Theory for phonon pumping by magnonic spin currents

In recent years several experimental observations and theoretical predictions of unique phenomena involving the interplay between spin currents and the coupled magnetization-elastic dynamics have invigorated the field of spintronics. One important experiment reported several years ago showed that elastic waves can produce spin pumping, that is, generation of spin currents in a metallic film in contact with a ferromagnetic material. Very recently the Onsager reciprocal of this effect has been observed in samples made of a film of the insulating ferrimagnet yttrium iron garnet in contact with a platinum strip with nanoscopic silver particles that is known to exhibit a giant spin Hall effect. By passing an electric current through the metallic strip, the spin current generated by the spin Hall effect produces a large magnonic spin current that excites phonons with microwave frequency, observed by Brillouin light scattering. Here we show that these experiments are explained by a theory based on a process in which one magnon in the spin current creates one phonon and another magnon, with conservation of energy and momentum. The theoretical value of the critical charge current in the metallic strip necessary to drive phonons and the values of the phonon frequencies are in good agreement with the values measured experimentally.