Efficient intrinsic spin-to-charge current conversion in an all-epitaxial single-crystal perovskite-oxide heterostructure of La0.67Sr0.33MnO3/LaAlO3/SrTiO3

We demonstrate efficient intrinsic spin-to-charge current conversion in a two-dimensional electron gas using an all-epitaxial single-crystal heterostructure of LaSrMnO3/ LaAlO3 (LAO)/ SrTiO3 (STO), which can suppress spin scattering and give us an ideal environment to investigate intrinsic spin-charge conversion. With decreasing temperature to 20 K, the spin-to-charge conversion efficiency is drastically enhanced to +3.9 nm, which is the largest positive value ever reported for LAO/STO. Our band-structure calculation well reproduces this behavior and predicts further enhancement by controlling the density and relaxation time of the carriers.


Recent observations of conversion phenomena between spin and charge currents
promise substantial reduction of power consumption in next-generation high-speed spintronics devices such as spin-orbit-torque magnetoresistive random-access memories [1]. While this conversion is well known to occur in heavy metals [2][3][4], recent studies have shown that it occurs also at various interfaces such as Ag/Bi, Fe/Ge, and Ag/α-Sn [5][6][7][8][9]. At these interfaces, the Rashba spin-orbit interaction and resulting spin splitting of the Fermi surface appear due to the broken space-inversion symmetry, causing spin-tocharge current conversion that is known as the inverse Edelstein effect (IEE) [10,11].
Very recently, a giant IEE was observed in a two-dimensional electron gas (2DEG) formed at the interface between insulating perovskite oxides LaAlO3 (LAO) and SrTiO3 (STO) [12]. In this heterostructure, carriers are provided from oxygen vacancies and form a high-mobility 2DEG at this interface [13]. The strong Rashba spin-orbit interaction at LAO/STO, which can be modulated by a gate voltage, makes this system very attractive for controllable efficient spin-charge conversion [14][15][16]; however, previously reported results for spin-charge conversion at LAO/ STO are divergent, and unified understanding of its intrinsic mechanism is still lacking [12,[17][18][19]. For example, in Ref. [12], a large conversion efficiency, so called the inverse Edelstein length λIEE, up to -6.4 nm was observed at 7 K. This value is much larger than that reported for Ag/Bi (λIEE = 0.3 nm). Meanwhile, in Refs. [17,18], the conversion signal strongly decreases to zero with decreasing temperature. The reason for these completely different temperature dependences is not clear at present, but this is likely attributed to inelastic transport of the spin current, which is predicted to reduce the conversion signal especially at low temperature. This inelastic spin transport is thought to be related to the crystal quality of samples. In metal systems, the interface quality is known to have a large influence on the conversion efficiency [20,21]. In all the previous studies on spin-charge conversion at LAO/ STO [12,[17][18][19], however, amorphous or poly-crystalline ferromagnetic films deposited by sputtering were used for the ferromagnetic layer, which may cause strong spin scattering especially at the interface between the ferromagnetic layer and LAO. In this Letter, to exploit the intrinsic IEE in the LAO/STO system, we focus on an allepitaxial single-crystal heterostructure of La0.67Sr0.33MnO3 (LSMO)/ LAO/ STO. LSMO is a strongly-correlated half-metallic ferromagnetic-perovskite oxide that can be epitaxially grown on STO due to the small lattice mismatch of ~0.8%. LSMO is thus an ideal candidate to explore the efficient spin injection and intrinsic spin-charge conversion at the LAO/STO interface.
For the experiments, we have prepared a sample composed of La0.67Sr0.33MnO3 [30 unit cell (u.c.) = 12 nm)]/ La(1-δ)Al(1+δ)O3 (LAO, 2 u.c. = 0.8 nm) grown on a TiO2terminated SrTiO3 (001) substrate via molecular beam epitaxy (MBE) [ Fig. 1(a)]. We used a shuttered growth technique with fluxes of La, Sr, Mn, and Al supplied by Knudsen cells. The LAO and LSMO layers were grown at 730°C with a background pressure of 7×10 -4 Pa due to a mixture of oxygen (80%) and ozone (20%). As shown later, the thickness of 2 u.c. of LAO is large enough to form a 2DEG at the LAO/STO interface because of the presence of the LSMO layer as with previous reports on LAO/STO with a metallic capping layer [12,22,23]. As shown in Fig. 1(b), in which we assume that a simple parabolic band structure is split due to the Rashba effect, the spin current that is To confirm that a 2DEG is formed only when c=82.5%, we measured the transport properties of reference samples of La(1-δ)Al(1+δ)O3 (8 u.c.= 3.2 nm)/STO with c=82.5% (named sample ref-A) and c=101% (named sample ref-B), which were grown with the same growth conditions as those for samples A and B, respectively. Actually, as shown in Fig. 2(b), sample ref-A (c=82.5%) shows metallic behavior while sample ref-B (c=101%) shows insulating behavior, confirming that a 2DEG exist only when c=82.5%.
By the Hall measurements, the sheet career density ns of the 2DEG was estimated to be 2.1 × 10 14 cm -2 and the mobility μ was 3.7 × 10 3 cm 2 V -1 s -1 at 20 K [ Fig. 2(c)]. As shown in Fig. 2(d), sample A shows similar metallic behavior, while sample B shows nearly the same temperature dependence of the sheet resistance as that of a single LSMO layer grown on STO (dotted curve reproduced from Ref. [25]). These results confirm the presence of the 2DEG only in sample A.
We have carried out spin pumping measurements using a TE011 cavity of an electronspin-resonance system with a microwave frequency of 9.1 GHz. We cut the samples into a small piece with a size of 2 × 1 mm and put it at the center of the cavity. For the measurements, a static magnetic field μ0H was applied along the [110] (y) direction in the film plane, which corresponds to the easy magnetization axis of LSMO. Meanwhile the microwave magnetic field hrf was applied along the ሾ1 ത 10ሿ direction. The used microwave power was 30 mW.
As shown in Figs. 3(a) and 3(b), the EMF peak appears at the FMR magnetic field at all the measurement temperatures, indicating that the measured EMF is induced by the FMR, like in general spin pumping experiments. We note that we can eliminate the influence of the thermal effects as discussed in Sec. 1 of the Supplemental Material (SM) [26]. To derive the IEE signal from the EMF, we extracted the symmetric component Vs, which includes the IEE signal, from the EMF-H curves (Sec. 2 in the SM [26]). Then, we estimated the sheet current density and w is the sample width (1 mm). In Fig. 3(c), one can see a drastic increase in ݆ ୡ with decreasing temperature.
To separate the IEE signal from the one originating from LSMO such as the galvanomagnetic effects, we derived the IEE-induced sheet current density ݆ ୡ ଶୈ by subtracting the sheet current density ݆ ୡ , which was measured for sample B (see Sec. 3 of SM [26]), from ݆ ୡ . As shown in Fig. 4(a), ݆ ୡ is much larger than ݆ ୡ especially at low temperatures, indicating that ݆ ୡ is mainly attributed to the IEE signal.
Using obtained ݆ ୡ ଶୈ (= ݆ ୡ − ݆ ୡ ) and the estimated value of the spin current density js, which is derived from the spectral linewidth of the FMR signals with a standard method described in Sec. 4 of SM [26], we estimated λIEE (= ݆ ୡ ଶୈ /js) at each temperature [red open circles in Fig. 4(b)]. In Fig. 4(b), λIEE drastically increases with decreasing temperature and amounts up to +3.9 nm at 20 K. This value is the highest positive value ever reported for the IEE at LAO/STO. This temperature dependence is similar to that in Ref. [19] but is completely opposite to that reported in Refs. [17,18].
As discussed below, this characteristic increase in λIEE with decreasing temperature mainly originates from the intrinsic feature of the IEE in the LAO/STO system. Following the approach in Ref. [27], we calculated the band structure of the LAO/STO interface using the effective-mass Hamiltonian with atomic spin-orbit coupling and interorbital nearest-neighbor hopping based on the six 3d-t2g orbitals of up and down spin components of the dxy, dyz, and dzx orbitals of Ti (see Sec. 5 in SM [26]). The calculated band structure is shown in Fig. 4 [26]), we estimated the EF positions in our samples, which are shown as the red dotted lines in Fig. 4(c). From the Boltzmann equation, for the n-th Fermi surface SFn, the two-dimensional (2D) current density ݆ ୡ ୗ and the non-equilibrium spin density ‫ݏߜ‬ ୗ are expressed by where e is the free electron charge, ħ is the Dirac constant, dSF is the infinitesimal area (= length in two dimensions) of the Fermi surface [28]. Here, Fx(k) and Sy(k) are defined as where F is the absolute value of the effective electric field that is applied to each electron state, and vx(k) is the x direction component of the group velocity v(k). We assumed that the relaxation time τ(k) is proportional to |k|. Then, ݆ ୡ ଶୈ , the total non-equilibrium spin density ‫,ݏߜ‬ and λIEE are expressed by The most important indication in the above equations is that the charge current is mainly carried by electrons with large vx(k). As shown in the calculated vx(k) mapping at the Fermi surface when EF = 210 meV [ Fig. 4(d)], which corresponds to the case of the measurement temperature of 20 K in our study, we see that electrons in the vicinity of ky = 0 mainly contribute to the charge current. In fact, especially the dxy states that are located Using the theoretical value of ݆ ୡ ଶୈ ‫ݏߜ/‬ (see Fig. S6 in SM [26]) and τ, we can predict λIEE that is expected in our system at each temperature [square points in Fig. 4(b)]. We see that predicted λIEE increases with decreasing temperature as with the experimental λIEE, which confirms that our result originates from the intrinsic IEE. The reason for the larger values of predicted λIEE than the experimental values especially at low temperatures is probably due to our overestimation of js (see Sec. 4 in SM [26]) or small influence of spin scattering.
Our study shows that the small thickness of LAO only of 2 u.c. and the high-quality single crystallinity are likely keys to suppressing the extrinsic effect and to obtaining intrinsic IEE. Furthermore, our band calculation suggests that λIEE will be dramatically enhanced if we can tune the EF position at around the Lifshitz point (see Sec. 6 in SM [26]). At the same time, we see that increasing τ is important to enhance the IEE, indicating that single crystalline 2D system with a high mobility is very promising for efficient conversion between spin and charge currents.

Influence of the thermal effects
The influence of the Seebeck effect on the electromotive force (EMF) is negligibly small, which can be understood from the linear microwave-power dependence of the electromotive force (EMF) measured for sample A (Fig. S1). The EMF signal induced by the Seebeck effect would be proportional to SΔT, where S is the Seebeck coefficient of the sample and ΔT is the temperature difference induced in the sample by microwave irradiation. Because S strongly depends on the temperature [ 29 , 30 ], the power dependence of the EMF would not be linear if it were affected by the Seebeck effect.
FIG. S1. Magnetic-field µ0H dependence of the EMF measured for sample A with various microwave powers at 20 K. The inset shows the value of the EMF peak as a function of the microwave power at 20 K.
The anomalous Nernst effect and longitudinal spin Seebeck effect generally have been reported to decrease to zero with decreasing temperature [31,32], which is clearly different from our result of the increase in the EMF with a decrease in temperature. Therefore, we can eliminate the influence of the thermal effects on the EMF.

Derivation of the symmetric component of the magnetic-field dependence of the EMF
To extract the signal of the inverse Edelstein effect (IEE) from the EMF, we need to separate the EMF-H curves (µ0H is a magnetic field) into a symmetric component

Spin pumping data of sample B
In Figs. S3(a)-S3(c), we show the results of the ferromagnetic resonance (FMR) and EMF measurements for sample B (LSMO/ LAO/ STO), which does not have a 2DEG and thus only shows AHE and PHE signals originating from LSMO. The generated sheet current density ݆ ୡ in sample B is much smaller than that obtained for sample A (݆ ୡ ) [see Fig. 3(c) in the main text], meaning that the obtained EMF in sample A is mainly attributed to the IEE and that AHE and PHE are very small.

Estimation of the spin current
We estimated the spin-current density js in sample A using where ℏ is the Dirac constant, ߱ is the angular frequency of the microwave, e is the elementary charge, ℎ ୰ is the microwave magnetic field, ߛ is the gyromagnetic ratio in LSMO, ߙ is the Gilbert damping constant, and ‫ܯ‬ ௦ is the saturation magnetization of LSMO [34]. ݃ ↑↓ is the real part of the spin-mixing conductance given by where ݀ ୗ is the thickness of LSMO (12 nm), and ߙ ୧ is the intrinsic Gilbert damping constant of LSMO with no spin current generation. Due to the spin current generation from LSMO in sample A, ߙ is larger than ߙ ୧ . ߙ and ߙ ୧ are obtained by where f is the frequency of the microwave, ߤ is the Bohr magneton, and ݃ is the effective electron ݃-factor (1.95 for LSMO [35]). Δ‫ܪ‬ and Δ‫ܪ‬ ୧ are the experimental FMR spectral linewidths for sample A and intrinsic LSMO (e.g. no spin injection), respectively. The obtained temperature dependence of ߙ is shown in Fig. S4(a). Here, we set ߙ ୧ to be 1.57×10 -3 , which was reported for a high-quality LSMO film in Ref. [36]. Depending on the difference of the crystal quality of the LSMO layers, this method may overestimate js and thus underestimate λIEE in our study. We have obtained ݃ ↑↓ = 73.5 nm -2 and ݆ ୱ = 1.06 × 10 5 Am -2 at 20 K. The obtained temperature dependence of ݆ ୱ is shown in Fig. S4(b).

Calculation of the band structure and the Fermi surface
Following Ref. [37], we calculated the band structure of the LAO/STO interface assuming that the Hamiltonian is a sum of the nearest-neighbor hopping with on-site interaction, H0, the atomic spin-orbit coupling, HASO, and the interorbital nearest-neighbor hopping, Ha. Using the six t2g orbitals of STO, dyz↑, dyz↓, dzx↑, dzx↓, dxy↑, and dxy↓, as basis functions, H0, HASO, and Ha are written as Here, ħ is the Dirac constant, kx and ky are the x-and y-direction components of the wave vector k, respectively, and σ 0 is the identity matrix in spin space. σx, σy, and σz are the Pauli matrices. ml and mh are the effective masses of the light and heavy electrons at the LAO/STO interface, respectively. ↑ and ↓ represent spin directions. ΔASO and Δz are coefficients that express the magnitudes of HASO and Ha, which were assumed to be 5 and 10 meV, respectively. ΔE expresses the energy difference between the dxy and the dzx, dyz bands due to the confinement of the wave function in the z direction. We determine ΔE to be 90 meV so that the carrier concentration becomes 1.8×10 13 cm -2 when the Fermi level EF position is located at the Lifshitz point (bottom of the dyz band at the Γ point), as experimentally confirmed [38]. Here, we calculated the density of states D(E) at the energy E using the Green function method: where ‫ܧ‬ ‫ܓ‬ is the dispersion relation of the LAO/STO interface. Using the derived D(E), we obtained the carrier density as a function of EF (Fig. S5). To derive the Fermi surface shown in Figs. 4(d) and 4(e) in the main text, we transformed the Schrödinger equation to Eq. (S5.5), following the method used in Ref. [39].

Calculation of the sheet current density and non-equilibrium spin density
Using Eqs. (1)-(3) in the main text, we calculated ݆ ୡ ଶୈ ‫ݏߜ/‬ as shown in Fig. S6, where ݆ ୡ ଶୈ is the sheet current density induced by IEE and δs is the non-equilibrium spin density defined by Eq. (3) in the main text. When EF > 0.2 eV, ݆ ୡ ଶୈ ‫ݏߜ/‬ is nearly constant as explained in the main text. At around EF=0.1 eV, we see a sharp peak, which corresponds to the Lifshitz point. If we can use this region by controlling the carrier concentration, a large inverse Edelstein length λIEE is expected.

Estimation of the relaxation time
In the same way as the derivations of Eqs. (1) and (2) in the main text, the following expression between ݆ ୡ ଶୈ and the electric field F in the x direction is obtained.
where e is the free electron charge, dSF is the infinitesimal area (= length in two dimensions) of the Fermi surface, F is the strength of the electric field in the x direction, vx(k) is the x direction component of the group velocity v(k), and n is the index of each Fermi surface SF . Using Eq. (S6.1) and the experimental conductivity of the twodimensional channel at the LAO/STO interface [see Fig. 2(d), where we neglect the small conductance of LSMO], we can obtain the relaxation time τ, which is expressed by The obtained τ at each temperature is shown in Fig. S7.