Magnonic quadrupole topological insulator in antiskyrmion crystals
- Date: Jun 3, 2020
- Time: 14:00
- Speaker: Prof. Daniel Loss
- Department of Physics, University of Basel
- Location: Zoom
- Host: Max Planck Institute of Microstructure Physics
Isolated antiskyrmions, a kind of skyrmion with opposite topological charge, as well as antiskyrmion crystals have been recently observed in acentric tetragonal Heusler compounds with D2d crystal symmetry . Furthermore, fractional antiskyrmions stabilized along the edges of the sample have also been observed in the same compounds. Our theoretical findings  reveal that the formation of fractional antiskyrmions plays a key role in the emergence of higher-order topological states of magnons, the quanta of spin waves. Higher-order topological phases of matter in a d-dimensional system are characterized by the presence of in-gap states that belong to boundaries of dimension lower than (d − 1), namely, to hinges or corners. A strict requirement for the realization of these topological states is the local preservation of the protecting symmetries at the corresponding higher- order boundaries. While the bosonic analogue of higher-order topological phases have been realized with phonons and photons, so far there have been only a few reports on magnons. This may be related to the fact that in the vicinity of sample boundaries, the magnetization field can get easily deformed, making it difficult to preserve crystalline symmetries.We predict that magnetic antiskyrmion crystals can realize a magnonic quadrupole topological insulator, whose hallmark signature are robust magnonic corner states. Tuning an applied magnetic field induces the self-assembly of fractional antiskyrmions along the sample edges, which, crucially, restore the protecting crystalline symmetries that allow the formation of magnonic corner states. Using the machinery of nested Wilson loops, adapted to magnonic systems supported by noncollinear magnetic textures, we demonstrate the quantization of the bulk quadrupole moment, edge dipole moments, and corner charges. We also discuss the engineering of magnonic corner states at select corners and inside the sample. Acentric tetragonal Heusler compounds  constitute an experimental platform to test our findings. Our work weaves concepts across the fields of magnetic antiskyrmions, magnonics, and higher-order topological quantum matter.
 A. Nayak, V. Kumar, T. Ma, P. Werner, E. Pippel, R. Sahoo, F. Damay, U. Roessler, C. Felser, and S. Parkin, Nature 548, 561 (2017).
 T. Hirosawa, S. Diaz, J. Klinovaja, and D. Loss, arXiv:2005.05884.
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