Spin-Hall-Like Magnon Transport in a Synthetic Antiferromagnetic Skyrmion Lattice

We investigate spin-Hall-like magnon edge transport in a synthetic antiferromagnetic skyrmion lattice composed of two antiferromagnetically coupled skyrmion lattice layers with opposite magnetic textures. Based on a relaxed bilayer texture from micromagnetic simulations, we construct the bosonic Bogoliubov-de Gennes Hamiltonian within linear spin-wave theory and calculate the bulk and strip magnon spectrum. We find counterpropagating in-gap edge modes with opposite layer polarization, whose layer-resolved propagation is further confirmed by dynamical micromagnetic simulations. A symmetry analysis shows that the fully coupled system lacks the pseudo-time-reversal symmetry required for a genuine bosonic Z2 topological phase. Thus, the observed edge modes are not Z2-protected helical magnon edge states, but layer-polarized, spin-Hall-like modes originating from the opposite Hall tendencies of the two skyrmion lattice layers. These results establish synthetic antiferromagnetic skyrmion lattices as a platform for spin-Hall-like magnon transport beyond a strict bosonic Z2 classification.