Observation of Gyromagnetic Spin Wave Resonance in NiFe Films

This Letter demonstrates spin wave resonance (SWR) owing to the gyromagnetic effect by propagating a Rayleigh-type surface acoustic wave (R-SAW) through ferromagnetic thin films. The SWR amplitude in a NiFe film shows a higher-order frequency variation than in a magnetoelastic Ni film. This frequency dependence is well understood in terms of the presence of a gyromagnetic field attributable to the local lattice rotation in the R-SAW. From the frequency dependence of the SWR amplitude, the gyromagnetic SWR could be separated from another SWR caused by a magnetoelastic effect of the ferromagnet.

Figure 1

(a)–(c) Schematic illustrations of effective dynamic fields originating from a R-SAW in a ferromagnetic thin film. The R-SAW propagates in the $x$ direction and decays in the $y$ (depth) direction. (a) A vorticity ${\mathrm{\Omega }}^z$ yields a Barnett field along the $z$ axis given by Eq. (3). (b),(c) A longitudinal strain ${ϵ}_{xx}$ leads to a ME field $h_{\mathrm{ME}}^{\mathrm{IP}}$ in the plane, while a transverse strain ${ϵ}_{xy}$ leads to a ME field $h_{\mathrm{ME}}^{\mathrm{OOP}}$ out of the plane, given by Eqs. (5) and (6), respectively. The color codes show the real parts of (b) ${ϵ}_{xx}$ and (c) ${ϵ}_{xy}$. (d) Measurement setup for observing a SWR excited by effective dynamic fields. A R-SAW propagates between a pair of interdigital transducers on a ${\text{LiNbO}}_3$ piezoelectric substrate. A static field was applied in the plane at an angle of $\varphi$ from the wave vector of the R-SAW. The R-SAW attenuation owing to SWR excitation can be measured from the $S_{21}$ signal using a vector network analyzer.

Figure 2

(a) A color plot of MW absorption $\mathrm{\Delta }{P}^{\mathrm{norm}}$ as functions of frequency and static field, and (b) the frequency dependence of the MW transmission measured for NiFe film at $\varphi =0$. (c) The MW absorption and (d) transmission measured for Ni film at $\varphi =\pi /4$. The period of the IDT finger was fixed at $2.4\mu \mathrm{m}$. Magenta guidelines in (a) and (c) show the MSBVW-dispersion relations for NiFe and Ni films, respectively [32].

Figure 3

The angular dependence of MW absorption in (a) NiFe and (b) Ni films. (c) R-SAW-frequency dependence of the MW absorption in NiFe ($\varphi =0$) and Ni ($\varphi =\pi /4$). Magenta guidelines in (a) and (b) are the dispersion relations of the spin wave for NiFe and Ni films, respectively [32]. Broken lines in (c) show the results of best fit with Eq. (12).