Edelstein effect, the spin-to-charge current interconversion at interfaces [1], has attracted much attention. An efficient interconversion at Cu/Bismuth oxide (Bi₂O₃) interface has been discovered [2, 3], which is attributed to a large Rashba splitting in the electronic state at the metal/oxide interface (see Fig. 1 (1)). However, the guiding principle of designing the metal/oxide interface with large Rashba splitting for the efficient conversion is missing. In this study, we report strong non-magnetic (NM) material dependence of spin splitting at NM/Bi₂O₃ interface and discuss the origin of the NM dependence with first-principles calculations.

Fig. 1. (a) Rashba spin splitting at NM/Bi₂O₃ interface. (b) Schematic of spin-to-charge conversion at the NM/Bi₂O₃ interface. A spin current is injected from the Py layer into the NM/Bi₂O₃ interface, and then converted to the charge current via the inverse Edelstein effect.

Fig. 2. (a) An asymmetry distribution of |Ψ|² generated by interfacial electric field. Purple line and blue line show the |Ψ|² under smaller and larger electric field, respectively. Green line show electrostatic potential V. (b) Absolute value of α_R estimated by the experiment and the calculation in different NM/Bi₂O₃ interfaces as a function of |ΔΦ_NM-Bi2O3|.

We employed spin pumping technique to inject spin current into the NM/Bi₂O₃ (NM = Al, Cu, Ag, Au) interface. The injected spin current is converted to charge current by the inverse Edelstein effect (spin-to-charge conversion at the interface, see Fig. 1 (b)). We evaluated the conversion coefficient and the Rashba parameter α_R which determines the splitting in momentum between spin-up and spin-down electrons. The evaluated α_R are −0.055, −0.25, +0.15 and −0.09 eV·Å for NM = Al, Cu, Ag and Au, respectively.

The Rashba parameter α_R can be described as,

,　　　　　 (1)

where c, ∂V/∂z and |Ψ|² are the speed of light, potential gradient and electron density distribution, respectively. Schematic illustration of V and |Ψ|² at NM/Bi₂O₃ interfaces based on our ab-initio calculation is shown in Fig. 2 (a). |Ψ|² can be modulated by the out-of-plane electric field E_inter at the interface. Note that E_inter originates from work function difference ΔΦ_NM-Bi2O3 between NM and Bi₂O₃. The asymmetry feature of |Ψ|² which depends on E_inter and ΔΦ_NM-Bi2O3 should be important for the magnitude and the sign of α_R.

Figure. 2(b) shows |α_R| estimated by experiment and calculation in different NM/Bi₂O₃ as function of |ΔΦ_NM-Bi2O3|. |α_R| decreases as |ΔΦ_NM-Bi2O3| increases and the trend of calculated |α_R| is in good agreement with the experiment. This trend can be explained as follows (see Fig. 2 (a)). |Ψ|² is strongly localized near NM nuclei when E_inter is small, while |Ψ|² could be shifted from nuclei and delocalized when E_inter is large. The steepest ∂V/∂z is located near NM nuclei. Thus, larger E_inter (larger |ΔΦ_NM-Bi2O3|) gives smaller integral in Eq. (1). The opposite sign of α_R between Ag/Bi₂O₃ and other interfaces may be explained by different sign of ΔΦ_NM-Bi2O3 at Ag/Bi₂O₃ from others. Assuming that Ag/Bi₂O₃ and Cu/Bi₂O₃ interfaces have similar hybridization state, the opposite direction of E_inter may shift the |Ψ|² to different side of NM or Bi₂O₃ and cause the sign change of the integral.

We found that the asymmetry feature of |Ψ|² which can be modulated by ΔΦ_NM-Bi2O3 results in strong NM dependence on α_R. Our study suggests that control of interfacial electron distribution by changing the difference in work function across the interface may be an effective way to tune the magnitude and sign of Rashba splitting and the spin-to-charge current interconversion at interface.

References

• [1] J. C. R. Sánchez et al., Nat. Commun. 4, 2944 (2013).
• [2] S. Karube, K. Kondou, and Y. C. Otani, Appl. Phys. Express 9, 033001(2016).
• [3] J. Kim, Y. T. Chen, S. Karube, S. Takahashi, K. Kondou, G. Tatara, and Y. Otani, Phys. Rev. B 96, 140409(R) (2017).

Authors

• H. Isshiki and Y. Otani