Universal Method for Separating Spin Pumping from Spin Rectification Voltage of Ferromagnetic Resonance

We develop a method for universally resolving the important issue of separating spin pumping from spin rectification signals in bilayer spintronics devices. This method is based on the characteristic distinction of spin pumping and spin rectification, as revealed in their different angular and field symmetries. It applies generally for analyzing charge voltages in bilayers induced by the ferromagnetic resonance (FMR), independent of FMR line shape. Hence, it solves the outstanding problem that device-specific microwave properties restrict the universal quantification of the spin Hall angle in bilayer devices via FMR experiments. Furthermore, it paves the way for directly measuring the nonlinear evolution of spin current generated by spin pumping. The spin Hall angle in a $\mathrm{Py}/\mathrm{Pt}$ bilayer is thereby directly measured as $0.021\pm 0.015$ up to a large precession cone angle of about 20°.

Figure 1

Sketch for the dc voltage induced in the FM/NM bilayer by (a) pure spin pumping and (b) pure spin rectification, which can be measured by tilting the direction of the external magnetic field slightly towards the $y$ and $x$ axes, respectively.

Figure 2

dc voltage measured on the $\mathrm{Py}/\mathrm{Pt}$ bilayer as a function of the magnetic field $H$ applied with angles (a) $\alpha =-1.5°$ and $\beta =0$, (b) $\beta =-0.65°$ and $\alpha =0$, (c) $\alpha =1.5°$ and $\beta =0$, and (d) $\beta =0.65°$ and $\alpha =0$, which reveal the distinct symmetries of $V_{\mathrm{SR}}$ and $V_{\mathrm{SP}}$. (e)–(h) The comparative results measured on the Py monolayer sample. The microwave frequency is fixed at 9 GHz with a low power of 31.6 mW.

Figure 3

Angular dependence of (a) $V_{\mathrm{SR}}$ and (b) $V_{\mathrm{SP}}$ measured at $\beta =0°$ and $\alpha =0°$, respectively. (c) FMR ${\omega }_r-H_R$ dispersions for both pure spin pumping (blue squares) and spin rectification (red circles). (d) Dependence of $V_{\mathrm{SR}}$ and $V_{\mathrm{SP}}$ on microwave power measured in the linear dynamic regime up to $P=31.6\mathrm{meV}$. (e) Frequency dependence of the ratio between $V_{\mathrm{SP}}$ and $V_{\mathrm{SR}}$ measured at the same microwave power. Here, $V_{\mathrm{SP}}$ and $V_{\mathrm{SR}}$ are measured at $\alpha =-1°$ and $\beta =-0.35°$, respectively.

Figure 4

(a) $V_{\mathrm{SP}}$ measured at $\alpha =0°$ and $\beta =-0.7°$ under different microwave excitation power (at a frequency $\omega /2\pi =6.0\mathrm{GHz}$). The insets show the full range spectra measured at $P=158\mathrm{mW}$ and the dependence of the pure spin pumping voltage on the cone angle. (b) Spin Hall angle of Pt calculated for different cone angles and different frequencies. Results from other experiments are plotted for comparison. (c) Spin current amplitude measured as a function of the microwave magnetic field $h$ and frequency $\omega$. It saturates at high microwave power.