Inverse spin Hall effect in Nd doped SrTiO3

Conversion of spin to charge current was observed in SrTiO3 doped with Nd (Nd:STO), which exhibited a metallic behavior even with low concentration doping. The obvious variation of DC voltages for Py/Nd:STO, obtained by inverting the spin diffusion direction, demonstrated that the detected signals contained the contribution from the inverse spin Hall effect (ISHE) induced by the spin dependent scattering from Nd impurities with strong spin-orbit interaction. The DC voltages of the ISHE for Nd:STO were measured at different microwave frequency and power, which revealed that spin currents were successfully injected into doped STO layer by spin pumping. The linear relation between the ISHE resistivity and the resistivity induced by impurities implied that the skew scattering was the dominant contribution in this case, and the spin Hall angle was estimated to be 0.17%. This work demonstrated that extrinsic spin dependent scattering in oxides can be used in spintroics besides that in heavy elements doped metals.


INTRODUCTION
The perovskite-type 3d 0 oxide SrTiO 3 (STO), as an insulator with a wide band gap of about 3.25 eV, 1 has attracted much attention for its potential physical properties, such as superconductivity, 2,3 quantum paraelectricity 4 and ferroelectricity 5 . These excellent physical performances can be introduced by the doping of a small amount of carriers through generating oxygen vacancies 6 or adding dopants such as Cr, La, Nb and Nd [7][8][9][10] . In recent decades, due to the increasing interest in spintronics, the spin Hall effect (SHE) in doped materials has been intensively investigated [11][12][13] , which is an important method for converting charge currents into spin currents. In addition to the intrinsic SHE originating from the intrinsic spin-orbit interaction (SOI) in the band structure, the SHE in the doped system is enhanced by the SOI effect in impurity, called the extrinsic SHE. The magnitude of the extrinsic SHE relies on the distinction of the SOI between the host and the impurity.  14 Here the intrinsic SHE in Cu is negligibly weak and the SHE signals mainly arise from scattering by impurities presenting strong SOI. Gradhand et al. proved the giant SHE in heavy metal Au induced by skew scattering at C and N impurities. 15 The reciprocal effect of SHE is called the inverse spin Hall effect (ISHE), by which spin currents are converted into charge currents as a result of the SOI in nonmagnetic materials as schematically shown in Fig. 1(a). It also provides a way to engineer the magnitude of the ISHE. As reported in the literature, the SOI effect in graphene increased linearly with the impurity coverage. 16 There are two types of mechanisms to take account for this extrinsic effect, namely the skew scattering 17   sputtering. During the measurements, the sample is placed at the center of microstrp fixture, where the external magnetic field is applied perpendicular to the direction across the electrodes in the film plane. In the Py/Nd:STO samples, the nonmagnetic layers no longer suppress the further diffusion of the spins due to the introduction of free electrons from impurities, which enables the spin currents to be effectively injected by spin pumping. Thus, the conversion of spin to charge current can be detected via the ISHE. As predicted by Fert, it can be explained by resonant scattering from impurity states split by the SOI, namely the spin Hall angle = 3 sin(2 2 − 1 ) sin 1 /(5 △) (with λ d being the impurity spin-orbit constant, △ being the resonance width, η 1 and η 2 being the mean phase shift at the Fermi level). 14 The effect is expected to be larger when the electrons are more localized, where △ is smaller, as in the case of doped insulators compared with that in metals. We utilize the two-step measurement with sample flipping to separate the ISHE signals (V ISHE ) in Nd:STO from the SRE signals (V SRE ). [20][21][22] As shown in Fig. 1(b), the DC voltages detected in doped STO are obviously different before (V be ) and after (V af ) flipping, which implies that these signals are attributed not only to the contribution from the SRE in Py films, but also to the contribution from the ISHE in doped layers. This significant change arises from the reversal of the sign of V ISHE due to the inverted spin injection by the sample flipping as shown in the inset of Fig. 1(b), and the signals of samples before and after flipping can be respectively described as the addition (V be = V SRE + V ISHE ) and subtraction (V af = V SRE -V ISHE ) of the DC voltages of two effects. Thus, the V ISHE is separated 3 from the V SRE through the subtraction of experimental data (V be -V af ). As depicted in the inset, the line shape of V ISHE is symmetric, which is typical as also shown in previous studies. 23,24 In contrast, there is no spin current injected into the interface of Py/STO because of the insulating STO suppressing the further diffusion of the spins. Thus, the DC voltage of this sample detected in this case is attributed to the contribution from the SRE in Py film, the line shape of which is a combination of the symmetric and asymmetric Lorentzian components as plotted by the red squares in Fig. 1(c). The SRE, rectifying the microwave current at the FMR, is associated with the precessing magnetization and microwave electric field, 19 but independent on the spin diffusion direction. 25 When the undoped samples are inverted at the steady external magnetic and microwave electric field, the voltage signal of Py/STO is not distinctly different from that of the sample before flipping as depicted by the blue circles in Fig. 1(c).

RESULTS AND DISCUSSION
where ↑↓ , , ℏ, , , 4 and denote the spin mixing conductance, gyromagnetic ratio, Dirac constant, amplitude of the microwave magnetic field, Gilbert damping coefficient, effective saturation magnetization and microwave angular frequency, respectively. It indicates that the DC spin current is proportional to the time averaged Gilbert damping term onto the external magnetic field direction, which depends linearly on the square of the magnetization-precession amplitude. 26,27 In terms of the relation between V ISHE and j s , V ISHE ∝ θ SH j s ×σ (with θ SH being the spin Hall angle, σ being the spin-polarization vector), 28 the electric voltage due to the ISHE is also proportional to the square of the amplitude of magnetization-precession, namely the microwave power P. 29,30 In our case, the measured linear dependence is consistent with this simplified consideration, which demonstrates the voltages with symmetric Lorentz shape extracted by sample flipping are due entirely to the ISHE induced by the spin pumping.
FIG. 2. The magnetic field dependence of V ISHE at various microwave power P. The inset shows P dependence of V ISHE at the resonance field H r .  Fig. 3(a), the effective saturation magnetization 4πM s for for Py/STO and Py/Nd:STO are determined to be 11.5 kOe and 10.9 kOe, respectively.
The difference of this parameter between pristine and doped samples is very small (about 5%), which may arise from the difference in surface roughness of substrates. In addition, it can be clearly seen that voltage curves of the ISHE broaden with increasing the FMR frequency. As shown in Fig.3(b), the FMR linewidth △H of doped sample is larger than that of the pristine STO, which experimentally provides the evidence of spin injection induced by the spin pumping 31 The Gilbert damping constant α can be extracted from the function ∆ = ∆ 0 + 4 /(√3 ), where △H 0 is the inhomogeneous contribution to the linewidth. 32 By fitting the data, we obtain the damping parameters α Py/STO = 0.010 and α Py/Nd:STO = 0.016. The enhanced damping contribution △ = / : − / is due to the spin flipping. The spin mixing conductance ↑↓ can be determined by where d F , , and μ B are the thickness of Py film, Landé factor, and Bohr magneton, respectively. Using Eq. (2) Intrinsic STO is an insulator with bandgap larger than 3.0 eV. Fig. 4(a) shows the transport properties of doped STO. The increase in the resistivity with increasing temperature is a typical metallic behavior caused by the introduction of impurities, consistent with the single crystal work of Tufte et al. 35 and Robey et al. 36 . The mobility is 5 cm 2 V -1 s -1 at room temperature and increases to 90 cm 2 V -1 s -1 at 80 K. The carrier density extracted from this data is of order 10 19 cm -3 and independence on temperature, which can be explained by small donor binding energy of STO due to its large dielectric constant. 37 In this case, an impurity band is formed in doped STO through the overlapping electronic pictures of individual impurity states. When the impurity band overlaps with the conduction band, it results in the transformation from insulator to semiconductor or metal.
The major contributions to the ISHE of doped cases are from the skew scattering or the side jump. In order to figure out the mechanism in Nd:STO, we measured the ISHE resistivity ρ ISHE at different temperatures by = △ /( ), where w is the width of sample, △R ISHE is the amplitude of the ISHE resistance, I C is the charge current induced by the ISHE, I S is the effective spin current injected into the Nd:STO and x is a correction factor. 38 As shown in Fig. 4(b), the ρ ISHE is approximately proportional to the resistivity ρ induced by Nd impurities with strong SOI, which provides an indication for the dominant contribution from skew scattering by impurities, compared with the case for the side jump, where the ρ ISHE is proportional to ρ 2 . The spin Hall angle θ SH , defined as the ratio of ρ ISHE and ρ, is estimated as (0.17±0.05)%, which is smaller than that for alloys (θ SH = 0.6% for Ag doped with Ir, and θ SH = 2.1% for CuIr) 39 , but larger than that for semiconductors, such as θ SH = 0.01% for p-Si 30 and θ SH = 0.02% for n-GaAs 40 . The enhancement may come from the extrinsic spin dependent scattering, where the intrinsic contribution is tiny in STO.