Emergent U (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 a U(1) Berry connection, with the emergent magnetic field equal to the topological charge density of the phonon Stokes vector on its Poincar´e sphere. Provided the projected coupling tensor is nonsingular and adiabatic following holds throughout the full Stokes texture, each phonon Poincar´e skyrmion contributes exactly one flux quantum Φ mag 0 =2π to the magnon. Applied to CoTiO 3 , the equilibrium PT symmetry restricts the phonon.magnon coupling to the axial channel S 3 σ z (Semenoff mass), giving an axial adiabatic length L (z) ad ≈0.007/η μm (η ∈[10 -2 , 1]). The circular phonon drive breaks PT and makes in-plane coupling symmetry-allowed; the anisotropy ratio r Λ = λ′ ⊥ /λ z controls the full-texture adiabatic length L full ad = L (z) ad /r Λ . 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-Poincar´e regime: under favorable conditions (L sk ∼1 μm, Γ∼0.1 meV, r Λ ≧0.15, η∼1), the emergent field deflects magnon wave packets, yielding κ xy ∼0.6 mW/(K·m) at 50 K, marginally above the detection floor; the response is suppressed by a Landau.Zener flux-capture factor F(r Λ , ξ) that vanishes as r Λ →0. The perturbative estimate for CoTiO 3 gives r Λ ∼ 10 -3 -10 -2 , placing it below the Drude-Hall detection threshold unless nonperturbative 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.