Spin Pumping at the Magnetic Insulator (YIG)/Normal Metal (Au) Interfaces

Spin injection across the ferrimagnetic insulator (YIG)/normal metal (Au) interface was studied by ferromagnetic resonance. The spin mixing conductance was determined by comparing the Gilbert damping in bare YIG films with those covered by a $\mathrm{Au}/\mathrm{Fe}/\mathrm{Au}$ structure. The Fe layer in $\mathrm{Au}/\mathrm{Fe}/\mathrm{Au}$ acted as a spin sink as displayed by an increased Gilbert damping parameter $\alpha$ compared to that in the bare YIG. In particular, for the $9.0\mathrm{nm}\mathrm{YIG}/2.0\mathrm{nm}\mathrm{Au}/4.3\mathrm{nm}\mathrm{Fe}/6.1\mathrm{nm}\mathrm{Au}$ structure, the YIG and Fe films were coupled by an interlayer exchange coupling, and the exchange coupled YIG exhibited an increased Gilbert damping compared to the bare YIG. This relationship between static and dynamic coupling provides direct evidence for spin pumping. The transfer of spin momentum across the YIG interface is surprisingly efficient with the spin mixing conductance $g_{\uparrow \downarrow }\simeq 1.2\times {10}^{14}{\mathrm{cm}}^{-2}$.

Figure 1

The field derivative of the FMR signal as a function of the external field. (a) $f=23.988\mathrm{GH}z$, bare YIG 9.0 nm. The FMR line required 3 Lorentzian absorption lines with the following parameters: $H_{\mathrm{res},1}=7.556\mathrm{kOe}$, $\Delta H_1=9.7\mathrm{Oe}$, and ${\mathrm{RA}}_1=60\%$; $H_{\mathrm{res},2}=7.551\mathrm{kOe}$, $\Delta H_2=7.7\mathrm{Oe}$, and ${\mathrm{RA}}_2=31\%$; and $H_{\mathrm{res},2}=7.563\mathrm{kOe}$, $\Delta H_2=7.2\mathrm{Oe}$, and ${\mathrm{RA}}_3=9\%$. (b) $f=23.9751\mathrm{GHz}$, $\mathrm{YIG}/2.0\mathrm{Au}/4.3\mathrm{Fe}/6.1\mathrm{Au}$. The three peaks in the bare sample became well split due to ferromagnetic coupling between the YIG and Fe layers. $H_{\mathrm{res},1}=7.380\mathrm{kOe}$, $\Delta H_1=31.3\mathrm{Oe}$, and ${\mathrm{RA}}_1=49\%$; $H_{\mathrm{res},2}=7.468\mathrm{kOe}$, $\Delta H_2=50.6\mathrm{Oe}$, and ${\mathrm{RA}}_1=40\%$; and $H_{\mathrm{res},3}=7.552\mathrm{kOe}$, $\Delta H_3=6.3\mathrm{Oe}$, and ${\mathrm{RA}}_3=11\%$. RA represents the relative area of the sample with the corresponding FMR parameters. Notice that the FMR lines for the areas (1, 2) are shifted towards lower magnetic fields and the line (3) is unshifted from the FMR field of the bare YIG film. The areas (1, 2) are coupled by ferromagnetic interlayer exchange coupling to the Fe layer.

Figure 2

FMR linewidth $\Delta H(f)$ as a function of microwave frequency for sample S1: $9.0\mathrm{YIG}/2.0\mathrm{Au}/4.3\mathrm{Fe}/6.1\mathrm{Au}$ and the bare corresponding YIG film. The solid square and circle points correspond to the areas (2, 1) in Fig. 1 which are coupled by ferromagnetic exchange coupling to the Fe layer. The solid lines correspond to S1. The dashed lines correspond to the bare YIG sample. The sample area (3) was not exchange coupled to the Fe film and showed no change in $\Delta H(f)$ compared to that in the bare YIG. The increase in zero frequency offset in $\Delta H_{1,2}(f=0)$ for the exchange-coupled areas compared to the bare YIG is caused by an inhomogeneous distribution of the interlayer exchange coupling.

Figure 3

FMR linewidth as a function of microwave frequency for sample S2: $9.0\mathrm{YIG}/6.1\mathrm{Au}/4.3\mathrm{Fe}/6.1\mathrm{Au}$ (squares) and the corresponding bare YIG film (circles). The FMR lines are described by two Lorentzian lines. Spin pumping contributions from both areas were similar. For clarity, the most intense line is shown.