Electromagnetic evanescent field associated with surface acoustic wave: Response of metallic thin films

Abstract

Surface acoustic waves (SAWs), coherent vibrational modes localized at solid surfaces, have been employed to manipulate and detect electronic and magnetic states in condensed-matter systems via strain. SAWs are commonly excited in a piezoelectric material, often the substrate. In such systems, SAWs not only generate strain but also electric field at the surface. Conventional analysis of the electric field accompanying the SAW invokes the electrostatic approximation, which may fall short in fully capturing its essential characteristics by neglecting the effect of the magnetic field. Here we study the electric and magnetic fields associated with SAWs without introducing the electrostatic approximation. The plane wave solution takes the form of an evanescent field that decays along the surface normal with a phase velocity equal to the speed of sound. If a metallic film is placed on the piezoelectric substrate, a time- and space-varying electric field permeates into the film with a decay length along the film normal defined by the skin depth and the SAW wavelength. For films with high conductivity, the phase of the electric field varies along the film normal. The emergence of the evanescent field is a direct consequence of dropping the electrostatic approximation, providing a simple but critical physical interpretation of the SAW-induced electromagnetic field.

Figures (3)

• Figure 1: Schematic illustration of the system, composed of a piezoelectric substrate ($z<0$), a conducting layer ($0<z<d$), and the vacuum ($z>d$). A piezoelectrically excited SAW, with wavenumber $q$ and phase velocity $v$ along $x$, travels on the surface of the substrate.
• Figure 2: Schematic illustration of the SAW-induced TM mode electromagnetic evanescent field. The purple and yellow curves with arrows represent the electric force and magnetic field, respectively. The length of the arrows indicate the strength of the coresponding fields. The green arrows show the local spontaneous polarization in the piezoelectric (e.g., LiNbO$_3$) substrate. The dense gray spheres represent lattice points of the substrate.
• Figure 3: (a-c) Schematic illustration of $(J_x,J_z)$ (a), $\rho$ (b), and $B_y$ (c) within the metallic thin film. The light and dense gray regions represent the piezoelectric substrate and the metallic thin film, respectively. The coordinate system is shown in (a), and the boundary of the two regions is situated at $z=0$. $J_z$ is almost invisible in (a) since it is several orders of magnitude smaller than $J_x$. In (b), positive (negative) induced charge density is expressed with red (blue). (d-f) Profile of $\abs{J_{x}}$ (d), $\abs{\rho}$ (e), and $\abs{B_y}$ (f) along $z$-axis. $(J_x,J_z)$, $\rho$, and $B_y$ are estimated from Eqs. (\ref{['eq:Jf_result']}), (\ref{['eq:rhof_result']}), and (\ref{['eq:B_result']}) with $\sigma_c=10^6\ /\qty(\mathrm{\Omega\cdot m})$, $\varepsilon_r=1$, $d=1$ nm, $v=3871$ m/s, $q = 2\pi / 10\ \upmu$m$^{-1}$, and $\abs{E_{x0}}=10$ V/cm. Note that $J_y$ and $(B_x,B_z)$ will also be induced in the TE mode.