Prediction of Attractive Level Crossing via a Dissipative Mode

The new field of spin cavitronics focuses on the interaction between the magnon excitation of a magnetic element and the electromagnetic wave in a microwave cavity. In the strong interaction regime, such an interaction usually gives rise to the level anticrossing for the magnonic and the electromagnetic mode. Recently, the attractive level crossing has been observed, and it is explained by a non-Hermitian model Hamiltonian. However, the mechanism of such attractive coupling is still unclear. We reveal the secret by using a simple model with two harmonic oscillators coupled to a third oscillator with large dissipation. We further identify this dissipative third party as the invisible cavity mode with large leakage in cavity-magnon experiments. This understanding enables one to design dissipative coupling in all sorts of coupled systems.