Ultrasonic attenuation in nickel and iron at 9.4 GHz

Abstract

Sound transmission experiments on single-crystal and polycrystalline nickel and iron samples 10–20 μm thick demonstrate an amplitude dependence on conductivity indicative of an electron damping effect. The samples form part of the common wall between two microwave cavities. Transverse sound waves were generated via magnetostriction with a static magnetic field perpendicular to the sample surface and perpendicular to the incident microwave magnetic field. Longitudinal sound waves were generated by direct electromagnetic excitation with a static magnetic field parallel to the sample surface and parallel to the incident microwave magnetic field. An exponential dependence of transmitted sound amplitude versus sample conductivity was observed as the temperature was varied. This exponential amplitude dependence on conductivity is what is expected from theories for sound wave attenuation in metals. For our samples this attenuation coefficient is of the order of 0.5 dB/μm. At low temperatures, where the product of the sound propagation constant and the electron mean free path approaches and exceeds unity, a decrease in the sound amplitude dependence on conductivity was observed, also in agreement with theory.

Energy-efficient spin injector into semiconductors driven by elastic waves

“…At the same time, it was shown experimentally that surface acoustic waves (SAWs) can propagate in a Ni film over the distance of several millimeters [41]. This absence of significant damping observed for the studied SAWs with frequencies not exceeding 500 MHz is very different from the results of Homer et al [50], who reported the decay length L dec ≈ 5.8 µm for the longitudinal wave with the frequency of 9.4 GHz in Ni. The reason for such a difference most probably lies in a drastic reduction of damping, which should happen when the frequency of the elastic wave changes from about 10 GHz to several hundreds of MHz.…”

“…The reason for such a difference most probably lies in a drastic reduction of damping, which should happen when the frequency of the elastic wave changes from about 10 GHz to several hundreds of MHz. As for the damping of transverse elastic waves in Ni, our results show that the magnetic damping of elastic waves (L dec ≈ 19 µm) could be stronger than the damping of electronic origin (measured L dec ≈ 29 µm [50]) at wave frequencies around 10 GHz.…”

“…These waves are characterized by oscillating strains ε ij (x, t) different from the strain ε xx (x, t) or ε xz (x, t) in the primary driving wave, and they were not reported in the previous work on the modeling of magnetization dynamics induced by longitudinal elastic waves in Ni [43]. The magnetoelastic feedback also influences the driving elastic wave, leading to a gradual reduction of its amplitude during the propagation in Ni, which adds to the "acoustic" decay caused by the wave attenuation of electronic origin [50]. At the considered wave frequencies ν ≈ 10 GHz, the decay resulting from the energy transfer to the magnetic subsystem is stronger than the acoustic decay for the transverse waves but small for longitudinal ones.…”

“…Second, in Sec. IV we consider Ni/GaAs bilayers comprising Ni films much thinner than the decay lengths of longitudinal and transverse elastic waves in Ni, which are measured to be 5.8 and 29 µm respectively at the relevant frequency of 9.4 GHz [50]. Micromagnetoelastic simulations were performed with the aid of a homemade software operating with a finite ensemble of nanoscale computational cells.…”

Viscoelastic measurement techniques

“…Ultrasonic measurements are commonly performed between 1 and 20 MHz, but it is possible by special methods to go to 1 GHz and beyond. 61,62 The electrical wave forms are usually bursts of several cycles at the frequency of interest. The bursts should be short enough in time to discriminate multiple echoes.…”