Symmetry of the dissipation of surface acoustic waves by ferromagnetic resonance

Abstract

We study the symmetry of the coupling between surface acoustic waves and ferromagnetic resonance in a thin magnetic film of CoFeB deposited on top of a piezoelectric Z-cut LiNbO3 substrate. We vary the orientation of the applied magnetic field with respect to the wavevector of the surface acoustic wave. Experiments indicate an unexpected 2-fold symmetry of the absorption of the SAW energy by the magnetic film. We discuss whether this symmetry can arise from the magnetoelastic torque of the longitudinal strain and the magnetic susceptibility of ferromagnetic resonance. We find that one origin of the 2-fold symmetry can be the weak in-plane uniaxial anisotropy present within the magnetic film. This phenomena adds to the previously identified other source of 2-fold symmetry but shall persist for ultrathin films when the dipolar interactions cease to contribute to the anisotropy of the slope of the spin wave dispersion relation.

Figures (6)

• Figure 1: a) Experimental configuration and definitions. The SAWs are excited using a split-52 IDT using the first port of a VNA and the transmission is collected at the second port. The IDTs periodicity is $\lambda_{\textrm{SAW}}=9\;\mu$m and the finger width is $w=0.9\;\mu$m. A CoFeB rectangle of length $d=800\;\mu$m is placed between the IDTs. {$xyz$} is the reference frame of the in-plane dc field $\vec{H}_0 \parallel \hat{\vec{x}}$, and {$XYZ$} is the reference frame of the LiNbO$_3$ crystal. EA stands for easy axis. b) Example of time-gated transmission signal $S_{21}$ defining the SAW frequencies $f_n=n f_1$ GHz for $n=$ 1, 2, 3, 4 and $f_1=0.43$ GHz. c) Field dependence of $\Delta S_{21}$ for a field oriented at $\psi=15^\circ$ and at $f_4=1.72$ GHz. The arrows sketch the field sweeping direction. d) Measured maximum (negative) value of $\Delta S_{21}$ at $f_4$ and $\mu_0|\vec{H}_0|=4$ mT versus the orientation of the applied field. Note the 2-fold symmetry.
• Figure 2: Illustration of the symmetries at play in magnetoelastic coupling, evaluated for a field of $\mu_0|\vec{H}_0|=4$ mT of variable orientation, and for a CoFeB magnetic film of thickness 34 nm. a) Tickle field (torkance) for an isotropic magnetic film subjected to a sole longitudinal strain according to ref. [weiler_elastically_2011]. b) Spin waves (SW) frequency [kalinikos_theory_1986] evaluated at SW wavevector $k_4 = 2.8$ rad/$\mu$m for an isotropic magnetic film. The green line represents the FMR $\omega_{\textrm{SW}}(k=0)$ value. c) FMR frequency evaluated for a uniaxial anisotropy field $\mu_0H_u=1.5$ mT oriented at $\varphi_u=105^\circ$. The vertical lines represent the easy and hard axes (EA, HA).
• Figure 3: Angular dependence of SAW-FMR coupling when varying the uniaxial anisotropy field $\mu_0H_u$ and keeping constants $\mu_0|\vec{H}_0|=4$ mT, uniaxial anisotropy angle $\varphi_u=105^\circ$, $\alpha=0.01$ and SAW frequency $f_4=1.72$ GHz. The vertical lines represent the easy and hard axes (EA, HA). The green curve is the best fit of the measurements.
• Figure 4: Angular dependence of SAW-FMR coupling when varying the uniaxial anisotropy angle $\varphi_u$ and keeping constants $\mu_0|\vec{H}_0|=4$ mT, uniaxial anisotropy field $\mu_0H_u=1.5$ mT, $\alpha=0.01$ and SAW frequency $f_4=1.72$ GHz. The vertical lines represent the easy and hard axes (EA, HA). The green curve is the best fit of the measurements.
• Figure 5: Angular dependence of SAW-FMR coupling when varying the SAW frequency $f_{\textrm{SAW}}$, and keeping constants $\mu_0|\vec{H}_0|=4$ mT, uniaxial anisotropy field $\mu_0H_u=1.5$ mT, the uniaxial anisotropy angle $\varphi_u=105^\circ$ and $\alpha=0.01$. The vertical lines represent the easy and hard axes (EA, HA).