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Topologically protected magnon surface states are highly desirable as an ideal platform to engineer low-dissipation spintronics devices. However, theoretical prediction of topological magnons in strongly correlated materials proves to be challenging because the ab initio density functional theory calculations fail to reliably predict magnetic interactions in correlated materials. Here, we present a symmetry-based approach, which predicts topological magnons in magnetically ordered crystals, upon applying external perturbations such as magnetic/electric fields and/or mechanical strains. We apply this approach to carry out an efficient search for magnetic materials in the Bilbao Crystallographic Server, where, among 198 compounds with an over 300-K transition temperature, we identify 12 magnetic insulators that support room-temperature topological magnons. They feature Weyl magnons with surface magnon arcs and magnon axion insulators with either chiral surface or hinge magnon modes, offering a route to realize energy-efficient devices based on protected surface magnons.

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