EmergentU(1) gauge field for antiferromagnetic magnons from phonon Poincaré skyrmions

It is shown that a spatially structured chiral phonon field acts on the magnon doublet of a collinear antiferromagnet as aBerry connection, with the emergent magnetic field equal to the topological charge density of the phonon Stokes vector on its Poincaré sphere. Provided the projected coupling tensor is nonsingular and adiabatic following holds throughout the full Stokes texture, each phonon Poincaré skyrmion contributes exactly one flux quantumto the magnon. Applied to CoTiO, the equilibriumsymmetry restricts the phonon-magnon coupling to the axial channel(Semenoff mass), giving an axial adiabatic lengthm (). The circular phonon drive breaksand makes in-plane coupling symmetry-allowed; the anisotropy ratiocontrols the full-texture adiabatic length. The Semenoff mass opens the Dirac gap but, being valley-symmetric, closes the quantum anomalous Hall channel. A real-space Drude Hall mechanism becomes accessible in the full-Poincaré regime: under favorable conditions (m,meV,,), the emergent field deflects magnon wave packets, yieldingmW (Km)at 50 K, marginally above the detection floor; the response is suppressed by a Landau-Zener flux-capture factorthat vanishes as. The perturbative estimate for CoTiOgives, placing it below the Drude-Hall detection threshold unless non-perturbative channels enhance the transverse driven coupling. The magnon interferometric phase difference between two open paths straddling a phonon skyrmion provides a phase-sensitive detection route if full-texture adiabaticity is satisfied.