Evolution of the spin Hall effect in Pt nanowires: Size and temperature effects
We have studied the evolution of the Spin Hall Effect in the regime where the material size responsible for the spin accumulation is either smaller or larger than the spin diffusion length. Lateral spin valve structures with Pt insertions were successfully used to measure the spin absorption efficiency as well as the spin accumulation in Pt induced through the spin Hall effect. Under a constant applied current the results show a decrease of the spin accumulation signal is more pronounced as the Pt thickness exceeds the spin diffusion length. This implies that the spin accumulation originates from bulk scattering inside the Pt wire and the spin diffusion length limits the SHE. We have also analyzed the temperature variation of the spin hall conductivity to identify the dominant scattering mechanism.
pacs:72.25.Ba, 72.25.Mk, 75.70.Cn, 75.75.+a
Recently a long-standing prediction of Spin Hall Effect (SHE) Dyankonov (); Hirsch (); Zhang () has been verified by means of both optical Kato (); Wunderlisch (); Sih (); Stern () and magneto-transport Valenzuela (); KimuraPRL (); Saitoh () measurements. The SHE originates from the spin-orbit coupling, which relates the spin of an electron to its momentum, producing a spin current in the direction transverse to the flow of electrons and a spin accumulation at lateral sample boundaries. This is the direct SHE (DSHE) where unpolarized charge currents are converted into pure spin currents with zero net charge flow. There is also the inverse effect called inverse SHE (ISHE) where a pure spin currents can be converted into charge currents by the spin-orbit interaction. The SHE is therefore regarded as a new tool for generating and detecting spin currents, crucial issues for future spintronics, that in principle does not require ferromagnetic elements and/or external magnetic field.
The SHE induced spin accumulation in Semiconductors (SCs) have drawn much attention because of its compatibility with conventional CMOS technology. However, up to now SCs have exhibited very small SHE and no electrical detection has been reported yet. On the contrary Pt metal has been successfully used to detect the SHE even at room temperature, exhibiting the largest spin Hall conductivity reported so far KimuraPRL (). The possible origins of the SHE can be classified in two categories, intrinsic and extrinsic, depending on the dominant influence of either band structure or impurities Revue (). The SHE is also expected to be strongly geometry dependent. In metals like Pt, the SHE may be mainly attributable to extrinsic mechanisms such as the side jump and the skew scattering, which are responsible for the anomalous Hall effect in ferromagnets. The different sign of the side jump or the skew scattering angle for the two spin channels results in the transverse spin current and spin accumulation at lateral boundaries. One should also remark here that recent theoretical analysis based on the first principle band calculation strongly suggests that the origin of the large SHE in Pt is of intrinsic nature Guo (). Thus it is important to perform systematically experiments in order to better understand the origin of the SHE.
The first electrical detection scheme, originally proposed by Takahashi and Maekawa Takahashi (), was successfully applied for alminum by Valenzuela et al Valenzuela (). But this method is not suitable for the material with a nanometer scale spin diffusion length due to strong spin-orbit interaction. Therefore in a previous studyKimuraPRL () we have demonstrated a new device design where the Cu wire transfers accumulated spins at the interface between ferromagnetic detector (or injector) and Pt with negligible relaxation for both DSHE and ISHE measurements. In the previous study, we assumed that the induced spin current at the Cu/Pt interface was completely absorbed by the Pt wire because of its small spin resistance. However, the absorption efficiency of the spin current may depend on the device geometry and the temperature. Therefore, we further modified the previous design to a lateral spin valve (LSV) structure with a Pt insertion, which enables us to determine explicitly the magnitude of the absorbed spin current. Thereby the spin Hall conductivity for the Pt wire can be well evaluated.
Our device is based on the LSV geometry Jedema (); JedemaPRB (); KimuraPRB () where a Pt wire is inserted, which can be either a spin current source for DSHE or a spin current absorber for ISHE experiments. The devices are prepared by means of conventional e-beam lithography, electron gun evaporation (base pressure Torr) and a lift-off process. The scanning electron image of a typical device is shown in Fig. 1.(a). A Pt wire 100 nm wide () with a thickness varied from 5 to 20 nm is in ohmic contact with a Cu wire running between two Permalloy (Py) wires 100 nm in width and 30 nm in thickness. The dimensions of the Cu wire are 160 nm in width and 100 nm in thickness. Prior to Cu evaporation a careful Ar Ion Beam Etching is carried out for cleaning surface to obtain highly transparent ohmic contacts KimuraPRB (). The measurements are carried out by using ac lock-in amplifier and an He flow cryostat. The magnetic fields between 4 kOe and 4 kOe are applied in the plane of the substrate.
The charge to spin conversion induced by SHE obeys a relation given by the vector product, with the spin (charge) current density and the spin orientation. Similarly the spin to charge conversion obeys the reciprocal relation, . In the case of DSHE, the spins of the unpolarized charge current in the Pt wire are therefore aligned along the -axis, accumulating in the vicinity of the top or bottom surface according to the spin orientation. The accumulated spins are transferred through the Cu wire to the left Py spin detector in Fig. 1 (a). The magnitude of the spin accumulation is measured as the spin signal where is the voltage between the contact leads B and C and (A) is the current flowing in the Pt wire through contact leads A and E. When the magnetic field is applied along axis, the spin signal exhibits a linear increase and gets saturated above the saturation field, reflecting a hard axis magnetization process of Py wire. This magnetization process is separately confirmed by the anisotropic magnetoresistance measurement as in the bottom of Fig. 1 (b). The overall change in the signal is about 0.18 m.
In the case of the ISHE curve in Fig. 1.(b), the spin current is injected by flowing a current of 240 A between B and C. The voltage is induced between E and A as a result of the spin to charge conversion since the spin current is preferentially absorbed in the Pt wire along the -axis. From the field variation, the overall change in charge accumulation signal is also determined to be 0.18 m which is equal to in the DSHE, indicating the reciprocity of the behavior. The angular variation of the spin and charge accumulation signals measured with rotating the applied field direction assure the relation among the vectors , and .
The efficiency of the spin absorption is studied by non local spin valve (NLSV) measurements detailed in KimuraPRB (). For this measurement the magnetic field is applied along the Py wires. For all devices the center to center distance between the Py wires is fixed to 800 nm. The inset in Fig. 2 compares the NLSV signals measured at 5 K for the devices with and without a Pt insertion between the two Py electrodes. The NLSV signal for 240 A clearly decreases once the Pt is inserted, indicating the spin current absorption into the Pt wire, in good agreement with previous experiments KimuraPRB (). For all the devices the NLSV signal is almost a factor of 5 decreased by the Pt insertion from 5 K to room temperature (RT). We now define the ratio , which is the ratio of the spin signal with and without a Pt insertion, and , repspectively. By solving the one dimensional spin diffusion model with transparent interfaces, can be calculated as
Here, and are the spin resistances for the Pt and Cu wires, respectively. is the spin diffusion length for the Cu wire.
Interesting is that the ratio varies from 0.35 at 5K to 0.2 at RT irrespective of the Pt thickness. This implies that the spin absorption into the Pt wire takes place only at the top interface between Pt and Cu wires. The reason for this may be due to the anisotropic Ar milling process which left side surfaces of the Pt insertion uncleaned. The deduced from the experimental results yields the spin resistance of the Pt wire as 0.22 both at RT and 5 K . Since the spin resistance of the Pt wire is given by , where and are the conductivity for the Pt and the effective cross section for the spin current in the Pt wire, can be estimated as 14 nm at 5 K and 10 nm at RT, in good agreement with the value of 14 6 nm at 4 K reported by Kurt et al Kurt ().
Figures 3 (a)-(c) represent the field dependences of the ISHE with different Pt thicknesses of 5, 10 and 20 nm measured at RT. Here, the distance is 350 nm. We have studied about 20 devices devices of = 5, 10, and 20 nm, with different values of varied from 250 to 500 nm to evaluate the thickness dependence of the SH signal. All the devices exhibit a gradual decrease of DSHE and ISHE with proportional to due to the spin relaxation in the Cu wire. Interestingly, a clear systematic decrease in with has been observed in the temperature range from 5 K to RT. Figure 3.(d) summarizes the values at RT and 5 K obtained for the distance of 350 nm. There is a very small decrease in while the thickness is below 10 nm. On the contrary there is a more pronounced decrease when the thickness is increased from 10 to 20 nm. This can be understood as follows. The spin accumulation at the top surface of the Pt due to the DSHE effectively takes place in the Pt while the thickness . Once exceeds , the spin accumulation should not increase under the condition of the constant current. For the ISHE, the vertical penetration of the spin current from Cu into Pt is limited by , leading to the same as . For more quantitative analyses, we calculate the thickness dependence of the spin accumulation due to DSHE at the top surface of the Pt wire. Since the spin relaxation in the Cu wire does not depend on , the thickness dependence of or is proportional to . Using the homogeneous spin Hall conductivity in the Pt wire with open circuit condition, can be calculated as
where is the excitation current flowing in the Pt wire. As shown in Figure 3(d), Eq. (2) with nm at RT and 14 nm at 5 K, which are deduced from the absorption experiment mentioned previously, fairly well reproduce the thickness evolution of . The data can be well reproduced when slightly reducing to 7 nm and 8 nm for RT and 5 K respectively. These features strongly support the bulk origin of the DSHE and ISHE.
Finally, we discuss the temperature dependence of the spin Hall conductivity. The spin Hall conductivity can be calculated as
with the parameters in Data () to estimate the ratio of charge to spin currents. The obtained value of is 330 S/cm at RT, which is larger than that in the previous experiment. This is because the assumption of the complete spin current absorption into the Pt wire in the previous analysis led to underestimate the spin Hall conductivity.
Using Eq. 3 with the temperature dependences of and the spin resistances for Pt, Cu and Py, we can compute . As shown in the inset of Fig. 4, the temperature dependence exhibits a very small variation of about 350 S/cm. It should be noted that the change in is much smaller than that in Guo () obtained from band structure calculation. Our values of are smaller at low temperatures but larger at RT (2000 S/cm and 240 S/cm in Guo () for low temperature and RT respectively). This difference could be due to the dominant contribution of impurities compared to the band structure considerations in the Pt wires. In Fig. 4 the SH resistivity () is likely to evolve in a quadratic form with the Pt resistivity with in this temperature range. This is expected evolution for side jump origin of the SHE.
In conclusion we have studied the evolution of the spin Hall effect in Pt wires in the regime where the size responsible for the spin accumulation is either smaller or larger than the spin diffusion length. Under the constant current the pronounced decrease in the SHE for demonstrates that the SHE is induced by bulk scattering inside the Pt wire. The analyses on the spin Hall conductivity of the Pt wires suggest a side jump origin of the SHE. These results will provide important information in determining the optimum geometry for the SHE.
We thank Profs. Y. Iye and S. Katsumoto of ISSP, Univ. of Tokyo for the use of the lithography facilities.
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