Non-Hermitian Topological Magnonics

The chirality diverts thermal flow into the gate, demonstrating that the second law of thermodynamics cannot be violated. A model was set up to show this effect in the magnetic field, with the magnetic wire at X and the gate interacting with the magnetic field in a chiral manner when the magnetization is tuned. Complications arise due to the wire also being a magnet, but when the magnetization between the wire and the film is parallel, the coupling is not chiral. However, chirality appears when the magnetization is anti-parallel, leading to asymmetric transmission of spin waves as shown by S parameters S12 and S21.

The surprise effect occurs when the current is turned on, with the spin current injected into the gate depending on the direction of the film magnetization. By considering this spin injection, it is found that the second law of thermodynamics is not violated. This summary confirms that the second law of thermodynamics cannot be violated.