Quantum Well State Induced Oscillation of Pure Spin Currents in $\mathrm{Fe}/\mathrm{Au}/\mathrm{Pd}(001)$ Systems

Spin pumping at the ferromagnetic metal (Fe)/normal metal (Au) interface and the subsequent spin transport in $\mathrm{Au}/\mathrm{Pd}$ heterostructures is studied using ferromagnetic resonance. The spin pumping induced damping in the $\mathrm{Fe}/\mathrm{Pd}$ structure is greatly suppressed by the addition of a Au spacer layer in the structure $\mathrm{Fe}/\mathrm{Au}/\mathrm{Pd}$. The rapid decrease in the interface damping with an increasing Au layer thickness does not correspond to an expectation based on a simple spin diffusion theory in the Au layer. It is possible to account for this behavior by introducing a partial reflection of spin current at the $\mathrm{Au}/\mathrm{Pd}$ interface. Furthermore, oscillations in the amplitude of spin pumping damping are observed in the $\mathrm{Fe}/\mathrm{Au}/\mathrm{Pd}$ structure as a function of Au thickness for thicknesses less than half the electron mean free path of bulk Au. This new effect indicates a formation of quantum well states in the accumulated spin density in the Au spacer that affect the time irreversible process of spin pumping.

Figure 1

Left: 35.6439 GHz FMR data for $\mathrm{GaAs}/17\mathrm{Fe}/20\mathrm{Au}$. The relevant fit parameters are $H_{\mathrm{FMR}}=7263.1\mathrm{Oe}$ and $\mathrm{\Delta }{H}_{\mathrm{FMR}}=49.9\mathrm{Oe}$. Right: FMR linewidth as a function of frequency for (squares, inverted triangles, and triangles) three different growths of $\mathrm{GaAs}/17\mathrm{Fe}/20\mathrm{Au}$ with ${\alpha }_{\mathrm{tot}}=0.00356$. These measurement have been used to define ${\alpha }_{17\mathrm{Fe}}\equiv 0.00356$. (diamonds) $\mathrm{GaAs}/17\mathrm{Fe}/250\mathrm{Au}/50\mathrm{Pd}/20\mathrm{Au}$ with ${\alpha }_{\mathrm{tot}}=0.00552$ and (circles) $\mathrm{GaAs}/17\mathrm{Fe}/50\mathrm{Pd}/20\mathrm{Au}$ with ${\alpha }_{\mathrm{tot}}=0.00650$ showing the increase in damping due to spin pumping ${\alpha }_{\mathrm{tot}}={\alpha }_{17\mathrm{Fe}}+{\alpha }_{\mathrm{sp}}$.

Figure 2

Main: spin pumping induced damping ${\alpha }_{\mathrm{sp}}$ multiplied by the Fe thickness in $\mathrm{GaAs}/17\mathrm{Fe}/d_{\mathrm{Au}}\mathrm{Au}/50\mathrm{Pd}$ structures as a function of Au spacer thickness $d_{\mathrm{Au}}$. The error bars include errors for both ${\alpha }_{\mathrm{tot}}$ and $d_{\mathrm{Fe}}$. Two important effects can be seen. (a) ${\alpha }_{\mathrm{sp}}$ rapidly reached a constant value by $d_{Au}\simeq 100$ AL. (b) An oscillatory behavior in ${\alpha }_{\mathrm{sp}}$ was observed for $d_{\mathrm{Au}}<100$ AL. The red line (upper) was calculated using spin diffusion theory for $17\mathrm{Fe}/\mathrm{Au}/\mathrm{FM}$ (perfect sink) and the blue line (lower) for $17\mathrm{Fe}/\mathrm{Au}$ (perfect reflection). The cyan line (central) was obtained by using Eq. (9). The vertical dashed lines represent the electron mean free path in bulk Au. Further details including the spin transport parameters are described in the text. Bottom inset: expanded view of the main figure. Top inset: the evaluated changes in $g_{\uparrow \downarrow }$ by employing Eq. (9).