Current-induced spin polarization on metal surfaces probed by spin-polarized positron beam

Current-induced spin polarization (CISP) on the outermost surfaces of Au, Cu, Pt, Pd, Ta, and W nanoscaled films were studied using a spin-polarized positron beam. The Au and Cu surfaces showed no significant CISP. In contrast, the Pt, Pd, Ta, and W films exhibited large CISP (3~15% per input charge current of 105 A/cm2) and the CISP of Ta and W were opposite to those of Pt and Pd. The sign of the CISP obeys the same rule in spin Hall effect suggesting that the spin-orbit coupling is mainly responsible for the CISP. The magnitude of the CISP is explained by the Rashba-Edelstein mechanism rather than the diffusive spin Hall effect. This settles a controversy, that which of these two mechanisms dominates the large CISP on metal surfaces.

sample center was electrically grounded. Reversible currents (6j c ) were applied to the samples through the two edges. The direct current was perpendicular to P 1 . A high purity Ge detector was placed perpendicular to the beam axis to record the annihilation c ray spectra.
Spin-polarized slow (low energy) positrons injected into a metallic thin film could lead to a remarkable formation of Ps by picking up the electrons on the outermost surface. The formation probability of ortho-Ps (F 3c Ps ), which is influenced by the spin polarization of the outermost surface electrons (P 2 ), could be derived from the positron annihilation c ray spectra as the Ratio between the intensity of the low energy region and the 511 keV peak region (denoted as R). A function DR is defined to quantitatively characterize the F 3c Ps (details shown in the section of methods): where R and R 0 are derived from the c ray spectra measured at E 1 550 eV and 12 keV, respectively. The component of surface spin polarization along y axis (P 2 cosw) is calculated by where w is the relative angle of P 2 to P 1 (y axis), DR zjc and DR {jc correspond to an input charge current density of 1j c and 2j c , respectively.
Experiments. All films were deposited by magnetron sputtering on different substrates (10 3 20 3 0.5 mm) at various growth temperatures. The details of the films are listed in Table 1. The thickness of Fe seed layer for Au film was 1 nm. The low resistivity (a phase: bcc structure) Ta and W films were grown on Al 2 O 3 (0001) substrates, and the high resistivity (b phase: A15 structure) Ta and W films were grown on 100 nm thick SiO 2 layers. The Au, Pt, Pd, a-Ta, and a-W films were single crystals, which were confirmed by observing the reflection high energy electron diffraction patterns. The Cu, b-Ta, and ba-W (a mixture of b and a phases in which b is dominant) films were polycrystals. The XRD patterns shown in Fig. 2 confirmed the a-Ta, b-Ta, a-W, and ba-W films [15][16][17] . At least two samples were subjected to the CISP measurement for each film. Input charge current densities j c are also listed in Table 1. To suppress the Joule heating, the applied electric powers were regulated to be less than 3 watts and the temperature was measured to be lower than 150uC. In this temperature range, fast Ps with the maximum energy of its work function (W Ps < 0.7 eV (Au), 2.5 eV (Cu), 2.9 eV (Pt), 0.4 eV (Pd), 4.0 eV (Ta(111)), 4.9 eV (W(111))) will be predominant over the thermal (, 100 meV) Ps [18][19][20][21] . Therefore, positrons will pick up surface electrons with the energy from E F (Fermi level) to E F 2 W Ps .
Material dependence of CISP. Figure 3 shows DR ( / F 3c Ps ) upon successive current reversal (1j c « 2j c ) of all the films. For the Au and Cu films, no regular changes of DR upon current reversal could     Table 1. Figure 4 shows P 2 cosw per input charge current of j c 5 1.0 3 10 5 A/cm 2 . The absolute values of P 2 cosw for the b-Ta and ba-W surfaces are 3 , 5 times greater than those for the Pt and Pd surfaces.
For both high resistivity Ta and W films, P 2 cosw are significantly bigger than those of low resistivity Ta and W films. Table 2 lists the h SH of undoped metals obtained by different experimental methods. The values of h SH are rather scattered. Even for Pt, which is the most commonly studied spin Hall material, h SH varies between 0.37% and 11.0%. The Pt, Pd, and Au films have positive h SH , while the Ta and W films have negative h SH . Furthermore, absolute values of h SH of Ta and W tend to be greater than those of Pt and Pd. The magnitudes of h SH of b phase Ta and W films have been reported to be much bigger than those in a phases 4,5 . These observations of h SH are mostly supported by theoretical studies of h SH in which the sign is positive (negative) if the outermost d-shell is more (less) than half filling 30,31 .

Discussion
The sign and relative magnitude of the CISP observed for the Pt, Pd, Ta, and W surfaces are in good agreement with those of h SH listed in Table 2. This reveals that the observed CISP for these surfaces are due to the SOC that is similar to SHE. According to the spin diffusion theory 32 , the energy width of polarized electrons in the density of states is given by the shift of chemical potential: Dm 5 2h SH l S j c r, where l S is the spin diffusion length. For h SH 510%, l S 510 nm, r550 mVcm and j c 5 1.0 3 10 5 A/cm 2 , one finds Dm51 meV. The typical density of states at E F is 10 23 cm 23 eV 21 , and hence the accumulated spin density will be 10 17 cm 23 . Assuming that positrons pick up electrons located from E F to E F 21 eV, the observable electron spin polarization will be ,10 24 %. Therefore, the huge CISP observed above is hardly explained in terms of the diffusive SHE. More specific aspects of the surfaces should be considered.
Recently, the so-called giant Rashba effect has been reported for heavy metal surfaces [7][8][9] . The largest Rashba effects are five orders of magnitude greater than that estimated from the free electron model. Such a giant Rashba effect is explained by considering both strong SOC and steep gradient of electric potential near the surface. The spin density AEds y ae induced by the Rashba effect is given by where e is the elementary charge, D 2D is the two-dimensional density   of states, E is the applied electric field, t is the electron relaxation time, and a R is the Rashba parameter (Rashba-Edelstein model) 33,34 . Assuming a R 5 3 3 10 210 eVm, D 2D 5 10 14 cm 22 eV 21 , t510 ps, E51 kV/m, one finds the spin polarization of the order of 5%. Thus, if the relaxation time is long enough, the above-observed huge CISP can be explained. A recent study reported the spin-to-charge conversion at Bi/Ag interface, which is a well-known giant Rashba system 35 . The spin density and the two-dimensional charge current density j 2D c at an interface are related through ds y ~ hj 2D c ea R ð Þ, which is essentially the same as Eq. (3). In the above study, excess spins of AEds y ae 5 2 3 10 7 cm 22 supplied to the Bi/Ag interface by the spin pumping induced j 2D c~1 0 {5 A=cm. In the Ag layer, the spin-to-charge conversion was negligible and independent of its thicknesses (5 to 20 nm). This would manifest that the spin-to-charge conversion was induced by an inverse Rashba effect but not inverse SHE. If we adopt this conversion efficiency in the present experiments, the twodimensional charge current density j 2D c (0.05 to 0.5 A/cm) will generate excess surface spins of AEds y ae 5 10 12 cm 22 at maximum. Thus, assuming again D 2D 510 14 cm 22 eV 21 , one finds the spin polarization of 1%. This is comparable orders of magnitude as the above estimation using Eq. (3) in spite of many differences in experimental conditions. The a R and h SH are related via h SH j j~ma 2 R t 36 . This may be the reason why the sign and the relative magnitude of the CISP observed here are in good agreement with those of h SH .
Furthermore, besides the Rashba effect at the outermost surface, one may naturally expect that the metal/substrate interface could also contribute to the spin polarization on the outermost surface. The thicknesses of the metallic films (10 and 25 nm) are close to the spin diffusion lengths of the electron in these transition metals. A potential gradient also exists at the metal/substrate interface due to the difference of the metal and the substrate. In consideration of the Rashba effect at the metal/substrate interface, the transverse spin polarization calculated from Eq. (3) will increase and be more consistent with the experimental result from spin-polarized positron beam. To check this assumption in a future research, a metal/substrate interface with a strong Rashba effect is needed for the experiment.
It is known that Pt and Pd nano-structures nearly satisfy the Stoner criterion and hence ferromagnetic behavior appears 37,38 . This implies that ferromagnetic order will easily be induced in Pt and Pd surfaces. A recent anomalous Hall effect study of a Pt=Al 2 O 3 00 10 ð Þ sample suggests that a magnetic moment of ,10 m B is induced by an applied electric field 39 . The Rashba field induced by the charge current may also contributes to the development of ferromagnetic order on the surface.
To summarize, we have observed huge CISP on the outermost surfaces of Pt, Pd, Ta, and W thin films by using a spin-polarized positron beam. The sign and magnitude of the CISP on these metal surfaces are explained by the Rashba-Edelstein mechanism. This work demonstrates that the spin-polarized positron beam is a useful technique for observing the outermost surface spin polarization of spintronics materials. Figure 5(a) shows the principle of Ps formation and annihilation. Spin-polarized positrons implanted into the sub-surface region are emitted into vacuum as Ps. Two types of Ps exist: spin-triplet ortho-Ps (jS, mae5j1, 0ae, j1, 1ae, j1, 21ae) and spin-singlet para-Ps (jS, mae5j0, 0ae), where S and m are the total spin and the magnetic quantum number, respectively. Ortho-Ps decays into three c rays, giving rise to a continuous energy distribution from 0 to 511 keV. Para-Ps decays into two c rays of , 511 keV, that overlaps with direct annihilation of positrons with electrons inside the sample. In the deep region of the metal, the probability of Ps formation is negligible. Shown as the shaded area in Fig. 5(b), the 3c annihilation of ortho-Ps (below 511 keV peak) near the surface is clearly observable.

Methods
The fraction of each spin state of Ps is given by 13 : where P 1 and P 2 are spin polarizations of the positrons and the electrons, respectively, and w is the relative angle of P 2 to P 1 . The formation probability of para-Ps is F 2c Ps~F 0,0 j i , and that of ortho-Ps is where 1 ð Þ and 0 ð Þ are detection efficiencies of annihilation c rays from j1, 1ae plus j1, 21ae, and j1, 0ae, respectively. The values of 1 ð Þ and 0 ð Þ depend on the angle between the c ray detector and P 1 .
The intensity of the annihilation energy spectrum below 511 keV is a function of F 3c where T is the total area under the intensity curve, U is the area under the 511 keV peak, and the subscripts 0 and 1 of R and U denote 0% and 100% Ps emission, respectively. For small F 3c Ps , DR~R{R 0 !F 3c Ps . Thus, the asymmetry of DR upon spin flip (1P 2 « 2P 2 ) can be written as 12 From the known values of P 1 , , and the experimental asymmetry, the transverse spin polarization (P 2 cosw) is determined. For the detector alignment in the present study (perpendicular to the positron beam), the factor 2 1 ð Þ{ 0 ð Þ ½ = 2 1 ð Þz 0 ð Þ ½ in Eq. (10) is 0.6.