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In anisotropic media, the existence of leaky surface acoustic waves is a well-known phenomenon. Very recently, their analogs at the apex of an elastic silicon wedge have been found in experiments using laser-ultrasonics. In addition to a wedge-wave (WW) pulse with low speed, a pseudo-wedge wave (p-WW) pulse was found with a velocity higher than the velocity of shear bulk waves, propagating in the same direction. With a probe-beam-deflection technique, the propagation of the WW pulses was monitored on one of the faces of the wedge at variable distance from the apex. In this way, their depth structure and the leakage of the p-WW could be visualized directly. Calculations were carried out using a method based on a representation of the displacement field in Laguerre functions. This method has been validated by calculating the surface density of states in anisotropic media and comparing the results with those obtained from the surface Green's tensor. The approach has then been extended to the continuum of acoustic modes in infinite wedges with fixed wave-vector along the apex. These calculations confirmed the measured speeds of the WW and p-WW pulses.
Anisotropy has been found to play an important role for the existence of edge-localized acoustic modes as well as for nonlinear effects in rectangular edges. For a certain propagation geometry in silicon, the effective second-order nonlinearity for wedge waves was determined numerically from second-order and third-order elastic moduli and compared with the nonlinearity for Rayleigh waves propagating in the direction of the apex on one of the two surfaces forming the edge. In the presence of weak dispersion resulting from modifications of the wedge tip or coating of the adjacent surfaces, solitary pulses are predicted to exist and their shape was calculated.
We revisit the quantitative analysis of the ultrafast magnetoacoustic experiment in a freestanding nickel thin film by Kim and Bigot [J.-W. Kim and J.-Y. Bigot, Phys. Rev. B 95, 144422 (2017)] by applying our recently proposed approach of magnetic and acoustic eigenmode decomposition. We show that the application of our modeling to the analysis of time-resolved reflectivity measurements allows for the determination of amplitudes and lifetimes of standing perpendicular acoustic phonon resonances with unprecedented accuracy. The acoustic damping is found to scale as ∝ω2 for frequencies up to 80 GHz, and the peak amplitudes reach 10−3. The experimentally measured magnetization dynamics for different orientations of an external magnetic field agrees well with numerical solutions of magnetoelastically driven magnon harmonic oscillators. Symmetry-based selection rules for magnon-phonon interactions predicted by our modeling approach allow for the unambiguous discrimination between spatially uniform and nonuniform modes, as confirmed by comparing the resonantly enhanced magnetoelastic dynamics simultaneously measured on opposite sides of the film. Moreover, the separation of timescales for (early) rising and (late) decreasing precession amplitudes provide access to magnetic (Gilbert) and acoustic damping parameters in a single measurement.
While most ultrafast time-resolved optical pump-probe experiments in magnetic materials reveal the spatially homogeneous magnetization dynamics of ferromagnetic resonance (FMR), here we explore the magneto-elastic generation of GHz-to-THz frequency spin waves (exchange magnons). Using analytical magnon oscillator equations, we apply time-domain and frequency-domain approaches to quantify the results of ultrafast time-resolved optical pump-probe experiments in free-standing ferromagnetic thin films. Simulations show excellent agreement with the experiment, provide acoustic and magnetic (Gilbert) damping constants and highlight the role of symmetry-based selection rules in phonon-magnon interactions. The analysis is extended to hybrid multilayer structures to explore the limits of resonant phonon-magnon interactions up to THz frequencies.
The technique of laser ultrasonics perfectly meets the need for noncontact, noninvasive, nondestructive mechanical probing of nanometer- to millimeter-size samples. However, this technique is limited to the excitation of low-amplitude strains, below the threshold for optical damage of the sample. In the context of strain engineering of materials, alternative optical techniques enabling the excitation of high-amplitude strains in a nondestructive optical regime are needed. We introduce here a nondestructive method for laser-shock wave generation based on additive superposition of multiple laser-excited strain waves. This technique enables strain generation up to mechanical failure of a sample at pump laser fluences below optical ablation or melting thresholds. We demonstrate the ability to generate nonlinear surface acoustic waves (SAWs) in Nb-SrTiO3 substrates, with associated strains in the percent range and pressures up to 3 GPa at 1 kHz repetition rate and close to 10 GPa for several hundred shocks. This study paves the way for the investigation of a host of high-strain SAW-induced phenomena, including phase transitions in conventional and quantum materials, plasticity and a myriad of material failure modes, chemistry and other effects in bulk samples, thin layers, and two-dimensional materials.
Femtosecond (fs) time-resolved magneto-optics is applied to investigate laser-excited ultrafast dynamics of one-dimensional nickel gratings on fused silica and silicon substrates for a wide range of periodicities Λ = 400–1500 nm. Multiple surface acoustic modes with frequencies up to a few tens of GHz are generated. Nanoscale acoustic wavelengths Λ/n have been identified as nth-spatial harmonics of Rayleigh surface acoustic wave (SAW) and surface skimming longitudinal wave (SSLW), with acoustic frequencies and lifetimes being in agreement with theoretical calculations. Resonant magnetoelastic excitation of the ferromagnetic resonance (FMR) by SAW’s third spatial harmonic, and, most interestingly fingerprints of the parametric resonance at 1/2 SAW frequency have been observed. Numerical solutions of Landau–Lifshitz–Gilbert (LLG) equation magnetoelastically driven by complex polychromatic acoustic fields quantitatively reproduce all resonances at once. Thus, our results provide a solid experimental and theoretical base for a quantitative understanding of ultrafast fs-laser-driven magnetoacoustics and tailoring the magnetic-grating-based metasurfaces at the nanoscale.
Nonlinear acoustic waves are considered that have displacements localized at the tip of an elastic wedge. The evolution equation governing their propagation is discussed and compared with its analogues pertaining to nonlinear acoustic surface and bulk waves. Solitary wave solutions of the evolution equation have been determined numerically for the cases of two rectangular edges which may be viewed as generated by splitting a half-space, consisting of crystalline silicon, into two quarter-spaces. For these two geometries, the kernel in the nonlinear terms of the evolution equation has been calculated from the second-order and third-order elastic constants of silicon, and weak dispersion due to tip truncation has been considered. Solitary pulse shapes have been computed and collisions of solitary pulses have been simulated for various relative speeds of the two collision partners. Collision scenarios for the two wedge geometries were found to differ considerably. Special attention is paid to the peculiar interaction of two initially identical solitary pulses.
Surface acoustic waves are propagated toward the edge of an anisotropic elastic medium (a silicon crystal), which supports leaky waves with a high degree of localization at the tip of the edge. At an angle of incidence corresponding to phase matching with this leaky wedge wave, a sharp peak in the reflection coefficient of the surface wave was found. This anomalous reflection is associated with efficient excitation of the leaky wedge wave. In laser ultrasound experiments, surface acoustic wave pulses were excited and their reflection from the edge of the sample and their partial conversion into leaky wedge wave pulses was observed by optical probe-beam deflection. The reflection scenario and the pulse shapes of the surface and wedge-localized guided waves, including the evolution of the acoustic pulse traveling along the edge, have been confirmed in detail by numerical simulations.
Laser ultrasound was used to determine dispersion curves of surface acoustic waves on a Si (001) surface covered by AlScN films with a scandium content between 0 and 41%. By including off-symmetry directions for wavevectors, all five independent elastic constants of the film were extracted from the measurements. Results for their dependence on the Sc content are presented and compared to corresponding data in the literature, obtained by alternative experimental methods or by ab-initio calculations.
Among the various types of guided acoustic waves, acoustic wedge waves are non-diffractive and non-dispersive. Both properties make them susceptible to nonlinear effects. Investigations have recently been focused on effects of second-order nonlinearity in connection with anisotropy. The current status of these investigations is reviewed in the context of earlier work on nonlinear properties of two-dimensional guided acoustic waves, in particular surface waves. The role of weak dispersion, leading to solitary waves, is also discussed. For anti-symmetric flexural wedge waves propagating in isotropic media or in anisotropic media with reflection symmetry with respect to the wedge’s mid-plane, an evolution equation is derived that accounts for an effective third-order nonlinearity of acoustic wedge waves. For the kernel functions occurring in the nonlinear terms of this equation, expressions in terms of overlap integrals with Laguerre functions are provided, which allow for their quantitative numerical evaluation. First numerical results for the efficiency of third-harmonic generation of flexural wedge waves are presented.