Tuning the spin Hall effect of Pt from the moderately dirty to the superclean regime

We systematically measure and analyze the spin diffusion length and the spin Hall effect in Pt with a wide range of conductivities using the spin absorption method in lateral spin valve devices. We observe a linear relation between the spin diffusion length and the conductivity, evidencing that the spin relaxation in Pt is governed by the Elliott-Yafet mechanism. We find a single intrinsic spin Hall conductivity $({\sigma }_{\mathrm{SH}}^{\mathrm{int}}=1600\pm 150{\mathrm{\Omega }}^{-1}\mathrm{c}{\mathrm{m}}^{-1})$ for Pt in the full range studied which is in good agreement with theory. We have obtained the crossover between the moderately dirty and the superclean scaling regimes of the spin Hall effect by tuning the conductivity. This is equivalent to that obtained for the anomalous Hall effect. Our results explain the spread of the spin Hall angle values in the literature and find a route to maximize this important parameter.

Figure 1

(a) Scanning electron microscopy (SEM) image of a Py/Cu lateral spin valve with a Pt wire between the two Py electrodes. The nonlocal measurement configuration, the direction of the applied magnetic field $\left(H\right)$, and the materials (Py, Cu, and Pt) are shown. (b) Nonlocal resistance as a function of $H$ measured at $I_C=100\mu \mathrm{A}$ and 10 K in the configuration shown in (a) for a Py/Cu lateral spin valve with (blue line) and without (red line) a Pt wire in between the Py electrodes. The solid (dashed) line corresponds to the increasing (decreasing) magnetic field. The reference spin signal $\left(\mathrm{\Delta }{R}_{\mathrm{NL}}^{\mathrm{ref}}\right)$ and the spin signal with Pt absorption $\left(\mathrm{\Delta }{R}_{\mathrm{NL}}^{\mathrm{abs}}\right)$ are tagged. (c) SEM image of the same device used now to measure the ISHE. The materials, the direction of $H$, and the measurement configuration for ISHE are shown. (d) ISHE resistance as a function of $H$ measured at $I_C=100\mu \mathrm{A}$ and different temperatures in the configuration shown in (c). The curves have been shifted for clarity. The ISHE signal $\left(2\mathrm{\Delta }{R}_{\mathrm{ISHE}}\right)$ for 10 K is tagged. Images and data correspond to device S2.

Figure 2

(a) Resistivity and (b) spin diffusion length of Pt as a function of temperature for all devices. Error bars are included. (c) Spin diffusion length of Pt as a function of longitudinal conductivity for all devices. Error bars are included. The black dashed line is a linear fitting of the experimental data. Since devices E1 and E2 (S1 and S2) were fabricated in the same chip, Pt was evaporated (sputtered) in the same deposition, hence it is assumed that E1 and E2 (S1 and S2) have the same ${\rho }_{\mathrm{Pt}}$ and ${\lambda }_{\mathrm{Pt}}$.

Figure 3

Spin Hall resistivity as a function of the square of the longitudinal resistivity of Pt for all devices. Error bars are included. Solid lines correspond to the fit of the data to Eq. (4). Inset: Zoom of the previous plot showing the data of the devices with evaporated Pt.

Figure 4

Spin Hall angle as a function of the longitudinal conductivity of Pt for all devices. Error bars are included. The regions with different scaling regimes are indicated. The black solid line corresponds to the intrinsic contribution of the spin Hall angle ${\theta }_{\mathrm{SH}}^{\mathrm{int}}={\sigma }_{\mathrm{SH}}^{\mathrm{int}}/{\sigma }_{\mathrm{Pt}}$, using ${\sigma }_{\mathrm{SH}}^{\mathrm{int}}=1600{\mathrm{\Omega }}^{-1}\mathrm{c}{\mathrm{m}}^{-1}$. The gray dashed line in the superclean region corresponds to the total spin Hall angle calculated with both intrinsic and skew scattering contributions, using the average value ${\alpha }_{ss}(\%)=0.6$ obtained for this region. Inset: Same data plotted as spin Hall conductivity. The scale of the horizontal axis is the same as in the main panel.