Velocity Modulation of Surface Acoustic Waves via Einstein-de Haas Effect

Abstract

Einstein-de Haas (EdH) effect is the fundamental phenomenon that the microscopic spin angular momentum is converted to the angular momentum of mechanical rotation. A mechanical torque due to the EdH effect, the magnitude of which is proportional to the time derivative of the magnetization, is difficult to be detected, which keeps its practical application away. However, recent development of microfabrication technology has enabled to sensitively detect the tiny EdH torque using micro-fabricated mechanical resonators [1,2]. These findings show that the EdH effect can be utilized for the new principle of the mechanical torque generation in sub-micron scale device. Moreover, it was demonstrated that the ultrafast demagnetization due to the laser heating excited the transverse strain wave in a Fe film due to the EdH effect, where the timescale and conversion efficiency of the angular momentum transfer were quantitatively estimated [3].Rayleigh-type surface acoustic waves (RSAWs), the displacement of which oscillates elliptically, have been widely used to excite the spin waves in a ferromagnetic thin film via the magnetoelastic interaction [4]. Recently, as the phenomena based on the angular momentum conversion from the lattice rotation to the magnetization or electron spin, the gyromagnetic spin-wave excitation [5] and the spin current generation in a nonmagnetic metal with a weak spin-orbit coupling [6] were demonstrated.In this study, we demonstrate both acceleration and deceleration of RSAW velocity in the ferromagnetic (FM) film based on the EdH effect. When the spin-wave is gyromagnetically excited by RSAW propagation through the FM film, the EdH torque is generated in the FM lattice as the back action of the spin-wave resonance (SWR) (Fig. 1(a)). As shown in Fig. 1(a), the direction of EdH torque is opposite to the time derivative of the magnetization. We theoretically expect that the transverse velocity of RSAW can be modulated by the EdH torque, resulting in the phase change of RSAW propagation. In the experiment, we successfully observed the phase change of RSAW propagation, whose magnitude and variation were consistent with our analytical prediction.Figure 1(b) shows the schematical experimental setup for measuring the phase change of RSAW. A pair of inter-digital transduces (IDTs) consisting of Ti(3)/Au(30) is fabricated on a piezoelectric LiNbO3 substrate by the electron beam evaporation. The numbers in the parentheses indicate the layer thickness in nanometers. The width and space of the electrode of IDT are 550 nm. The Ni81Fe19 (NiFe) film with a lateral size of 400×400 μm2 is sputtered between a pair of IDTs. By applying a microwave with the fundamental frequency of RSAW excitation into one of IDTs, RSAWs are excited via the piezoelectric effect. The RSAWs propagating through the NiFe film are electrically detected by the other of IDTs using a vector network analyzer (VNA) as the inverse process of the RSAW excitation. Figures 2(a) and 2(b) show the reduced RSAW energy dissipation ΔPnorm and phase difference Δθ, respectively, as a function of external magnetic field swept in the direction parallel to the RSAW wave vector at the RSAW frequency of 1.75 GHz. Steep peaks appear at 4.6 and -4.0 mT in Fig. 2(a), showing that the spin-wave is excited because the values of the resonant field and resonant frequency are matched with the spin wave dispersion of a 20-nm-thick NiFe film. A bipolar change of Δθ is observed in the vicinity of the resonance field of spin-waves. From the angle between the applied external field and RSAW wave vector, it can be seen that the spin-wave is excited via gyromagnetic effect, not the magnetoelastic coupling [5]. The increase and decrease in Δθ can be explained by our analytical model consisting of the elastic motion equation with the EdH torque term. The maximum value of phase change Δθmax is -0.035 rad at 5.0 mT. This value is as large as that in case using the magnetoelastic coupling in a single Ni film [7]. In addition, the order of Δθmax is comparative to the value analytically obtained by assuming a loss-less conversion of the angular momentum. The consistency in Δθmax suggests that the EdH effect is robust in the angular translation from the magnetization to the lattice in the gigahertz regime. **