Magneto-Optical Detection of the Spin Hall Effect in Pt and W Thin Films

The conversion of charge currents into spin currents in nonmagnetic conductors is a hallmark manifestation of spin-orbit coupling that has important implications for spintronic devices. Here we report the measurement of the interfacial spin accumulation induced by the spin Hall effect in Pt and W thin films using magneto-optical Kerr microscopy. We show that the Kerr rotation has opposite sign in Pt and W and scales linearly with current density. By comparing the experimental results with ab initio calculations of the spin Hall and magneto-optical Kerr effects, we quantitatively determine the current-induced spin accumulation at the Pt interface as $5\times {10}^{-12}{\mu }_B{\mathrm{A}}^{-1}{\mathrm{cm}}^2$ per atom. From thickness-dependent measurements, we determine the spin diffusion length in a single Pt film to be $11\pm 3\mathrm{nm}$, which is significantly larger compared to that of Pt adjacent to a magnetic layer.

Figure 1

(a) Microscope image of a Pt Hall bar with the current running top-down (parallel to $x$). (b) Laser beam path through the focusing objective. The arrows in the Pt or W wire represent the spin accumulation. (c) Depth profile of the calculated spin accumulation (shaded) in a 30-nm-thick wire for $l_s=9\mathrm{nm}$. The dashed line represents the depth-dependent sensitivity of the MOKE.

Figure 2

(a), (b) Line scans of the optical reflectivity across $20\text{−}\mu \mathrm{m}$-wide wires of (a) 15-nm Pt and (b) 10-nm W. (c), (d) Thermally induced change of the reflectivity $-\mathrm{\Delta }R/R$ for (c) Pt at $j=1.5\times {10}^7\mathrm{A}{\mathrm{cm}}^{-2}$ and (d) W at $j=5.3\times {10}^6\mathrm{A}{\mathrm{cm}}^{-2}$. (e), (f) Current dependence of $-\mathrm{\Delta }R/R$ for (e) Pt and (f) W. The solid lines are fits to a $j^2$ function. Points left of the origin were measured with the reversed optical path, with $s$ denoting the sign of the incidence angle of the laser beam.

Figure 3

SHE-induced Kerr rotation. (a) Line scan of ${\theta }_K$ across a $20\text{−}\mu \mathrm{m}$-wide, 15-nm-thick Pt wire at a current density $j=1.5\times {10}^7\mathrm{A}{\mathrm{cm}}^{-2}$ and (b) a 10-nm-thick W wire at $j=5.3\times {10}^6\mathrm{A}{\mathrm{cm}}^{-2}$. (c), (d) ${\theta }_K$ as a function of $j$. The data points represent line scan averages; statistical error bars from averaging multiple line scans are indicated. The solid lines are linear fits to the data. Points left of the origin were measured with the reversed optical path, $s$.

Figure 4

Ab initio spin-resolved Hall conductivity $\mathrm{Re}[{\sigma }_{xz}^y(\omega )]$ as a function of photon energy $\hslash \omega$ of (a) Pt and (b) W. The influence of a spin accumulation on the calculated Re[${\sigma }_{xz}^y(\omega )$] is shown by the dashed curves (for an induced magnetization of $M^y=0.1{\mu }_B$ per atom). (c,d) Calculated longitudinal Kerr rotation spectrum for $s$-polarized light incident at 37° in the $yz$ plane, for $M^y=0.01{\mu }_B$ (magenta line) and $M^y=0.02{\mu }_B$ (dashed cyan line) for Pt and W, respectively.

Figure 5

Kerr rotation vs Pt thickness for $j={10}^7\mathrm{A}{\mathrm{cm}}^{-2}$. The symbols are obtained from linear fits of ${\theta }_K$ as a function of $j$, as shown in Fig. 3. The solid curve is a fit using Eq. (2) and ${\sigma }_{xz}^{\mathrm{SH}}=1880{\mathrm{\Omega }}^{-1}{\mathrm{cm}}^{-1}$, $l_s=11.4\mathrm{nm}$ as free parameters. The dashed line is a fit with constant $l_s\rho =2.6\mathrm{f}\mathrm{\Omega }{\mathrm{m}}^2$.