Non-Hermitian Topological Magnonics

The signal is a microwave transmission. Transmission S21 means exciting the left wire and detecting at the right one, while transmission S12 means exciting the right wire and detecting at the left one. With a magnetic bias, only transmission at S21 is observed, with no transmission at S12 due to dipolar interaction. The wire only interacts with spin waves propagating to the right, meaning excitation of the left wire will excite the right wire mediated by the spin wave. This indicates that the left wire can influence the right wire, but not vice versa, showing a chiral interaction between the two wires.

If an area of magnetic wire is fabricated on top of the magnetic field, chiral coupling is observed with different coupling constants γ R connecting the left wire to the right wire and γ L connecting the right wire to the left wire. This results in a current in the hopping right, leading to the construction of a hopping model similar to the Hatano-Nelson model with long-range coupling between the two wires.