Phase-resolved imaging of coherent phonon-magnon coupling

Abstract

We use a direct phase-resolved optical technique to study the coherence of spin waves (SWs) that are driven by surface acoustic waves (SAWs) via resonant magnetoelastic coupling. For this, we employ a piezoelectric lithium tantalate (LiTaO$_{3}$) substrate, equipped with micropatterned interdigital transducers for SAW excitation, which interact with SWs in a 5 nm thin and 20 $μ$m wide Co$_{40}$Fe$_{40}$B$_{20}$-waveguide. We detect the SAW and the SW using a phase-locked micro-focused optical polarization detection experiment and use the characteristic polarization dependence to separate the SAW and SW signals. Our measurements directly image the resonant and coherent excitation of the SW by the SAW.

Figures (3)

• Figure 1: (a) Schematic depiction of the experimental setup employing phase-locked micro-focused optical polarization analysis, commonly referred to as the µFR-MOKE-technique. The reflected laser light is analyzed in its polarization and intensity state at fixed temporal wave phase $\omega t=\text{const.}$ (b) A sketch of the investigated sample: On a LiTaO3-piezoelectric substrate, sets of IDTs excite coherent SH-SAWs toward a 5 nm thick and 20 µm wide Co40Fe40B20-waveguide. (c) The in‑plane‑polarized shear‑strain profile of the propagating SH‑SAW mode. The strain amplitude of $\varepsilon_{xy}$ is shown in false color. (d) Example line-scan measurement of a SH-SAW mode on LiTaO3, measured at $f=3.41\;$GHz. The real and imaginary part of the $S_\text{21}$ parameter, measured by the VNA, encode the phase-information of the detected SAW. (e) Line-scan measurement of a spin wave on a 40 nm thick permalloy film, excited by a microwave antenna, measured at $f=7\;$GHz and $\mu_0H_\text{ext}=30\;$mT in Damon-Eshbach geometry ($k_\text{SW}\perp\mu_0H_\text{ext}$). (f) The light intensity as a function of the polarization, analyzed by the rotatable $\lambda/2-$plate measured after the polarizer, relative to the incoming polarization on the sample. The incoming, unmodulated light is linearly p-polarized. (g) Polarization dependence of the detected amplitude of the real-part of the SH-SAW and SW-signals, respectively. Notably, the SAW signal maximizes at highest sensitivity on intensity modulation and not undergoing a sign change from negative to positive polarization analysis, showing an even symmetry. Comparably, the SW is detected most efficiently at polarization modulating sensitivity and exhibiting a sign change from negative to positive polarization analyzing angle, representing an odd symmetry. The inset illustrates the origin of the sign flip of the SW detection, which occurs when the polarization is rotated due to a different selection of the analized polarization orientation.
• Figure 2: (a) Shows a sketch of the investigated structure and the measurement geometry. We orient the sample in backward-volume geometry ($k_\text{SAW}\|\mu_0H_\text{ext}$). The SAW-signal is picked up near the end of the waveguide (marked by ROI SAW). The SW signal shown in Fig. \ref{['fig:SW-fieldsweep']} is measured at the start of the Co40Fe40B20-strip. (b) Shows the derived SAW dispersion relation (blue) and of the SW dispersion relation (green) at $\mu_0H_\text{ext}=11\;$mT computed using the thin-film approximation derived by Kalinikos-Slavin equation kalinikosTheoryDipoleexchangeSpin1986. The SAW frequency ($f=3.41$ GHz) and wave vector ($k=5.3$ rad/µm) excited by our IDT intersect the SW dispersion relation at the external field of $\mu_0H_\text{ext}=11\;$mT, fullfilling the resonance condition. (c) Shows the measured SAW signal as $\text{Re}(S_{21})$ and $\text{Im}(S_{21})$, detected at "ROI SAW" indicated in (a) at 0° polarization analyzing position, when the SAW is detected most sensitively. At the resonance magnetic field of $\pm11\;$mT (gray dashed lines) we observe a decrease in SAW amplitude as well as a phase shift, compared to the off-resonant case as a back action of the SW-system on the SAW.
• Figure 3: Spin-wave signal extracted in the ROI SW region, indicated in Fig. \ref{['fig:SAW-fieldsweep']} a) near the start of the ferromagnetic waveguide. At an external magnetic field of $\mu_0H_\text{ext}=11\;$mT, the SAW resonantly drives the spin wave. This becomes apparent by the increase in the detected amplitude and the phase difference of 90° of the signal, as marked by the gray dashed lines. The result clearly shows that the SAW drives a coherent SW precession.