Magnetoelastic parametric instabilities of localized spin waves induced by traveling elastic waves

A theory of parametric interaction between spin waves localized in a waveguide and traveling elastic waves is developed for ferromagnetic thin films. The presented theoretical formalism takes into account an arbitrary spatial distribution of the displacement field in the acoustic waves and an arbitrary magnetization in spin waves. Using the theory, we examine interaction of forward-volume spin waves (FVSW) localized in a narrow waveguide and Rayleigh surface acoustic waves traveling in a substrate underneath the waveguide. We show that, in contrast to classical electromagnetic pumping, the symmetry of the magnetoelastic interaction allows for the generation of first-order parametric instabilities in spin waves with circular precession, such as FVSW. At the same time the localization of spin waves modifies the momentum conservation law for the parametric process to include the transfer of momentum to the waveguide, which allows for a frequency separation of the interacting counterpropagating spin waves. The frequency separation enables amplification of a localized spin wave without generation of a traveling idler wave, which results in a greater amplification efficiency.

Figure 1

Sketch showing the geometry of the confined spin-wave waveguide located on a substrate.

Figure 2

Top view of a setup for spin-wave and surface acoustic wave parametric interaction. A Rayleigh surface acoustic wave excited, for example, by an interdigitated transducer (IDT), propagates in the substrate, while a spin wave propagates in the magnetic waveguide (green). The magnetic field $\mathit{B}$ is applied perpendicular to the plane.

Figure 3

(a) Parametric interaction coefficient $V_0$ for the surface acoustic waves and spin waves in a rectangular waveguide as a function of the waveguide width $w$ and the projection of the SAW wave vector perpendicular to the waveguide $k_{\perp }$. (b) Numerically calculated spin-wave spectrum in a rectangular YIG waveguide. (c) Amplitude of spin waves under a parametric pumping for an obliquely (blue solid line) and normally (orange dashed line) incident SAW; vertical dotted lines enclose the pumping region. The amplitude of the strain in the acoustic wave is selected as $a=31\mathrm{ppm}>a_{\text{th}}\left(\varphi \right)$. See text for the parameters of the waveguide and materials.