Realizing novel topological states in magnonic systems unlocks robust, low-power spin-wave devices. In this paper, we show that incorporating left-handed spin waves (antimagnons) fundamentally reorganizes band topology, and enables tunable spin-wave coupling and chirality. We proposed a two-dimensional Su-Schrieffer-Heeger-like model, the 2D-SSH4 chain, where dipolar interactions between magnons and antimagnons generate topological bands with nonzero Chern numbers. This framework explains the origin of topological surface states in ferromagnetic multilayers and shows they share the same topological origin as classic magnetostatic surface spin waves. Our model also offers a straightforward framework for designing more complex magnetic multilayers connected by dipolar interactions, such as antiferromagnetic/ferromagnetic multilayers. In these dipolar-coupled multilayers, both coherent and dissipative interlayer spin-wave couplings, together with the layer-resolved chirality, are tunable via external magnetic fields and spin torques. Our results provide a practical platform for topological magnonics, enabling control of magnon chirality and coupling in future devices.

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• Dipolar interaction
• Magnons
• Magnetic systems
• Su-Schrieffer-Heeger model