Topological phases have been explored in various fields in physics such asspintronics, photonics, liquid helium, correlated electron system andcold-atomic system. This leads to the recent foundation of emerging materialssuch as topological band insulators, topological photonic crystals andtopological superconductors/superfluid. In this paper, we propose a topologicalmagnonic crystal which provides protected chiral edge modes for magnetostaticspin waves. Based on a linearized Landau-Lifshitz equation, we show that amagnonic crystal with the dipolar interaction acquires spin-wave volume-modeband with non-zero Chern integer. We argue that such magnonic systems areaccompanied by the same integer numbers of chiral spin-wave edge modes within aband gap for the volume-mode bands. In these edge modes, the spin wavepropagates in a unidirectional manner without being scattered backward, whichimplements novel fault-tolerant spintronic devices.
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