Spin-Cherenkov radiation caused by a magnonic black or white hole
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A system of spin waves interacting with a spin-polarized current in a ferromagnetic material has recently been suggested as a black-hole-analogue. When a spin wave encounters such a black or white hole, it is partly reflected and partly transmitted, similar to a quantum mechanical particle encountering a potential step. We calculate the reflection and transmission coe fficients of this spin wave and use these coeffi cients to determine the Green's function that is needed to calculate how spin waves are emitted from imperfections at the horizon Cherenkov processes. This way we fi nd an expression for the wave function describing the Cherenkov radiation on both sides of the black or white hole. We discuss subtleties concerning current conservation in our results, and make suggestions for further research.