  Unveiling intrinsic spins of propagating waves usually offers people a
fundamental understanding of the geometrical and topological properties of
waves from classical to quantum aspects. A great variety of research has shown
that transverse waves can possess non-trivial quantum spins and topology
without help of strong wave-matter interaction. However, until now we still
lack essential physical insights about the spin and topological nature of
longitudinal waves. Here, demonstrated by elastic waves we uncover unique
quantum spins for longitudinal waves and the mixed longitudinal-transverse
waves that play essential roles in topological spin-momentum locking. Based on
this quantum spin perspective, several abnormal phenomena beyond pure
transverse waves are attributed to the hybrid spin induced by mixed
longitudinal-transverse waves. The intrinsic hybrid spin reveals the complex
spin essence in elastic waves and advances our understanding about their
fundamental topological properties. We also show these spin-dependent phenomena
can be exploited to control the wave propagation, such as non-symmetric elastic
wave excitation by spin pairs, uni-directional Rayleigh wave and spin-selected
elastic wave routing. These findings are generally applicable for arbitrary
waves with longitudinal and transverse components.
