). In TEY (Fig. 3d), the spectrum exhibits four main features corresponding to the transition from 2p3/2 (L3 edge) and 2p1/2 (L2 edge) levels to the 3d levels split into t2g and eg states by the crystal field. The spectrum looks close to the one expected from Ti 4+ (as in SrTiO3 for example [23] ), with albeit some noticeable differences in line shape and intensities. As we probe deeper in the sample using TFY (Fig. 3e), the spectrum exhibits additional components, and peaks at lower energy grow in intensity [24,25] . We interpret this as the signature of Ti 3+ ions for which XAS features shift to lower photon energies due to the smaller binding to the 2p levels and present a richer multiplet structure due to the splitting of the t2g and eg states, expected for a 3d 1 configuration. Finally, the XEOL spectrum (Fig. 3f) suggest the presence of an almost pure 3+ state [21,26] , very rarely reported in the literature (presumably because most XAS experiments used TEY detection and thus only probed the Ti 4+ rich dead layer at the surface [27] ).

The data in Fig. 3d-f provide information [28] on the effective volume fraction of regions in which Ti is 4+. Fig. 3g presents linear combinations of pure Ti 4+ [23] and "pure" Ti 3+ XAS spectra (we use our XEOL data for which Ti is very close to pure 3+). By comparison with the experimental spectra we can estimate that the XAS data collected in TEY correspond approximately to a 80:20 Ti 4+ :Ti 3+ ratio and in FY to a 10:90 ratio. Since in TEY the probing depth is about 5 nm, this indicates that a region near the film surface with an effective thickness of 4 nm contains Ti 4+ only. This layer contributes to the XAS in TFY, and the 10:90 ratio suggests a probing depth of 40 nm in TFY, which is reasonable. The good correspondence between this equivalent thickness of pure Ti 4+ and the thickness of the magnetic living-dead layer strongly suggests that the deviation from a 3+ valence near the film surface triggers the paramagnetic response of the Dy ions.

To test our hypothesis of a link between the titanium valence state and the observed paramagnetic signal, we measured the magnetic field dependence of the dichroic signal at the Dy M5 and Ti L3 edges using X-ray Resonant Magnetic Scattering (XRMS) to obtain elementselective magnetic hysteresis cycles as function of temperature, see Figure 4. Both Ti and Dy show a hysteresis cycle at low temperature (Fig. 4a and4c), with a magnetic transition occurring around 60 K, in good agreement with the SQUID data for thick samples. This observation supports the globally ferrimagnetic magnetic order of DyTiO3 observed in Refs. [12,13] (see bottom sketch in Fig. 4b). The main point is that while the titanium develops a purely ferromagnetic response, the dysprosium shows a superposition of a ferromagnetic and a paramagnetic response. The signal at the Dy edge is thus the superposition of the response of Dy ions coupled with the Ti 3+ by exchange and of uncoupled (paramagnetic) Dy ions in a Ti 4+ environment. This demonstrates the causality between the change in the titanium valence at the sample surface and the living dead layer phenomena. We can now come back to the analysis of Fig. 2b and2d, assuming that the paramagnetic signal with a large magnetization at high field comes from uncoupled Dy 3+ ions (model 2). The moment of such a 4f 10 system is 10.6 µB per ion at saturation. From simulations of its Brillouin function

𝑚(𝐻) = 𝑔𝐽 ( 2𝐽 + 1 2𝐽 coth ( 2𝐽 + 1 2𝐽 𝑥) - 1 2𝐽 coth( 1 2𝐽 𝑥))
where g is the Landé factor, 𝑥 = , we determine that the moment is 8.3 µB at our maximum field of 5 T. We thus set mP=8.3 µB/f.u. The fits of mtotal vs t for both thin film series are shown as blue lines. The agreement with the data is good within error bars and yields tP=4-5 nm for the pure Ar series and tp=1-2 nm for the O2 series. To sum up, both the XAS and SQUID data point to the presence of a 4-5 nm thick dead layer at the surface of the films, comprising Ti 4+ ions and behaving as a paramagnet (see top sketch of Fig. 4b). The effective dead layer inferred from (in situ) XPS is thinner, 1.3 nm, which probably reflects some additional surface overoxidation after air exposure.

Finally, we have explored several possibilities to "revive" the magnetic dead-layer. Following Xu et al [7] the presence of the titanium 4+ at the surface of rare-earth titanates might be explained by oxygen ions migrating to interstitial sites during the cooling process. We have thus attempted to reduce the surface of a DyTiO3 film by capping it with different materials.

Starting with a 10 nm DTO film with a high Ti 4+ level and relatively poor magnetic response, we first investigated the effect of a 5 unit-cell cap of LaAlO3 grown by PLD in the same conditions as the DTO film. In Figure 5a we compare the XPS response of the DTO film right after growth, and of the very same film after in situ capping. We see that the 3+ components of the titanium 2p levels are enhanced by the addition of 5 u.c. of LAO; we estimate that the 3+/4+ ratio increases from 29:71 to 45:55. To see a clear effect on the magnetic properties, we grew a similar sample with a 30 nm LAO capping layer, and also studied films with 30 nm Au and Al caps. The Figure 5b shows a clear improvement of the ferrimagnetic properties of the DTO capped with the reducing materials (LAO and Al), with a much higher remanent magnetization, and a lower magnetization at 5 T. Both Al and LAO are reducing materials and it is thus expected that the excess of oxygen at the interface with DTO will be partially diminished. On the contrary Au, a noble metal, does not have such a strong effect. These results suggest that a reducing process takes place to restore the 3+ valence at the surface by taking the excess oxygen out.

In summary, we have shown the presence of a 4-5 nm thick "living-dead" layer at the surface of a ferrimagnetic rare earth titanate, DyTiO3. In this region, the valence of the Ti strongly deviates from 3+ towards 4+, which empties the Ti 3d band thus killing the ferrimagnetic response but exhuming a massive paramagnetic signal from uncoupled Dy 3+ ions. Through in situ XPS and ex situ XAS at the Ti edge with different probing depth, we have found that while in the bulk of the films Ti is clearly 3+, Ti 4+ is progressively more visible as the most superficial regions are probed. The observed concomitant decrease of the remanent magnetization and increase of the saturation magnetization when reducing film thickness indicates the presence of a paramagnetic dead layer. This picture of magnetically coupled Ti and Dy ions coexisting with some paramagnetic Dy is corroborated by element specific hysteresis cycles. Our results shed light on the reported anomalies in XAS and XMCD spectra in nominally trivalent Ti oxides, and suggest severe materials compatibility constrains for titanate-based quantum heterostructures.

Experimental section

Sample preparation

The samples have been grown on (001)-oriented LAO substrates (from CrysTec GmbH). A polycrystalline target (PiKem) consisting of a mixture of Dy2O3, TiO2 and Dy2Ti2O7 with an overall 1:1 Dy:Ti ratio was ablated by a Coherent Compact KrF (248 nm) excimer laser at a repetition rate of 2 Hz and with a fluence of 2 J/cm 2 . The deposition has been done at a substrate temperature of 900 °C. Two different atmospheres are suitable for the growth of DTO, 410 -7 mbar of O2 or 110 -3 mbar of pure Ar. The Ar has been used to control the scattering of lighter species (mainly O -) and the pressure of 1x10 -3 mbar is optimum to that effect [29,30] . The substrate-to-target distance was set to 4.5 cm. After deposition the samples were cooled in the same growth atmosphere at 50 °C.min -1 . The LAO capping was grown in the same condition as the DTO deposition. A PLASSYS magnetron sputtering at room temperature has been used to grow the 30 nm layers of Au and Al.

Structural characterization

We used an Panalytical Empyrean X-rays diffractometer to acquire the 2θ-ω scans. For that we used for the incident beam a Ge(220) mirror prefix module with a 1/8° receiving slit and a mask of 2 mm. For the detector optic a 1/4° anti-scatter slit was placed before a 3D PIXcel detector.

The absence of Laue fringes in the 2θ-ω scans may be ascribed to the surface roughness of about 1 nm and to the composition gradient near the surface. Film thickness was determined through X-ray reflectometry on the same setup.

X-ray photoemission spectroscopy

X-ray photoemission spectroscopy was performed using an Mg Kα source (hν= 1253.6 eV).

Spectra analysis was carried out with the CasaXPS software. The depth detection limit has been previously measured to be 15 u.c. of LAO (≈5.6 nm) [31] .

Figure 1 .

 1 Figure 1. 2θ-ω scans for DTO films with a thickness ranging from 5 to 80 nm grown in pure

Figure 2 .

 2 Figure 2. Thickness dependence of the remanent ((a) and (c)) and saturation magnetization ((b)

Figure 3 .

 3 Figure 3. (a-c) XPS spectra of the Ti 2p core levels in 20 nm DTO films grown in Ar ((a) and

Figure 4 .

 4 Figure 4. Magnetic field dependence of the XMRS signal at the Ti L3 edge (a) and the Dy M5

Figure 5 .

 5 Figure 5. (a) XPS spectra of the Ti 2p core levels for a 10 nm DTO film, before (top) and

Acknowledgements

The authors acknowledge fruitful discussions with N. Reyren, D.C. Vaz, A. Sander and A.

Barthélémy. This work received support from the European Research Council Consolidator Grant #615759 "MINT," the région Île-de-France DIM "Oxymore" (project "NEIMO"), and the ANR project "NOMILOPS." R.A. thanks the French Ministry of Higher Education and

The table of contents entry

A peculiar magnetic "dead layer" is detected at the surface of thin films of DyTiO3, a ferrimagnetic Mott insulator. Depth-dependent X-ray spectroscopy indicate that this layer is associated with a deviation of the Ti valence from 3+ towards 4+ at the film surface, suppressing the magnetic coupling between Ti ions and unleashing a strong paramagnetic response from uncoupled Dy ions.

X-ray resonant magnetic scattering

The XRMS measurements were carried out at the synchrotron radiation source BESSY II of the Helmholtz-Zentrum Berlin at the VEKMAG end station installed at the PM2 beamline [START_REF] Noll | Proc. MEDSI2016[END_REF] .

Element selective magnetic hysteresis loops were obtained in reflection geometry at energies across the Dy M5-and Ti L3 edges showing maximum dichroic signal at a gracing incidence angle of 15° for the the incoming circularly polarized radiation. After fixing the energy at one of the maximum of dichroism in reflection mode at a 15° angle, we plotted this value as a function of field to obtain the hysteresis cycle of Figure 4.

X-ray absorption spectrocopy

The XAS experiments was performed at the Swiss Light Source (SLS) on the XTreme beamline [START_REF] Piamonteze | [END_REF] . We obtain the XAS spectra under a 5 T magnetic field at 20 K. They have been acquired in three detection modes Total Electron Yield (TEY), Total Fluorescence Yield (TFY), X-rays Excited Optical Luminescence (XEOL). The TEY was acquired by measuring the ground current and the fluorescence data in TFY (without energy selection; however, the photodiode for TFY is capped with an Al foil which ensures that visible photons and electrons do not reach the diode). For XEOL measurements, a similar type of photodiode was used, sensitive to both visible photons and X-rays but mounted at the back of the sample ensuring that no X-rays are transmitted to the photodiode.

program Alembert funded by the IDEX Paris-Saclay (ANR-11-IDEX-0003-02) for financing his stay at CNRS/Thales. We thank HZB for the allocation of synchrotron radiation beamtime.

The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement n.°312284.

Received: ((will be filled in by the editorial staff))

Revised: ((will be filled in by the editorial staff)) Published online: ((will be filled in by the editorial staff))


Diogo Castro Vaz

Agnès Barthélémy
email: agnes.barthelemy@cnrs-thales.fr

D C Vaz

M Bibes

Oxide spin-orbitronics: New routes towards low-power electrical control of magnetization in oxide heterostructures

published or not. The documents may come

Oxide spin-orbitronics: New routes towards low-power electrical control of magnetization in oxide heterostructures

Introduction: Electrical control of magnetization

Spintronics utilizes both the charge and spin degrees of freedom of electrons to store, transmit and process information 1) . Historically, spin-based information has been recorded by the magnetization direction in a ferromagnetic metaltypically a transition metal alloy based on Co, Fe and/or Niand manipulated by the application of a magnetic field generated by current lines. Although this approach led to a first generation of non-volatile magnetic random-access memories (MRAM), commercialized in 2006, their design and very large power consumption prevented reaching higher storage densities. A first technological breakthrough towards denser memories came with the discovery of spin-transfer torque, a mechanism by which a spin-polarized current running through a ferromagnet is able to switch its magnetization 2) . This led to simpler and more compact designs as well as a significant reduction in write energies, remaining however one to two orders of magnitude above desirable values.

Interestingly, the first experimental demonstration of spin-transfer torque magnetization switching was reported in 1999 3) , almost concomitant with the rediscovery of magnetoelectric multiferroics 4) , an important family of materials that attracted a huge attention in the following decades 5,6) . Multiferroics are appealing for spintronics because they possess at least two ferroic (or antiferroic) order parameters (often being ferroelectric and magnetic) that can be coupled, which provides a route to control magnetism electrically 7) . Importantly, multiferroics are insulators, meaning that they are not controlled through the application of an electrical currentas with spin-transfer torquebut by an electric field, allowing much lower power consumption together with non-volatility (in contrast with approaches based on dielectrics such as MgO 8) ).

The route from the concept of magnetoelectric switching using multiferroic materials to its practical realization has been long and tortuous [9][10][11][12] . Reasons include the virtual inexistence of ferroelectrics with a large magnetization, imposing the need to combine multiferroics with ferromagnets, the limited number of room-temperature multiferroics and the modest amplitude of the magnetoelectric coupling. However, recent results 13,14) have aroused the interest of major electronics companies 15,16) , boosting the use of multiferroics in next-generation spin-based transistors that require ultralow power consumption.

While oxide materials have only played a small part in the development of spin-transfer torque, they have been at the heart of the research on multiferroics, with materials such as BiFeO 3a room-temperature ferroelectric with non-collinear antiferromagnetic order -on the spotlight 17) . Additionally, materials such as SrTiO 3 are starting to be used to convert charge currents into spin currents, opening new doors for spintronic devices that operate without external magnetic fields. In this review, we will discuss the potential of oxide materials for the low-power electrical control of magnetism through spin-orbit-based mechanisms. With conventional materials such as heavy metals, this approach already allows a decrease of power required to switch magnetization in current-based schemes and aims to rival the performance of magnetoelectric switching, providing enhanced endurance and exciting prospects for spin-current detection. As we explain hereinafter, oxides may have an unanticipated but essential role to play in this new arena.

Direct and inverse spin Hall and Rashba-Edelstein effects

A new paradigm for magnetization manipulation aims at harnessing pure spin currents from charge currents, in materials or interfaces with large spin-orbit interactions. This concept is at the heart of spin-orbitronics, where the interplay between charge and spin currents is exploited via spin-to-momentum coupling, enabled by the spin-orbit coupling (SOC). Two important physical effects that allow the creation of pure spin currents from charge currents (and vice versa) are the spin Hall effect (SHE 18,19) ) and inverse spin Hall effect (ISHE 20,21) ), both observed in bulk materials with SOC (see Figure 1a). Their origin is attributed to either extrinsic effects, such as impurity scattering, or intrinsic effects of the SOC on the band structure. Moreover, the conversion factor between charge and spin currents is set by the spin Hall angle ( H ), i.e., the ratio between a 3D spin current (j s ) and a 3D charge current (j c ). An advantage of the SHE and ISHE over electrical spin injection is that they realize spin-to-charge interconversion without using a ferromagnetic conductor and thus circumvent drawbacks like the intrinsic limitation of the transferred angular momentum per unit charge observed in conventional spin torque experiments. Indeed, spin currents generated by the SHE in non-magnetic heavy metals have been shown to efficiently generate spin-orbit transfer torques that are able to control the magnetization of a FM material 22,23) , move magnetic domain walls 24) , generate magnetic oscillations 25) or amplify spin waves 26,27) in heavy metal/ferromagnet bilayers; all of this with a reduced power consumption.

Recently, the realization of efficient spin-to-charge interconversion in two-dimensional electron gases (2DEG), at surfaces of topological insulators or in semiconductor quantum wells (via SOC) has been widely recognized and has attracted much attention. At these interfaces (surfaces), due to their two-dimensional nature, the combination of the spatial symmetry breaking, that results in a built-in electric potential along the direction normal to the interface (or surface) z ⃗, and SO interaction is at the essence of the so-called Rashba effect 28) . The corresponding Rashba Hamiltonian can be expressed as

H R = α R (k ⃗⃗ × σ ⃗ ⃗⃗) • z ⃗,
where  ⃗ ⃗⃗ is the vector of the Pauli spin matrices, k ⃗⃗ the momentum and  R the Rashba coefficient, proportional to the electric field strength and the SO interaction. In a Rashba system the momentum and spin degrees of freedom are locked (Figure 1b) and the spin degeneracy of the 2D band structure is lifted (see light dashed lines in Figure 1c corresponding to the steady state). When a charge current flows along -x, it will induce an equal shift by k x of both inequivalent Fermi contours (Figure 1c, black lines), thus yielding a spin accumulation with polarization along y; an effect called the Rashba-Edelstein effect (REE). This spin accumulation can diffuse in an adjacent conducting material through the interface and generate a pure 3D spin current without net charge current. Conversely, when a spin accumulation is induced at the interface, by injection of a spin current along z ⃗, the two inequivalent Fermi contours are shifted in equal magnitude but opposite directions (see dark lines in Figure 1d), yielding a net charge current along -x; an effect called the Inverse Rashba-Edelstein Effect (IREE). The efficiency of this effect can be estimated with its figure of merit,  IREE , given by the ratio between the 2D charge current generated, j c 2D , and the 3D spin current injected, j s 3D . Note that since one current is 2D and the other 3D,  IREE has the dimension of a length and is usually expressed in nm. In the simplest case of circular contours,  IREE is also proportional to the Rashba coefficient  R and the relaxation time , so that

 IREE = α R τ ħ
. A way to optimize the spin-to-charge conversion is thus to find interfaces housing large electric fields (together with large SOC) or even to use external gate voltage to tune the Rashba SOC (as we demonstrate further ahead). For the REE, the charge-to-spin current conversion efficient is given by q REE , which represents the ratio between the 3D spin current generated and the 2D charge current injected.

In principle, spin-to-charge interconversion through the REE and IREE does not satisfy the Onsager reciprocity due to the inequivalence of the considered spin currents. The efficiency of the IREE, given by  IREE = j c 2D j s 3D , is calculated with the spin current injected into the Rashba interface (by spin pumping for example), whereas for the REE the conversion efficiency (previously introduced in spin torque ferromagnetic resonance (ST-FMR) experiments 29,30) ) is similarly given as q REE = j s 3D j c 2D . It must be noted that the definition of j s 3D is not the same in these two experiments. When performing spin pumping, the broadening of the FMR line gives the final spin current j s 3D injected into the 2DEG after crossing the interface, so that  IREE does not depend on the transmission by the interface but only on the intrinsic properties of the Rashba system 31) . In contrast, in ST-FMR experiments, j s 3D is the spin current absorbed by the magnetic material, so that q REE depends on both the intrinsic properties of the Rashba system and the interface transmission 32) .

Several experiments performed at interfaces with large Rashba SOC between two metals 33- 36) , two-dimensional materials 35,[37][38][39] and topological surfaces states [40][41][42][43][44][45] have also recently been considered for the realization of the REE and IREE effects, opening a route to an efficient control of magnetization at lower energy consumption 42,46) . From here on, we address the potential of transition metal oxides for efficient spin-to-charge interconversion.

Inverse and direct spin Hall with oxide materials

The investigation of the direct and inverse spin Hall effects in oxide conductors is in its infancy and systematic studies as a function of structural parameters or across materials families are still lacking. The first experimental measurement of an inverse spin Hall effect in an oxide was in indium-tin oxide (ITO) through spin-pumping experiments from a La-doped yttrium iron garnet (La-YIG) thin film 47) . No details on the structural quality of the ITO films were provided, but it can be assumed that they were polycrystalline films.

Indeed, one of the advantages of ITO is that highly conductive films can be grown on top of it, without a strong dependence on their crystalline quality or epitaxial nature. A few months later, similar experiments were reported with ITO combined with a NiFe film and a small spin Hall angle  SHE =0.00650.001 was determined 48) .

While ITO While the oxide perovskite family is mostly known for its members possessing ferroic properties (ferroelectrics, ferromagnetic metals and multiferroics 50) ), it also comprises a number of non-magnetic conductors based on 3d, 4d and 5d elements, as illustrated in Table 1. With LSMO now established as an efficient spin injector (with Gilbert damping coefficients as low as 5.10 -4 (Ref. 51) ) and thus better than most ferromagnetic metals), such conductive oxides could be advantageously integrated into high-quality epitaxial spintronics architectures to assess their spin Hall response. In particular, it would be interesting to explore trends across the 4d and 5d row as well as to probe the role of crystal orientation and of possible interface dipoles.

Inverse and direct Rashba-Edelstein effect in SrTiO 3 -based heterostructures

In the search for alternative systems to explore 2D Rashba physics, oxide interfaces emerge as prominent candidates, for their exotic and unusual electronic properties. The acclaimed LaAlO 3 /SrTiO 3 (LAO/STO) system serves as a great example of an all-oxide system that exhibits fascinating properties such as interfacial conductivity with high mobilities 52) , superconductivity 53) and traces of magnetism [54][55][56] . Additionally, Caviglia et al. 57) showed that the quasi two-dimensional electron gas formed at the interface also shows strong gate-tunable Rashba SOC, ideal for further exploration of spin-to-charge interconversion.

Several groups have since then confirmed this effect through magnetotransport [58][59][60][61] and theory [62][63][64] , using both the LAO/STO interface as well as other STO-based systems 65) .

Importantly, one unique feature of these systems is that the Rashba SO coupling is extremely dependent on the position of the Fermi level, hinting for the potential use of external gate voltages to tune the effect.

In bulk SrTiO 3 , the cubic crystal field lifts the degeneracy of the 3d orbitals, so that the energy of the t 2g triplet is lowered with respect to the e g doublet. The t 2g triplet, forming the conduction band, is composed of three degenerate ellipsoidal Fermi surfaces centered in the Γ point and aligned along the main lattice directions. At the LAO/STO interface, when a 2DEG is formed, the degeneracy is lifted due to the perpendicular confining electric field that breaks inversion symmetry. In this scenario, a light d xy band is split towards lower energy [76] with respect to the other two heavier d xz and d yz bands. At low carrier densities, hence low Fermi level, only the d xy band is occupied. In this regime, transport is carried out with only one type of carrier and the spin splitting is expected to be rather small, since the Rashba parameter is only a few meV 68,69) . By increasing the carrier density, the d xz and d yz bands become populated and their Rashba coefficient is calculated to have a sign opposite to one of the d xy band 62,70) . At an energy level close to the crossing of both light and heavy bands the Rashba parameter increases about one order of magnitude as a result of the strong mixing between both orbital characters. Naturally, this level of tunability of the Rashba coefficient unlocks the possibility to tune both the amplitude and the sign of the spin-to-charge conversion, by shifting between one-band and multi-band occupation.

Such experiments were demonstrated by Lesne et al. in NiFe/LAO/STO heterostructures 71) .

The NiFe layer is used to pump a pure spin current towards the 2DEG formed at the LAO/STO interface, where it is converted into a 2D charge current. A voltage peak was measured, which appears at the very same magnetic field corresponding to magnetization precession in a steady state in FMR experiments (see Figure 2a). The conversion efficiency was tuned through electrostatic doping by using back-gate voltage, as displayed in Figure 2b. For negative gate voltages the 2DEG is depopulated to a carrier density of about 1x10 13 cm -2 . With the Fermi level at a lower position, only the light d xy band is occupied, so that the charge current measured is low. As expected, by slightly changing the amplitude of the gate voltage (i.e. from -200V to -50 V) the current produced is almost unaltered, as no new bands were populated. For 0 V, the detected signal drops to zero, revealing that heavy d xz/yz bands start to be occupied and their Rashba coefficient starts to counteract the one from lighter bands. Reaching the crossing point, at about 3x10 13 cm -2 , the increasing Rashba parameter is accompanied by a peak in the charge current detected, corresponding to a λ IREE = 6.4 nm. Note that this value is one order of magnitude higher than the one observed in Ag/Bi bilayer 33) and also higher than λ IREE = 2.1 nm found at the surface of the topological insulator α-Sn 44) . Additionally, a relaxation time of τ ∼ 1.4 ps can be derived for the given λ IREE and a Rashba parameter of α R ∼ 0.03 eV.Å (deduced from theory 72) and magnetotransport measurements 57,58) ). At higher positive gate voltages, the signal decreases again, presumably due to the highly non-trivial interaction between other bands that become populated for higher carrier densities.

A priori, the results stated above for the LAO/STO interface are rather surprising, considering that its Rashba parameter of 0.03 eV.Å is one order of magnitude smaller than the 0.56 eV.Å found for Bi (111) surface 33) . However, since λ IREE ~ α R τ, one can understand the importance of having a protected high mobility 2DEG mediating the spin-to-charge conversion, thus providing higher momentum relaxation times than the ones found in conventional metal/metal interfaces.

Although the work by Lesne et al. was done at low temperatures, several other groups have investigated spin-to-charge conversion up to room temperature. At 300K, the dielectric constant of STO becomes as low as 300, compared to 20000 below 4 K, hampering the generation of large electric fields at the interface. Also, the mobility of charge carriers in the LAO/STO 2DEG is known to be 1000-5000 cm 2 /V.s at low temperature, but two orders of magnitude lower at higher temperatures, driving the relaxation time to lower values.

Chauleau et al. found that λ IREE drops to 1 nm at 75 K and about 0.15 nm at room temperature 73) . Contradictorily, other groups have found an increase of the detected IREE voltage with increasing temperature 74) . In view of the decrease of the momentum relaxation time with temperature, these results seem hard to reconcile with a simple inverse Rashba-Edelstein picture. Lastly, Zhang et al. performed similar experiments on Ar+ irradiated STO and found a λ IREE = 0.23 nm 75) . The low conversion efficiency might however be due to the increased roughness (and reduced mobility of the 2DEG).

Regarding the reciprocal effect, experimental results on the REE are still scarce. Wang et al. 76) have demonstrated through ST-FMR experiments that when driving a RF charge current through the LAO/STO 2DEG (see Figure 2c), a non-equilibrium spin density is propagated perpendicularly towards the ferromagnetic top layer. This leads to magnetization precession under the influence of the induced damping-like torque, revealed by the large symmetric contribution to the measured voltage signal (Figure 2d). The charge-to-spin conversion efficiency was estimated to be q REE = 0.63 nm -1 at room temperature and was found to fall drastically when temperature decreases. This decrease was attributed to a lower conduction of spin-polarized electrons through defect states in the LAO barrier.

Using a Hall-bar like geometry, Jin et al. demonstrated charge-to-spin and spin-to-charge conversion within the same device 77) . In these experiments, a charge current injected between the source and the drain induces a perpendicular spin current (through the REE).

The spin current propagates in the 2DEG channel, is reconverted to a charge current (through IREE) and gets nonlocally detected at the adjacent contacts of the Hall-bar (see Figure 2e). Since the propagating spin current has a polarization perpendicular to the plane, applying an in-plane magnetic field induces Larmor precession of the spins, so that for large enough fields the spins will become parallel to the plane. This effect can be seen in Figure 2f, where Hanle experiments showed a decrease of the detected voltage with increasing magnetic field.

Additionally, anisotropic magnetoresistance measurements suggest that the REE might also be responsible for the appearance of a unidirectional component in transport 78) . Depending on the magnetization direction of the magnetic overlayer, the produced spin current might be either absorbed (through spin-transfer torque) or reflected, allowing two different resistive states. This effect, labeled unidirectional spin Hall magnetoresistance, have been demonstrated in ferromagnet/metal bilayers 79) and other topological systems 80,81) , but is yet to be realized for oxide-based heterostructures. Finally, let us mention that IREE has also been reported at the interface of other oxides such as Bi 2 O 3 82)

, which provides another approach for spin-charge interconversion with oxide materials.

Conclusion

The broad variety of properties displayed by transition metal oxides, especially perovskites, and their excellent structural compatibility are key features to their integration into countless types of multifunctional devices. Although the energies driving their physical response are usually related to crystal field (with corresponding level splitting due to oxygen rotations, Jahn-Teller distortions and polar shifts) and to on-site Coulomb repulsion (strong electronic correlations), spin-orbit coupling should not be neglected and may in fact produce phenomena of giant amplitude, as illustrated by the record inverse and direct Rashba-Edelstein effect observed in LaAlO 3 /SrTiO 3 . Importantly, in such SrTiO 3 -based systems, electrons in the 2DEG are protected from leakage towards neighboring metals by a potential barrier (e.g. a thin LaAlO 3 film), which provides an optimization route to achieve long scattering times at room temperature 83) . However, attempts to quantify the influence of spin-orbit coupling through transport measurements in oxides have been scarce so far. Yet, with several metallic compounds with 4d and 5d elements, perovskites are promising materials for efficient direct and inverse spin Hall effects, and systematic investigations should be undertaken. In addition, the strongly ionic nature of most oxides implies that the electric fields generated at interfaces between dissimilar compounds can be larger than with other materials families. If one of the materials is a ferroelectric, this can be an efficient way to achieve strong Rashba coefficients, which may be electrically tunable in a non-volatile way. In parallel, novel materials beyond perovskites may also be interesting candidates, as illustrated by the giant Rashba splitting recently discovered in delafossites 84) . Effect (IREE). When a spin current is injected perpendicularly to the 2DEG with the spin polarization along the y axis, the spin population is altered in the steady state causing a displacement in momentum space of the two inequivalent Fermi surfaces (red and blue lines) by ±Δk x . This results in a net charge current generated perpendicularly to the spin current and to its spin polarization 86) . Table 1 -Examples of metallic perovskite oxides based on different 3d, 4d and 5d transition metals. All mentioned 4d and 5d, as well as Ti, V and Ni compounds do not show magnetic ordering. Some of the mentioned Cr, Mn and Co compounds as well as SrFeO 3 are magnetic below some critical temperature but maintain a metallic behavior in the paramagnetic state.

Figure Caption

Figure 1 -

 1 Figure 1 -(a)Representative sketch of the Spin Hall effect. When an electrical current passes through a non-magnetic metal with SOC, spin accumulations appear on the two surfaces of the sample perpendicular to the charge current applied. In other words, a pure spin current perpendicular to the charge current is generated. Conversely, a pure spin current injected through a material with SOC will generate a transverse charge current; the Inverse Spin Hall Effect (ISHE). (b) The momentum-dependent spin split subbands plotted as brown and blue parabolic lines in the (k x k y )-E plot. In a Rashba system, this spin splitting is caused by broken inversion symmetry and SO interaction that lift the spin degeneracy of the band structure85) . (c) Representation of the Rashba-Edelstein Effect (REE). A charge current (j c ) injected at the interface along -x induces a shift k x of both Fermi contours, resulting in a spin accumulation polarized along the y axis due to the inequivalence of the two contours. (d) Representation of the Inverse Rashba-Edelstein

Figure 2 -

 2 Figure 2 -(a) Schematic of the FMR-spin pumping measurement configuration. Two contacts are made to probe the voltage generated through the IREE after the injection of a pure spin current into the 2DEG through spin pumping. A third contact is used as back-gate voltage, allowing an electrostatic tuning of the properties of the 2DEG and ultimately a

Figure 1 (

 1 Figure 1

Figure

  Figure 2

  contains In and Sn, two 4d elements, oxides based on heavier atoms with strong atomic spin-orbit coupling are potentially more interesting candidates to realize a strong spin-to-charge interconversion via spin Hall effects. Indeed, working with amorphous and polycrystalline IrO 2 thin films, Fujiwara et al. were able to measure a spin Hall angle of SrRuO 3 , combined into epitaxial heterostructures with La 0.7 Sr 0.3 MnO 3 (LSMO) used as a spin injector. Below T C =160 K, SrRuO 3 is a ferromagnet, and ISHE has been demonstrated both in its paramagnetic phase and down to 50 K below T C . The maximum response was  SHE =-0.0270.018 at 190 K.

	 SHE =0.065 and 0.04 respectively through nonlocal ISHE experiments in lateral
	spin-valves with NiFe electrodes 49) . Combined with its high resistivity, this large SHE
	angle makes IrO

2 a promising material for the detection of spin currents at room temperature.

Finally, to this date spin Hall angle measurements have been done for only one perovskite material,

Table 1

 1 Sr x TiO 3 SrVO 3 La 1-x Sr x CrO 3 La 1-x Sr x MnO 3 SrFeO 3 La 1-x Sr x CoO 3 LaNiO 3

	2

Acknowledgements

The authors thank A. Fert for useful discussions. This work was supported by the ERC Consolidator Grant #615759 "MINT", the French Research Agency (ANR) as part of the "Investissement d"Avenir" program (LABEX NanoSaclay, ref. ANR-10-LABX-0035) through project "AXION" and the ANR project "OISO".