Nonreciprocal propagation of surface acoustic wave in ${\mathrm{Ni}\text{/}\mathrm{LiNbO}}_3$

We investigated surface acoustic wave propagation in a Ni/${\mathrm{LiNbO}}_3$ hybrid device. We found that the absorption and phase velocity are dependent on the sign of the wave vector, which indicates that the surface acoustic wave propagation has nonreciprocal characteristics induced by simultaneous breaking of time-reversal and spatial inversion symmetries. The nonreciprocity was reversed by ${180}^{\circ }$ rotation of the magnetic field. The origin of the nonreciprocity is ascribed to interference of shear-type and longitudinal-type magnetoelastic couplings.

Figure 1

(a) A schematic diagram of a Ni/${\mathrm{LiNbO}}_3$ hybrid SAW device used in this study. A rectangular ferromagnetic Ni film was evaporated on device. (b) Typical transmission spectrum. The 13th harmonic of approximately 2.23 GHz was used in this study. (c),(d) Amplitude oscillograms for (c) input and (d) output signals at $f=2.2335$ GHz. Note that SAW signal and EMW noise were successfully separated in the time domain using a microwave homodyne circuit. (e) Magnetization curve of Ni film. In the higher magnetic field region, the magnetization is decreased because of a diamagnetic signal from the ${\mathrm{LiNbO}}_3$ substrate. (f) Microwave absorption of Ni film at 280 K.

Figure 2

(a),(b) Absorption, $A\left(H\right)$, of SAWs propagating along (a) “$+k$” and (b) “$-k$” directions shown in Fig. 1 as a function of external magnetic field along $\varphi ={45}^{\circ }$. (c),(d) Relative change in phase velocity of SAW $\mathrm{\Delta }v/v_0$ propagating along (c) “$+k$” and (d) “$-k$” directions as a function of magnetic field along $\varphi ={45}^{\circ }$. The dashed lines emphasize the asymmetry of magnetic field dependence of absorption and the relative change in phase velocity. (e),(f) The nonreciprocities of (e) the absorption, $A\left(H\right)-A(-H)$, and (f) relative change in phase velocity, $\mathrm{\Delta }v/v_0\left(H\right)-\mathrm{\Delta }v/v_0(-H)$, for $+k$ and $-k$.

Figure 3

(a) Magnetic field dependence of SAW absorption $A\left(H\right)$ in several magnetic field directions. The dashed lines emphasize the asymmetry of the magnetic field dependence. (b) The SAW absorption $A\left(H\right)$ at ${\mu }_{0}H$ = 100 mT as a function of angle $\varphi$. (c) Averaged nonreciprocity of absorption $\overline{A(-H)-A\left(H\right)}$ as a function of angle $\varphi$. We averaged $A(-H)-A\left(H\right)$ in the field region of 40 mT $\le |{\mu }_{0}H|\le$ 150 mT. Solid lines are theoretical angle dependence (see text).