Highly nonlinear frequency-dependent spin-wave resonance excited via spin-vorticity coupling

A nonuniform vorticity of lattice deformation in a surface acoustic wave (SAW) can generate a spin current (SC) in nonmagnetic metals via spin-vorticity coupling (SVC). We demonstrated a strong enhancement of SVC-derived SC generated in Cu and Pt films with increasing the frequency of the SAW by observing the spin-wave resonance (SWR) in an adjacent NiFe film. The comparative amplitudes and high-order frequency variations of SWR in NiFe/Cu and NiFe/Pt bilayers imply that the amplitude of the SC generated via SVC in a SAW is robust against the strength of spin-orbit interaction in nonmagnetic metals.

Figure 1

(a) Schematic illustration of an SWR excited by propagating an R-SAW through a NiFe/NM bilayer. The R-SAW generates a nonuniform alternating SC via SVC in NMs. When a static magnetic field is applied at an angle $\varphi$ from the propagation direction of the R-SAW, a spin wave is possibly excited in the NiFe layer due to the spin-transfer torque by the injected SC, the Barnett field, and/or the ME field. (b) Measurement setup for observing the SWR. The R-SAW attenuation owing to the SWR can be measured from the $S_{21}$ signal using a vector network analyzer.

Figure 2

Color plots of the MW absorption $\mathrm{\Delta }{P}^{\mathrm{norm}}$ as functions of frequency and magnetic field measured for (a) NiFe/Cu, (b) NiFe/Pt, and (c) NiFe/Ti bilayers, and (d) NiFe and (e) Ni single layers. The period of the IDT finger was set to 2.4 $\mu \mathrm{m}$ and the magnetic field was applied at (a–d) $\varphi =0$ and (e) $\varphi =\pi /4$. The MW absorption was observed at magnetic fields where the excitation frequency of the spin wave matches the eigenfrequency of the R-SAW.

Figure 3

Color plots of the MW absorption $\mathrm{\Delta }{P}^{\mathrm{norm}}$ as functions of angle $\varphi$ and magnitude of magnetic field measured for (a) NiFe/Cu and (b) NiFe/Ti bilayers, and (c) NiFe and (d) Ni single layers. Magenta broken lines represent the resonant condition for SWR which is given by Eqs. (9)–(11).

Figure 4

Peak value of $\mathrm{\Delta }{P}^{\mathrm{norm}}$ measured for (a) NiFe/NM bilayers and NiFe single layer and (b) Ni single layer as a function of angle $\varphi$ of the external field application.

Figure 5

R-SAW-frequency dependence of the MW absorption in NiFe/Cu, NiFe/Pt, NiFe/Ti, NiFe ($\varphi =0$) and Ni ($\varphi =\pi /4$). The MW absorption in NiFe/Cu and NiFe/Pt showed higher-order changes in frequency than those in NiFe/Ti, NiFe, and Ni. The dashed lines show the results of fitting the data points with linear functions.

Figure 6

Frequency dependence of $P_{21}(f_{\mathrm{ref}},H_{\mathrm{ref}})$.