Berry curvature for coupled waves of magnons and electromagnetic waves

In this paper, we introduce Berry curvature, topological Chern number and topological chiral edge mode, that emerge from a hybridization between magnon and electromagnetic wave in a ferromagnet insulator. By focusing on the energy conservation, we first reformulate the Landau-Lifshitz-Maxwell equation into a Hermitian eigenvalue equation. From the eigenvalue equation, we define the Berry curvature of the magnon-photon coupled waves. We show that the Berry curvature thus introduced shows a prominent peak around a hybridization point between magnon mode and photon mode, and a massive hybrid mode takes a non-zero Chern number ($\pm 1$) due to the magnon-photon coupling. In accordance with the non-zero Chern number, the topological edge modes emerge inside the hybridization gap at a domain wall between two ferromagnetic insulators with opposite magnetizations.