Doctoral Thesis: Topological magnon materials and transverse magnon
transport

This thesis reports on a theoretical study of fundamental topological properties of magnons. Magnon spectra of two- and three-dimensional magnets are characterized by topological invariants calculated within the framework of linear spin-wave theory. Magnonic counterparts of electronic topological Chern insulators, Weyl semimetals, and nodal-line semimetals are identified. They respectively host topologically protected edge magnons, magnon arcs, and magnon drumhead surface states. The nontrivial topology of magnon spectra leads to transverse transport, e.g., a thermal magnon Hall effect. To complement the results obtained in the limit of non-interacting magnons, a method for the computation of the magnon transport properties is developed, which is based on classical atomistic spin dynamics simulations and the Kubo formula. It is applied to the topological magnon insulator Cu(1,3-benzenedicarboxylate) and to skyrmion crystals that exhibit the topological magnon Hall effect.

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