Topological magnonic dislocation modes

Spin fluctuations in two-dimensional ferromagnets in the presence of crystalline lattice dislocations are investigated. We show the existence of topologically protected nonpropagative modes that localize at dislocations. These in-gap states, termed magnonic dislocation modes, are characterized by the ${Z}_{2}$ topological invariant that derives from broken parity symmetry induced by sublattice magnetic anisotropy. We uncover that bulk topology existing in the perfect crystal is robust under the influence of lattice defects, which is monitored by the real-space Bott index. It is also revealed that the topology of magnonic dislocation modes remains unaffected when bulk topology becomes trivial and is remarkably resilient against magnetic disorder. Our findings point to the intriguing relationship between topological lattice defects and the spectrum of topological spin excitations.