Spin transport parameters in ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}/\mathrm{Ru}$ and ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}/\mathrm{Ta}$ bilayers

We present a systematic study of the spin transport properties in two different bilayer systems, ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}/\mathrm{Ru}$ and ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}/\mathrm{Ta}$, combining ferromagnetic resonance (FMR) and inverse spin Hall effect (ISHE) voltage measurements. We have estimated the effective spin mixing conductance $g^{\uparrow \downarrow }$ by analyzing the permalloy (Py) thickness dependence of the FMR linewidth obtaining $g^{\uparrow \downarrow }=(3.8\pm 0.7)\times {10}^{15}{\mathrm{cm}}^{-2}$ and $g^{\uparrow \downarrow }=(1.3\pm 0.4)\times {10}^{15}{\mathrm{cm}}^{-2}$ for Py/Ru and Py/Ta, respectively. Analyzing the Ta thickness dependence of the ISHE voltage, we have been able to extract the spin diffusion length, ${\lambda }_{SD}=1.5\pm 0.5$ nm, and spin Hall angle, ${\Theta }_{SH}=-0.03\pm 0.01$, of Ta. From the two series of Py/Ta bilayers—with thickness variation of ferromagnetic and nonmagnetic layers, respectively—we demonstrate a path to estimate the spin diffusion length from the experimental data, independent of the spin Hall angle and the microwave field amplitude.

Figure 1

(a) Sketch of the geometrical setup of the sample, the microwave field $\left({\mathbf{h}}_{\mathrm{RF}}\right)$, and the external dc field, $\mathbf{H}$. (b) Coordinate reference system chosen to analyze the FMR and the inverse spin Hall voltage measurements.

Figure 2

Typical voltage signal $(V_{\mathrm{ISHE}})$ and FMR absorption spectra (inset) in two bilayers of Py in contact with different metals: (a) Ru; (b) Ta. The distance $\left(L\right)$ between the electrical contacts is 2.2 and 2.3 mm, respectively.

Figure 3

Dependence of the peak to peak linewidth of (a) $\mathrm{Py}\left(t_{\mathrm{Py}}\right)/\mathrm{Ta}$(5 nm) and (b) $\mathrm{Py}\left(t_{\mathrm{Py}}\right)/\mathrm{Ru}$(10 nm) series as a function of the microwave excitation frequency. (c) Total Gilbert damping parameter as a function of the inverse of the Py layer thickness for both sets of samples.

Figure 4

(a) ISHE voltage signal measured in an X-Band FMR experiment performed in the Py(5 nm)/Ru(10 nm) bilayer for different orientations of the magnetic field with respect to the film normal $\left({\varphi }_H\right)$. (b) Peak value of the symmetric contribution as a function of the angle of the equilibrium magnetization $\left(\varphi \right)$ normalized by the $V_{\mathrm{ISHE}}$ acquired at ${\varphi }_H={90}^{\circ }$. The solid line corresponds to the values obtained from Eq. (9) using the FMR data. Explored angles are ${\varphi }_H=\pm {90}^{\circ },\pm {60}^{\circ },\pm {40}^{\circ },\pm {20}^{\circ },\pm {10}^{\circ }$, and $0^{\circ }$.

Figure 5

Angular variation of the resonance field (full symbols) and the linewidth (open symbols) in the bilayer Py(5 nm)/Ru(10 nm) obtained from X-Band FMR experiments. The solid line corresponds to the fitting using Eqs. (5) and (6), from which we obtained $H_{\mathrm{eff}}=5920$ Oe. The dotted line is a guide to the eye.

Figure 6

Thickness dependence of the effective anisotropy field $\left(H_{\mathrm{eff}}\right)$ and the $g$ factor of the Py(t)/Ta and Py(t)/Ru series.

Figure 7

Power dependence of the maximum inverse spin Hall voltage measured at $H=H_r$. In the inset we show the Lorentzian shape of $V_{\mathrm{ISHE}}$ curves in the neighborhood of $H_r$. Data correspond to the bilayer Py(5 nm)/Ru(10 nm) varying $P$ from 4 mW to 200 mW.

Figure 8

$\overline{\rho }$ signal as a function of magnetic field for (a) $\mathrm{Py}\left(t_{\mathrm{Py}}\right)/\mathrm{Ta}$(5 nm) and (b) $\mathrm{Py}\left(10\mathrm{nm}\right)/\mathrm{Ta}\left(t_{\mathrm{Ta}}\right)$ series.

Figure 9

Dependence of $\overline{\rho }$ as function of the thickness of (a) Py layer and (b) Ta layer. The continuous lines are the fits obtained with Eq. (12) and the parameters indicated in the figure.