Recent studies show that an engineered sound field can possess a locally rotational velocity field v that may be regarded as acoustic spin 19, 20, 21, similar to electric spin deriving from the local rotation of electric field. This is because although longitudinal waves such as airborne sound can carry OAM 14, 15, 16, 17, 18, they are spin-0 in nature. SOIs are unique to transverse waves such as light and are absent for longitudinal waves. The couplings between spin and OAM, referred to as spin–orbit interactions (SOIs), can give rise to intriguing phenomena and applications in optics 2, 3, 4, 5, 6, 7, 8, such as photonic spin-Hall effect 9, 10, 11 and spin-dependent vortex generation 12, 13. OAM originates from the spatial phase gradient (scalar degree of freedom) of waves and manifests as a helical wave front 1. Spin is associated with circular polarization (vector degrees of freedom) of waves and is characterized by the local rotation of a vector field. Spin and orbital angular momentum (OAM) are intrinsic properties of classical waves. The acoustic SOIs can provide new perspectives and functionalities for sound manipulations beyond the conventional scalar degree of freedom and may open an avenue to the development of spin-orbit acoustics. In addition, we show that the scattering of the transverse sound by a dipole particle can generate spin-dependent acoustic vortices via the geometric phase effect. We demonstrate that acoustic activity of the metamaterial can induce coupling between the spin and linear crystal momentum k, which leads to negative refraction of the transverse sound. This enables the realization of acoustic SOIs with rich phenomena beyond those in conventional acoustic systems. Here, we theoretically and experimentally demonstrate that airborne sound can possess artificial transversality in an acoustic micropolar metamaterial and thus carry both spin and orbital angular momentum. However, it is counterintuitive that SOIs can exist for sound, which is a longitudinal wave that carries no intrinsic spin. Spin-orbit interactions (SOIs) endow light with intriguing properties and applications such as photonic spin-Hall effects and spin-dependent vortex generations.
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