  Spin and orbital angular momenta are fundamental physical characteristics
described by polarization and spatial degrees of freedom, respectively.
Polarization is a feature of vector fields while spatial phase gradient
determines the orbital angular momentum ubiquitous to any scalar field. Common
wisdom treats these two degrees of freedom as distinct and independent
principles to manipulate wave propagations. Here, we demonstrate their synergy.
This is achieved by introducing two orthogonal $p$-orbitals as eigenbases,
whose spatial modal features are exploited to generate orbital angular momenta
and the associated orbital orientations provide means to simultaneously
manipulate polarizations. Through periodic modulation and directional coupling,
we realize a full cyclic evolution of the synchronized and synergized
spin-orbital angular momenta. Remarkably, this evolution acquires a nontrivial
geometric phase, leading to its representation on a M\"obius strip.
Experimentally, an acoustic cavity array is designed, whose dipole resonances
precisely mimic the $p$-orbitals. The acoustic waves, uniquely, see the
pressure (scalar) field as a spatial feature and carry an intrinsic
polarization defined by the velocity (vector) field, serving as an ideal
platform to observe the synergy of spin and orbital angular momenta. Based on
such a property, we further showcase a spin-orbital-Hall effect, highlighting
the intricate locking of handedness, directionality, spin density and spatial
mode profile. Our study unveils a fundamental connection between spin and
orbital angular momenta, promising avenues for novel applications in
information coding and high-capacity communications.
