Inverse spin-Hall effect voltage generation by nonlinear spin-wave excitation

We investigate spin currents in microstructured permalloy/platinum bilayers that are excited via magnetic high-frequency fields. Due to this excitation spin pumping occurs at the permalloy/platinum interface and a spin current is injected into the platinum layer. The spin current is detected as a voltage via the inverse spin-Hall effect. We find two regimes reflected by a nonlinear, abrupt voltage surge, which is reproducibly observed at distinct excitation field strengths. Micromagnetic simulations suggest that the surge is caused by excitation of a spin-wave-like mode. The comparatively large voltages reveal a highly efficient spin-current generation method in a mesoscopic spintronic device.

Figure 1

(a) Sketch of the Py/Pt bilayer. The magnetization $\vec{m}$ precesses around the static magnetic field $\vec{H}$ with the cone angle $\theta$. The spin polarization $\vec{\sigma }$ is aligned parallel to $\vec{H}$. A spin current ${\vec{j}}_s$ is pumped into the platinum layer that is converted into a charge current ${\vec{j}}_c$ via the ISHE. (b) Scanning-electron micrograph of a Py/Pt bilayer sample. The inset shows a closeup of the center region. The bilayer is placed on top of the insulating HSQ over the signal conductor of the CPW. The copper leads are connecting the bilayer to a voltmeter.

Figure 2

(a) Broadband-FMR spectroscopy of a Py/Pt bilayer for ${\mu }_0{H}_{\mathrm{rf}}=0.19$ mT. Low (high) transmission $T$ through the waveguide is indicated by black (white) color. A horizontal profile (blue) and a vertical profile (red) is shown. The green line is a Kittel fit. (b) Peak width at half-height $\mathrm{\Delta }f$ as a function of the frequency, obtained by the frequency-dependent Lorentzian fits for every field step. The black line is a fit using Eq. (5). (c) Peak width at half-maximum $\mathrm{\Delta }H\left(f\right)$ for different high-frequency fields $H_{\mathrm{rf}}$ indicated in the figure.

Figure 3

Comparison of field reference and frequency reference method: Transmission spectra $\mathrm{\Delta }T$ for a constant frequency of 7 GHz and ${\mu }_0{H}_{\mathrm{rf}}=0.19$ mT for one sample with (cyan line) and one without (dashed yellow line) a Pt layer, using a reference field of ${\mu }_{0}H=90$ mT that is aligned along the $y$ direction. In addition the transmission spectra $\mathrm{\Delta }{T}_{\mathrm{f}}$ for a constant frequency of 7 GHz and ${\mu }_0{H}_{\mathrm{rf}}=0.19$ mT for one sample with (blue line) and one without (dashed red line) a Pt layer are displayed, obtained with a reference frequency of $f_{\mathrm{ref}}=2$ GHz. The transmission spectra $\mathrm{\Delta }{T}_{\mathrm{f}}$ are shown without offsets.

Figure 4

(a) Field-dependent transmission spectra for a constant frequency of 7 GHz and various high-frequency field strengths. Evaluation of the transmission peak heights (b) and full widths at half-maximum (c).

Figure 5

Transmitted excitation power $\mathrm{\Delta }{T}_{\mathrm{f}}$ and inverse spin-Hall effect voltage $\mathrm{\Delta }V$ for (a) an up and (b) a down sweep of the external static magnetic field ${\mu }_{0}H$ for a constant frequency of 7 GHz and a high-frequency field amplitude of 0.19 mT. The transmission is plotted as light blue line, the voltage data are the blue circles and the black line is a Lorentzian fit. (c) Voltage measurements for different excitation frequencies of the high-frequency field with a constant amplitude of 0.19 mT.

Figure 6

Inverse spin Hall voltage $\mathrm{\Delta }V$ versus static magnetic field $H$ for low high-frequency field amplitudes $H_{\mathrm{rf}}$ (a) and high amplitudes (b) with a constant excitation frequency of 7 GHz.

Figure 7

ISHE voltage peak amplitudes $\pm \mathrm{\Delta }{V}_{\max }$ versus high-frequency field amplitude $H_{\mathrm{rf}}$ for positive (cyan) and negative (fuchsia) field branch and a constant excitation frequency of 7 GHz. Note, that in (a) only low high-frequency field amplitudes up to ${\mu }_0{H}_{\mathrm{rf}}=0.47\mathrm{mT}$ are displayed, while (b) shows amplitudes up to 1.89 mT. In (c) the high-frequency field dependence for additional frequencies is supplemented for the positive field branch.

Figure 8

Micromagnetic simulations of the permalloy rectangles' magnetization dynamics. Shown is the average ${sin}^2\left(\theta \right)$ in the center region of the permalloy rectangle. It is displayed for an excitation field up to 0.55 mT in (a) and up to 1.0 mT in (b). In (c) and (d) exemplary plots of the local cone angle $\theta$ for excitation field strengths of 0.2 and 0.9 mT at 7 GHz are shown. The black rectangles mark the region of the permalloy rectangles between the voltage leads that are used for the calculation of the average ${sin}^2\left(\theta \right)$.

Figure 9

(a) Voltage measurements of a Py/Pt (blue circles) and a Py/- (yellow circles and line) sample for an rf excitation field of 0.19 mT. (b) Voltage measurements of a Py/Pt (green circles) and a Py/- (yellow circles and line) sample for an rf excitation field of 1.06 mT. All measurements are performed with an excitation frequency of 7 GHz.