Conditions for effective coupling between surface acoustic waves and spin waves

Abstract

The frequencies and wave vectors of dipolar dominated spin waves (SW) and surface acoustic waves (SAW) cover the same ranges. Therefore, the propagating waves of both kinds can potentially scatter each other - in other words, the necessary condition for the interaction in a linear regime can be satisfied. The simplest structure in which the magnetoelastic coupling between SW and SAW can be observed is the magnetostrictive layer deposited on the substrate. The confinement of SWs in the magnetic layer is necessary to induce the dipolar interaction and surface localization of SAW ensures the co-existence of both kinds of waves in the magnetostrictive layer deposited on the surface.The strength of the magnetoelastic interaction depends on the orientation of the wave vector concerning the direction of the static magnetic field[1]. Moreover, this interaction is different for different types of SAWs, specifically, Rayleigh-SAWs (R-SAW) and Love-SAWs (L-SAW)[1,4] – see Fig.1. Thus, the coupling is strongly anisotropic and cannot be observed for arbitrary selected SAWs and SWs, even if their frequencies and wave vectors match. This effect is well-known and broadly discussed in the literature[1].Our study shows an additional factor limiting the interaction between SAWs and SWs. The SAW/SW coupling proves to require an appropriate profile of the elastic wave near the surface of the magnetostrictive structure, at distances much smaller than the wavelength. For R-SAWs the tangential component of displacement ux can have nodes within the magnetic layer, resulting in a reduction of the net strength of magnetoelastic interaction even if the strain εxx is locally significant. In an L-SAW the displacement uy does not have any nodes (uy changes monotonously in the normal direction). We have shown that this additional factor plays a role for some types of surface acoustic waves (R-SAWs), while other types (L-SAWs) are insensitive to it. We think that the studies on magnon-phonon interaction in confined geometries (surfaces, cavities) are very promising and can reveal unusual interaction mechanisms.SampleWe studied [Co20Fe60B20/Au]20 multilayer of the thickness 60 nm as a magnetostrictive medium. In Co20Fe60B20 layers (2.1 nm) the magnetization is oriented in-plane and the presence of Au layers (0.9 nm) reduces the SWs’ frequencies due to out-of-plane anisotropy. The multilayer was deposited on top of a 4 nm titanium (Ti) and a 15 nm gold (Au), which buffers the naturally oxidized (001) silicon substrate.MethodWe measured the dispersion relations of thermally excited SAWs and magnetostatic SWs using a six-pass tandem Brillouin spectrometer (Scientific Instrumentsc©TFP2-HC), which ensures a contrast of 1015. A frequency-stabilized diode-pumped solid-state laser (Coherentc©VERDI V5) operating at λ0= 532 nm was used as a source of incident light. The measurements were performed in the 180o backscattering geometry with crossed (p-s)polarization of the incident and scattered light for SWs and non-crossed (p-p) polarization for SAWs. Using the finite element method in COMSOL Multiphysics©, we solve numerically the coupled equations of motion for magnetization and mechanic displacement.AcknowledgementThe authors hereby acknowledge the financial support from the National Science Centre, Poland, project No. UMO-2016/21/B/ST3/00452. S. Mies. would like to additionally acknowledge the support from the National Science Centre, Poland, project No. UMO-2020/36/T/ST3/00542.  Fig.1 (left) - the illustration of the Rayleigh and Love surface acoustic waves (R SAW and L SAW). (right) -the numerically calculated profiles of the strain tensor playing the most significant role for magnetoelastic interaction of spin waves with R SAW (magnetic field applied the 45 deg) and L SAW (magnetic field applied at 0 deg). Please note that the interaction with R SAW can be canceled due to the nodal line.