Spin Hall angle and spin diffusion length of permalloy

In recent years, with the dramatic advances in the field of spintronics, two key technologies are of emerging importance: the generation and the detection of pure spin currents. A pure spin current, as a flow of spin angular momentum without transporting any net charges, is hard to be detected and controlled directly in a conventional way. One of the promising methods to detect pure spin currents is through the utilization of inverse spin Hall effect (ISHE),¹ which converts a spin current into an electrical charge current via the spin-orbit interaction (SOI). On the other hand, a spin current can be generated by spin pumping.^2–4 Typically, a ferromagnetic material (FM) is used as a spin pump to transfer spin momentum into a nonmagnetic material (NM) through the ferromagnetic resonance (FMR) technique. Consequently, the FM/NM bilayer systems are often adopted to study the spintronic properties of materials or devices, including the efficiency of spin injection at a FM/NM interface and the efficiency of spin-to-charge conversion in a NM.^5,6

In a single FM layer such as permalloy (Py), FMR-induced dc voltage has been reported and called the self-induced ISHE.^7,8 It seems a FM itself also has a considerable SOI, the same mechanism responsible for the anomalous Hall effect (AHE).^9,10 However, there is a lack of clear evidence that the origin of the dc voltage in a FM is the ISHE. The small SOI of a FM makes the detection of ISHE in single FM layers challenging due to the dominance of other accompanying effects. The most common ones include the planar Hall effect (PHE) and the magnonic charge pumping (MCP),¹¹ which has been reported in Py single layers.¹² MCP, as predicted by the Onsager reciprocity relations, is the reciprocal phenomenon of the spin-orbit torque. The MCP has a symmetrical voltage spectrum as the ISHE does, hence causing it hard to be identified. In this work, we demonstrate the validity of ISHE observed in Py single layers, and derive spin Hall angle (θ_SHE) and spin diffusion length (λ_Py) of Py, two important parameters in the study of spintronics.

Py thin films were deposited on (100) silicon substrates for the measurement of spin pumping and AHE. The samples were fabricated by the magnetron sputtering system (CVT TFS-4700) at room temperature. The base pressure was less than 4.0 × 10⁻⁷ torr and the deposition pressure was 2.5 × 10⁻³ torr. The power for deposition was 75 W, and the deposition rate was 2.38 Å/s. Prior to the deposition the substrates had been cleaned by acetone, ethanol, 2-propanol and DI water (in such a sequence).

The Py samples used in the spin pumping study were of rectangular shape with the dimensions of 1.5 mm × 3.0 mm, and the thicknesses (t_Py) range from 5 nm to 40 nm. The two ends of a Pt wire were connected to a nanovoltmeter (Keithley 2182A) and the other two were attached to the sample surface with silver pastes as shown in Fig. 1(a). The FMR and spin pumping measurements were conducted in a Bruker EMX electron spin resonance system at room temperature. The samples were placed at the center of a TE₁₀₂ microwave cavity, where the RF magnetic field (h_rf) was maximized and the RF electric field was minimized. A microwave with a frequency of 9.8 GHz and a power of 100 mW was applied in the cavity under a magnetic field H, sweeping from 600 Oe to 1600 Oe, while a nanovoltmeter was used to record the dc voltage.

For the sample used for the AHE measurement, the dimensions were 1.5 mm × 10.0 mm with t_Py fixed at 50 nm. The measurement was performed in a physical properties measurement system (PPMS, Quantum Design) at 300 K. During the measurement, a magnetic field was applied perpendicularly to the sample plane while an excitation current (I_c = 1 mA) was applied along the film plane as shown in Fig. 1(b).

The dc voltage measured along the y axis for the sample with t_Py = 20 nm is shown in Fig. 2. The inset shows the FMR spectrum of the sample. The resonance field (H_r) and linewidth (W) of the spectrum are defined as the center point of a spectrum (indicated by the arrow) and the full width at half maximum (FWHM) respectively. The H_r and W of the sample are determined to be 1048.2 Oe and 48.5 Oe, respectively. Fig. 2 reveals a nontrivial voltage peak recorded around the H_r. The voltage around the H_r is highly asymmetrical from which a symmetrical part can be separated by the fitting of the following equation:

Here Γ denotes the damping constant. The obtained symmetrical part of the voltage (V_sym, red dotted curve) and the asymmetrical part of the voltage (V_asy, blue dotted curve) are shown in Fig. 2. The V_asy is mainly contributed from AHE,^1,6,7 while the V_sym does not solely come from ISHE but has other origins as well. Here, we consider all the possibilities: ISHE, PHE, and MCP.

First, we consider the PHE as a possible contribution to the V_sym. PHE comes from the charge current the non-vanishing electrical field of the microwave induces on the sample, and hence PHE is highly dependent on the experimental configuration as well as the cavity mode used in the measurement.¹³ Several comprehensive studies on the PHE have been reported,^13–15 and V_PHE is calculated with $VPHE∝sinθHcosθM4πMs2γ2cos4θM+4ω2$⁠,^6,7,16 where θ_H and θ_M are the angles of the magnetic field H and the magnetization M with respect to the sample’s surface plane. Both θ_H and θ_M are zero in our measurement, hence the PHE does not make any contribution to the V_sym. Therefore, the V_sym measured in this study originates only from MCP and ISHE.

To further understand the results, we divide V_sym by the resistance of the samples and convert it into the charge current I_c. The dependence of I_c on t_Py is shown in Fig. 3. The resistivity for samples of different t_Py is listed in Table I, and a constant resistivity (ρ ∼ 40 μΩ cm) is assumed for the fitting shown in Fig. 3. We note that I_c is negative with t_Py ranging from 5 nm to 10 nm, and it becomes positive at t_Py = 13 nm, reaching its peak at t_Py around 25 nm. The change of sign can be accounted by a combination of the currents generated by ISHE and MCP. In our experimental configuration, the voltage given by the MCP is negative.¹² I_MCP, the charge current given by MCP, is described by the following equation:¹² 

where σ_Si(Py) is the conductivity of Si (Py), Δρ is the anisotropic magneto-resistivity, Λ^(d) parametrizes the spin orbit coupling, and h_rf is the RF magnetic field of the microwave. The only parameter that implicitly depends on t_Py in Eq. (2) is the damping constant α.¹⁷ The ISHE, on the other hand, is positive in our measurement and is given by^1,6

where J_s is the spin current and σ the spin polarization. I_ISHE, the charge current given by ISHE, can be described by the following equation:⁶ 

where θ_SHE and λ_Py are the spin Hall angle and the spin diffusion length, a pair of important parameters for Py. $jsPy$⁠, the spin current density driven by the spin accumulation³ at the Py/Si interface, is flowing into the Py layer, and is implicitly dependent on t_Py as^18–21 

The $gr↑↓$ and the $geff↑↓$ in Eq. (5) are the real part of the mixing conductance and the effective mixing conductance of the Py/Si interface. We fit the experimental data to the summation of Eq. (2) and Eq. (4), and the result is shown in Fig. 3. Here, a constant value of ρ_Py is assumed. The obtained values of θ_SHE and λ_Py are 0.00034 ± 0.00005 and 7.0 ± 1.0 nm, respectively.

Fig. 4 shows the Hall resistivity ρ_xy as a function of the magnetic field H, along with the definition of the anomalous Hall resistivity, ρ_AH. The sample has a longitudinal resistivity (ρ_xx) of 40.7 μΩ cm. The θ_AHE is defined as θ_AHE = ρ_AH/ρ_xx, and the value of θ_AHE is determined to be 0.005% for Py.

The θ_SHE of a FM is suggested to be related to its θ_AHE. θ_SHE = (1/p)θ_AHE⁷ only for the skew scattering mechanism, where p is the spin polarization. Using the values of θ_AHE and θ_SHE obtained in this work, the spin polarization p then can be estimated to be 0.14 for Py. However, the estimated p is smaller than the value obtained using lateral spin valves.²² The difference may come from the temperature effect, since the simple relation between θ_AHE and θ_SHE will no longer give an accurate estimate of p at high temperatures due to the phonon scattering.²³ 

Our experimental results reveal that the FMR-induced dc voltage changes its sign with varying t_Py, an observation that can only be accounted by the co-existence of ISHE and MCP. Hence, we demonstrate the dc voltage in Py single layers is indeed partially contributed from ISHE. Furthermore, we estimate the values of θ_SHE and λ_Py to be 0.034% and 7.0 nm. The relation between θ_SHE and θ_AHE for a FM leads us to an estimated value of 0.14 for the spin polarization of Py.

This work was financially supported in part by the Ministry of Science and Technology (MOST) and the Ministry of Education in Taiwan under the projects of MOST 105-2112-M-002-010-MY3 and NTU-107L900803 respectively.