Intrinsic spin of elastic waves.

Unveiling spins of physical systems usually gives people a fundamental understanding of the geometrical properties of waves from classical to quantum aspects. A great variety of research has shown that transverse waves can possess nontrivial spins and spin-related properties naturally. However, until now, we still lack essential physical insights about the spin nature of longitudinal waves. Here, demonstrated by elastic waves, we uncover spins for longitudinal waves and the mixed longitudinal-transverse waves that play essential roles in spin-momentum locking. Based on this spin perspective, several abnormal phenomena beyond pure transverse waves are attributed to the hybrid spin induced by mixed longitudinal-transverse waves. The unique hybrid spin reveals the complex spin essence in elastic waves and advances our understanding about their fundamental geometrical properties. We also show that these spin-dependent phenomena can be exploited to control the wave propagation, such as nonsymmetric elastic wave excitation by spin pairs, a unidirectional Rayleigh wave, and spin-selected elastic wave routing. These findings are generally applicable for wave cases with longitudinal and transverse components.