Giant Room Temperature Interface Spin Hall and Inverse Spin Hall Effects

The spin Hall angle (SHA) is a measure of the efficiency with which a transverse spin current is generated from a charge current by the spin-orbit coupling and disorder in the spin Hall effect (SHE). In a study of the SHE for a $\mathrm{Pt}|\mathrm{Py}$ ($\mathrm{Py}={\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$) bilayer using a first-principles scattering approach, we find a SHA that increases monotonically with temperature and is proportional to the resistivity for bulk Pt. By decomposing the room temperature SHE and inverse SHE currents into bulk and interface terms, we discover a giant interface SHA that dominates the total inverse SHE current with potentially major consequences for applications.

Figure 1

(a) Schematic illustration of the scattering geometry. Electrons flow ($j_c^z$) from the perfectly crystalline left lead to the right one through a disordered region of pure bulk Pt where atoms are displaced from their equilibrium positions by populating phonons [34]. Transverse spin currents arising from the SHE flowing along the $x$ and $-y$ directions are polarized in the $y$ ($j_{sy}^x$) and $x$ ($j_{sx}^y$) directions, respectively. (b) Calculated transverse spin current densities in Pt normalized by $j_c^z$ at room temperature. The error bars are a measure of the spread of ten random configurations. The dashed black line shows the extracted SHA. Inset: Integrated spin current density in a length $L_{\mathrm{Pt}}$ of disordered Pt. The dashed black line illustrates a linear least squares fit from which a SHA for pure bulk Pt of ${\mathrm{\Theta }}_{\mathrm{sH}}=0.033\pm 0.001$ is extracted.

Figure 2

Calculated SHA of pure bulk Pt as a function of temperature. Inset: Calculated SHA replotted as a function of electrical resistivity on a log-log scale. The solid red line illustrates a linear dependence.

Figure 3

SHE in a $\mathrm{Py}|\mathrm{Pt}$ bilayer at room temperature. The calculated transverse spin current densities ($j_{sx}^y$ and $j_{sy}^x$) normalized by the longitudinal electron current density are shown as a function of the distance from the interface in the Pt part of a $\mathrm{Py}|\mathrm{Pt}$ bilayer. Near the interface at $z=0$, the transverse spin current densities are much larger than the asymptotic bulk Pt values. The error bars measure the spread found for 30 random disorder configurations. The dashed black line shows the value of ${\mathrm{\Theta }}_{\mathrm{sH}}$ extracted for bulk Pt. Inset: Integrated spin current density in Pt, where the bulk SHA ${\mathrm{\Theta }}_{\mathrm{sH}}=0.030\pm 0.001$ is determined from the slope of a linear least squares fit shown by the dashed line.

Figure 4

ISHE in a $\mathrm{Py}|\mathrm{Pt}$ bilayer at room temperature. (a) Spin current density injected from Py into Pt. The current is polarized along the $-x$ direction in Py and loses this polarization in Pt by spin-flip scattering. The Pt spin-flip diffusion length $l_{\mathrm{sf}}=5.6\pm 0.1\mathrm{nm}$ is obtained by an exponential fit (solid blue line). Note the logarithmic $y$ axis. (b) Transverse charge current density generated in Pt by the ISHE. The thick orange line shows the calculated longitudinal spin current density multiplied by the extracted value of the bulk SHA (${\mathrm{\Theta }}_{\mathrm{sH}}=0.030$). Inset: Effective SHA (red dots) calculated by integrating the corresponding transverse charge current density and longitudinal spin current density in a certain range of Pt ($0\le z\le L_{\mathrm{Pt}}$). The solid green line is a fit using Eq. (2).