Proposal to Observe Transverse Sound in Normal Liquid \(^3\)He in Aerogel

In the Fermi liquid metallic state, a static local magnetic moment is induced on the application of a circularly polarized electromagnetic wave, via the inverse Faraday effect (IFE). The direction of this moment is along the direction of propagation of light, and the magnitude of the moment depends on the frequency of light, the temperature and various material parameters characteristic of the metal. I propose an analogous effect in the Fermi liquid state of \(^3\) ${}^3$ He. A static circulating current is induced when liquid \(^3\) ${}^3$ He is driven by a circularly polarized transverse acoustic wave. For liquid \(^3\) ${}^3$ He filled into aerogel, the coupled system supports a low-attenuation transverse sound mode. I estimate the magnitude of induced circulating currents for this system and find that these are within the range of experimental measurement in the low-attenuation regime. The axis of circulation is along the direction of propagation of the acoustic wave. I propose this analogue of the inverse Faraday effect as a scheme to experimentally demonstrate the propagation of transverse sound in \(^3\) ${}^3$ He-aerogel.