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Honeycomb Lattice;Non-Hermitian;Spin Waves


Jeffrey Rau



Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


In this thesis, we study a simple model for a ferromagnet starting with Heisenberg exchange interaction including the effects of dissipation. Gilbert damping is consid- ered and generalized from an on-site term to include non-local damping interactions between neighbouring spins. The strength of the damping interaction between neigh- bours can be tuned individually to provide the freedom to change the parameters of the system and explore the range of possible non-Hermitian behaviours. We consider the example of a honeycomb lattice ferromagnet featuring Dirac cones and two sub- lattices and analyse the resulting spectra and eigenstates. Under periodic boundary conditions, we find the Dirac magnons that are present in the Hermitian case are split into pairs of exceptional points connected by nodal lines. Open boundary condi- tions are then studied, including cases with a periodic boundary along one direction and an open boundary along the other, to explore the presence of the non-Hermitian skin effect in this model. We find the spectra under open boundary conditions differ substantially from that of periodic boundary conditions and the eigenstates are often localized on the boundary. Lastly, we discuss open questions and future directions for exploring non-Hermitian physics in magnetic systems.