Dependence of spin-pumping spin Hall effect measurements on layer thicknesses and stacking order

Voltages generated from inverse spin Hall and anisotropic magnetoresistance effects via spin pumping in ferromagnetic (F)/nonmagnetic (N) bilayers are investigated by means of a broadband ferromagnetic resonance approach. Varying the nonmagnetic layer thickness enables the determination of the spin diffusion length in Pd of 5.5 ± 0.5 nm. We also observe a systematic change of the voltage line shape when reversing the stacking order of the F/N bilayer, which is qualitatively consistent with expectations from spin Hall effects. However, even after independent calibration of the precession angle, systematic quantitative discrepancies in analyzing the data with spin Hall effects remain.

Figure 1

(a) Schematic of the spin pumping spin Hall effect experiment showing the respective polarity (rf input, external field, and dc voltage contacts) used for the measurement. (b) Layout of voltage contacts used for the measurements (sketch not up to scale).

Figure 2

(a) AMR-SHE spectra for (GaAs/$x$Pd/15Py) ($x$ = 0, 5, 10, 15 nm) measured at 7 GHz. (b) Thickness dependence of the weight $W$ of the antisymmetric component for Pd. (c) Estimation of the spin diffusion length for Pd for all measured frequency.

Figure 3

(a) AMR-SHE spectra for a GaAs/15Py/15Pd sample at 4 and 7 GHz, 40° applied field angle and 5 dBm. (b) Measurements under identical conditions for the reverse stack order (GaAs/15Pd/15Py). Frequency dependence of the weight $W$ of the antisymmetric component of the AMR-SHE voltage for both stacking orders with Pd(c) and Pt (d).

Figure 4

Frequency dependence of $W$ for a GaAs/15Py/15Pd (solid symbols) and a GaAs/15Pd/15Py (open symbols). The line shape remains unchanged with applied field angle (a) and rf output power (b).

Figure 5

AMR-FMR measurements at 6 GHz and rf output power 5, 8, and 11 dBm for (a) SiO${}_2$/15Pd/15Py (open symbols) and (b) SiO${}_2$/15Py/15Pd (solid symbols). Insets in (a) and (b) show the corresponding dc magnetoresistance with the field applied perpendicular to the long direction (easy axis) of the samples. (c) Frequency dependence of the precession angle at resonance.

Figure 6

(a) Frequency dependence of the FMR linewidth showing the additional damping due to spin pumping. (b) Estimation of the product spin mixing conductance × spin Hall angle for Pt, Pd, and Au following the independent calibration of the cone angle.