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Clear variation of spin splitting by changing electron distribution at non-magnetic metal/Bi2O3 interfaces

Large spin splitting at Rashba interface, giving rise to strong spin-momentum locking, is essential for efficient spin-to-charge conversion. Recently, a Cu/Bismuth oxide (Bi2O3) interface has been found to exhibit an efficient spin-to-charge conversion similar to a Ag/Bi interface with large Rashba spin splitting. However, the guiding principle of designing the metal/oxide interface for the efficient conversion has not been clarified yet. Here we report strong non-magnetic (NM) material dependence of spin splitting at NM/Bi2O3 interfaces. We employed spin pumping technique to inject spin current into the interface and evaluated the magnitude of interfacial spin-to-charge conversion. We observed large modulation and sign change in conversion coefficient which corresponds to the variation of spin splitting. Our experimental results together with first-principles calculations indicate that such large variation is caused by material dependent electron distribution near the interface. The results suggest that control of interfacial electron distribution by tuning the difference in work function across the interface may be an effective way to tune the magnitude and sign of spin-to-charge conversion and Rashba parameter at interface.

Rashba interface, that has a momentum-dependent spin splitting due to atomic spin-orbit coupling (SOC) and broken inversion symmetry at the interface, plays a key role in spintronics 1,2 . Recently, the Rashba interface has been employed for efficient spin-charge (S-C) current interconversion 3,4 . The conversion efficiency between spin and charge currents can be comparable or even larger than typical spin Hall materials such as Pt and W 5 . Thus, Rashba effect has been studied intensively as an alternative phenomenon of spin Hall effect (SHE) to control the magnetization by spin current in spintronics devices 6,7 . Figure 1a shows the Rashba spin splitting in x-y plane, of which Rashba Hamiltonian can be described as ; where σ is the vector of Pauli spin matrices, p is the momentum, and α R is so-called Rashba parameter which determines the splitting in momentum between spin-up and spin-down electrons. The conduction electron spins are aligned to the fictitious field along ×p z direction, forming a clockwise or counterclockwise spin texture. Flow of the charge current in the Rashba interface thus generates non-equilibrium spin accumulation, whose gradient drives a diffusive spin current into an adjacent conductive layer. This charge-to-spin (C-S) conversion is called the direct Edelstein effect (DEE). In reverse, injecting the spin current into the interface generates charge current via the interfacial Rashba effect. This phenomenon is called the inverse Edelstein effect (IEE), which has recently been demonstrated using Ag(111)/Bi interface with large Rashba splitting 3 .
More recently, we found the similar S-C conversion at the Cu/Bismuth oxide (Bi 2 O 3 ) interface by means of several techniques [8][9][10] . The experimental results revealed the presence of large spin splitting at the Cu/Bi 2 O 3 interface. In order to obtain more efficient S-C conversion, it is worth understanding how to tune the spin splitting at this metal/oxide type interface. The Rashba parameter α R can be described as 11 where c, ∂ ∂ V z / and ψ 2 are respectively the speed of light, potential gradient and electron density distribution. z = 0 at the center of atoms at interface. Figure 1b shows a schematic illustration of V and ψ 2 at NM/Bi 2 O 3 interfaces based on our ab-initio calculation. Most of the electrons are localized near the NM nuclei because of less charge density in the insulating Bi 2 O 3 layer than the conductive NM layer. The potential gradient ∂ ∂ V z / in the vicinity of nuclei is dominant by the antisymmetric Coulomb force of the nucleus as shown in Fig. 1b 12,13 ; electron density distribution ψ 2 is determined by the hybridization state at the interface. Because the integral in equation (1) is strongly affected by asymmetric feature of ψ 212,13 , even a small modulation of ψ 2 can have notable effect on α R , i.e. tuning Rashba spin splitting by changing surface potential 14 . This suggests that the Rashba spin splitting can be controlled effectively by tuning the interfacial condition. In this study, we investigated the S-C conversion and Rashba parameter in various NM/Bi 2 O 3 interfaces and demonstrate the clear variation of Rashba spin splitting by changing electron distribution.

Experimental Results
Detection of spin-to-charge conversion in NM (Ag, Cu, Au, Al) /Bi 2 O 3 interfaces. Figure 1(c) is a schematic illustration of the measurement setup. We prepared four different NM material samples. Each Ni 80 Fe 20 (Py: 5 nm)/NM (Ag, Cu, Au, or Al 20 nm)/Bi 2 O 3 (30 nm) tri-layer wire is placed beside a signal line of coplanar waveguide (CPW). The measured samples are fabricated by using photo-lithography and e-beam evaporation (see Method). The length and width of the wire are 200 μm and 14 μm, respectively. Figure 1(d) is the schematic of spin-to-charge conversion at the NM/Bi 2 O 3 interface. Ferromagnetic resonance (FMR) in Py layer is excited by rf current generated magnetic field h rf in the CPW. Spin current caused by FMR is injected into NM/Bi 2 O 3 layer. This spin current gives rise to an electric dc voltage V through the inverse spin Hall effect (ISHE) and/or inverse Edelstein effect (IEE). All measurements were performed at room temperature. The measurement results are shown in Fig. 2. Clear signals due to S-C conversion are detected for all samples. At the vertical axis, we show the output current values estimated from V because the sample resistance R is different in each sample. The angle θ is the angle between sample wire and external magnetic field H as shown in Fig. 1(c). From this measurement, a strong NM materials dependence in amplitude and sign of detected signals is observed. The signal amplitude is almost the same between Py/Cu/Bi 2 O 3 and Py/Ag/Bi 2 O 3 , but surprisingly their signs are opposite each other. While the amplitude of Py/Au(Al)/Bi 2 O 3 is one order or two orders of magnitude smaller than Cu/Bi 2 O 3 . While the contribution of ISHE in Au may be notable since SHA of Au is one order of magnitude lager than Cu and Ag 16,17 . To estimate the contribution of ISHE in Au, we prepared the reference sample of Py/Au/Al 2 O 3 trilayer. Figure 2(c) shows the output spectrum of Py/Au/Al 2 O 3 and Py/Au/Bi 2 O 3 . From the signal amplitude in Py/Au/ Al 2 O 3 , we estimated spin Hall angle θ SH in Au layer is +0.40 ± 0.07% (see section 1 in supplementary information), which is in good agreement with reported values 17,18 . By comparing the signal amplitudes of Py/Au/Al 2 O 3 and Py/ Au/Bi 2 O 3 , we found that the sign of S-C conversion at Au/Bi 2 O 3 interface should be opposite to SHA in Au.
The rf power-dependence of 5 samples is shown in the upper insets to Fig. 2(a-d). The detected signals increase linearly with the rf power, being consistent with the prediction of spin pumping model 19 : It also indicates that the spin pumping experiment are in the linear regime of FMR. Furthermore, the angular dependence of the normalized signal is shown in the lower insets to Fig. 2(a-d). All of them show the sinusoidal shape which is consistent with typical IEE model for 2D electron gas. This confirms that the observed S-C conversion signals arise from FMR spin pumping.  where γ e , M s , ω, h rf , t N , and λ N are the gyromagnetic ratio, saturation magnetization, angular frequency, applied rf field, thickness of NM layer, and spin diffusion length of NM, respectively. More detailed experiment and calculation methods for estimation of spin current density is explained in Methods. This spin current is converted to charge current at the interface by IEE. The resulting charge current density j c flowing in the two-dimensional interface is expressed as = j V wR / c , where V , w, and R are detected voltage, the width of the sample wire, and total resistance of the wire, respectively. For NM=Ag, Cu, Al, the conversion coefficient λ IEE is calculated by

Spin-to-charge conversion coefficient and effective Rashba parameter in NM/Bi 2 O 3 interfaces.
Here, the units of j c and J s(NM/Bi O ) 2 3 are A/m and A/m 2 , respectively. Therefore, λ IEE has a unit of length. The estimated λ IEE at NM/Bi 2 O 3 (NM = Cu, Ag) interfaces is comparable with the reported value λ IEE = 0.3 nm for Ag/Bi interface measured by spin pumping method 4 , and is one-order larger than λ IEE = 0.009 nm for Cu/Bi measured by lateral spin valves method 21 . For NM = Au case, we separated the contribution of SHE and IEE for estimating λ IEE . (see section 1 in supplementary information).
The λ IEE can be expressed by using the Rashba parameter α R and momentum relaxation time τ e int at the interface 22 , In previous study, we showed that τ e int is governed by the momentum relaxation time τ e in the NM layer in contact with Rashba interface [8]. By using τ e instead of τ e int from the resistivity of NM layer, , effective Rashba parameter α R eff was calculated. First-principles calculations. The details of electronic state such as charge density and electrostatic potential at NM/Bi 2 O 3 interface were investigated by first-principles calculations. Figure 3(a-b) show the electronic states of the NM(111)/α-Bi 2 O 3 interfaces of which local crystallographic configuration is similar to that of our sample (see Figure S1 in supplementary information). The in-plane length of unit cell is based on the experimental lattice constant of each NM. We also assumed other local crystallographic configuration for the NM/Bi 2 O 3 interfaces in terms of the out of plane arrangement of NM and the crystal phases of Bi 2 O 3 (e.g. NM(110)/β-Bi 2 O 3 ). The calculated α R is in the same order of magnitude for both interfaces. From our thickness dependence calculation, we found that the electronic structures were insensitive to the number of NM layers once the number of layers exceeds 16. The value of α R can be determined from the calculated band structure of each NM(111)/α-Bi 2 O 3 interface (see Figure S3 in supplementary information). The calculated α | | R in NM(111)/α-Bi 2 O 3 interface are shown in Table 1. The experimental values of α | | R are about 3 times smaller than the calculated values; this difference may come from the different structure between real samples and the calculations. In the experiment the deposited Bi 2 O 3 layer is amorphous and the NM(111) layer has about 1 nm roughness, so it is reasonable that the smaller α R is obtained by experiments. The strength dependence of SOC in Bi on the α R is shown in Fig. 3(c). The α R without SOC of Bi is in the order of each NM (111) material. For NM = Cu and Ag, the α R drastically increases as the strength of SOC of Bi increases, while the α R slightly decreases for NM = Au. The charge density distribution for the corresponding Rashba state ψ | | 2 and potential V are shown in Fig. 3(d-f). The gradient of potential ∂ ∂ V z / in NM = Cu is smaller than Ag and Au case, however, α R of Cu/Bi 2 O 3 is larger than others. This indicates that, in the case of Cu/Bi 2 O 3, ψ | | 2 is the dominant essence instead of ∂ ∂ V z / . For NM = Cu and Au, the peak of ψ | | 2 shifts to NM side, while for NM = Ag, it shifts to Bi 2 O 3 side. This difference of the asymmetry feature of ψ | | 2 may have an influence on the magnitude and, especially, sign of Rashba parameter. In addition, for NM = Cu, the peak of ψ | | 2 is strongly localized at the peak of potential, while for NM = Au, the peak of ψ | | 2 becomes broaden; this difference between the localized features may also have an influence on the magnitude of Rashba parameter.

Discussion
From the experiments and the first principle calculations, we can confirm that the strong NM dependence of α R comes from the asymmetric charge density distribution ψ | | 2 at interfaces, which is originated from the broken inversion symmetry at interfaces. Besides that, the SOC of the materials is another important essence of Rashba effect. Firstly, we compare the influence of SOC of different NM materials. Even though Au has one order larger SOC than Ag and Cu, its Bi 2 O 3 interface has smaller α | | R eff . This result suggests that the SOC of NM layer is not essential to Rashba effect at NM/Bi 2 O 3 interfaces. This trend is the same with the first-principles calculations and experimental results in ARPES measurement in Ag(111)/Bi and Cu(111)/Bi Rashba interfaces 23

Fig. 3(c) shows that the SOC of Bi dominant the large Rashba spin splitting at NM/Bi 2 O 3 interface in NM = Ag and
Cu cases. Therefore, the strong NM dependency is not due to different SOC strength of NM materials. Secondly, since ψ | | 2 should be modulated by the electric field, we discuss here the contribution of interface structure and Fermi energy difference between NM and Bi 2 O 3 layer which determine the electric field at the interfaces. In the metallic Rashba interface such as Ag/Bi, the interface alloying structure is essential for originating the giant Rashba splitting because it induces strong in-plane potential gradient 24 . For NM/Bi 2 O 3 interfaces, the value of Rashba parameter at Ag/Bi 2 O 3 interface is one order smaller than Ag(111)/Bi, and Cu/Bi 2 O 3 is about half of Cu(111)/Bi 23 . This reduction might be caused by the lack of interface alloying and in-plane potential gradient, because Bi atoms are much more strongly bonded to oxygen atoms than to the NM. In this situation, α R at NM/Bi 2 O 3 interface is not only determined by interface alloying structure and the out-of-plane electric field at the interface should become an important essence to induce broken inversion symmetry and the interfacial spin splitting. Since the out-of-plane electric field at the interface originates from work function difference ΔΦ NM-Bi2O3 (Fermi energy difference) between NM and Bi 2 O 3 , α R may be related with ΔΦ NM-Bi2O3 . Figure 4(a) shows absolute value estimated by experiment and calculation in different NM/Bi 2 O 3 interfaces as a function of |ΔΦ NM-Bi2O3 |. Here, the ΔΦ NM-Bi2O3 is defined as Φ NM -Φ Bi2O3 . We use reported value of work function Φ of Cu (111) 25 , Ag(111), Au(111), Al(111) 26 Fig. 1(b), which is supported by the calculation results in Fig. 3(c and e). When the interfacial electric field E inter , is quite small, the asymmetric ψ 2 is strongly localized near NM nuclei as shown by purple line. If E inter becomes large enough, the peak of ψ 2 could be shifted from nuclei and delocalized by charge transfer due to interfacial electric field as shown by blue line. As the result of larger E inter , the integral of eq. (1) becomes smaller because ψ 2 is not localized in the largest potential region, and therefore when |ΔΦ NM-Bi2O3 | increases, α | | R decreases. That is to say, ψ 2 modulated by interfacial electrical field can drastically change α R . This charge-transfer-induced delocalization of ψ 2 is often discussed in ferroelectric oxides by Wannier functions 28 .
Additionally, we found that there is a sign change of α R eff at Ag/Bi 2 O 3 interface as shown in Fig. 4(b). In eq. (1), because the ∂ ∂ V z / is almost an antisymmetric function with respect to the nucleus, sign of α R is determined by whether the excess electron density is localized on NM side or Bi 2 O 3 side. The opposite sign between Ag/Bi 2 O 3 and Cu/Bi 2 O 3 should come from the different asymmetry of ψ 2 . When there is a sign change of ΔΦ, the E inter in Fig. 1(a) has opposite direction. Assuming that Ag/Bi 2 O 3 and Cu/Bi 2 O 3 interfaces have similar hybridization state, the opposite direction of E inter may shift the ψ 2 to different side of NM or Bi 2 O 3 and then cause the sign change of α R . This opposite direction shift is demonstrated by calculation results in Fig. 3(e). Also in case of Gd(0001) and O/Gd(0001) surface, it has been reported that the sign change behavior is caused by asymmetry of ψ 2 due to top oxide layer 29 . While in case of Al/Bi 2 O 3 interface, the sign is not as expected by the same scenario as NM = Ag, Cu, and Au. Since Al itself has quite different electronic state with Ag, Cu, and Au (group 11 elements), the In summary, we have demonstrated the large magnitude variation and sign change of S-C conversion originated from Rashba spin-splitting at various NM/Bi 2 O 3 interfaces. This strong variation comes from the material dependent electron distribution near the interface. The experimental results, supported by calculation, suggest that ψ 2 could be controlled by tuning interfacial electric field between NM and Bi 2 O 3 . This study provides a further understanding of the origin of the large spin-splitting at NM/Bi 2 O 3 interfaces, and also shown an effective way to tune the magnitude and sign of S-C conversion by changing the electron distribution. Furthermore, our results and measurement technique may provide a guiding principle for finding novel NM/oxide interfaces with large spin-splitting in the future.  Figure 5(b) shows the half width at half maximum (HWHM) as a function of rf current frequency. From the slope, we can estimate an effective magnetic damping constant δ eff for Py using the following equation 30 ,

Methods
where γ e and ΔH 0 are the gyromagnetic ratio of electrons and the offset of the HWHM, respectively. For Py/Cu bilayer, almost all of the injected spin current is reflected back to the Py layer without spin relaxation in Cu layer 31   , where t N and λ N are the thickness and spin diffusion length of NM, respectively. For NM = Ag, Cu, Al, their λ N is larger than 300 nm on room temperature 32,34,35 , which is much larger than λ N = 20 nm; therefore there is almost no effect of the decay term. For NM=Au, we use λ N = 35 nm from a reported value (see section 1 in supplementary information).
First-principles calculation method. We performed density functional calculations within the general gradient approximation 36 using OpenMX code 37 , with the fully relativistic total angular momentum dependent pseudopotentials taking spin-orbit interaction (SOI) into account 38 . We adopted norm-conserving pseudopotentials with an energy cutoff of 300 Ry for charge density including the 5d, 6s and 6p-states as valence states for Bi; 2s and 2p for O; 3s, 3p, 3d and 4s for Cu; 4p, 4d and 5s for Ag; 5p, 5d and 6s for Au. We used 16 × 12 × 1 regular k-point mesh. The numerical pseudo atomic orbitals are used as follows: the numbers of the s-, p-and d-character orbitals are three, three and two, respectively; The cutoff radii of Bi, O, Cu, Ag and Au are 8.0, 5.0, 6.0, 7.0 and 7.0, respectively, in units of Bohr. The dipole-dipole interaction between slab models can be eliminated by the effective screening medium (ESM) method 39 .