# Microscopic origin of level attraction for a coupled magnon-photon system in a microwave cavity

## TL;DR

This paper explores the microscopic mechanisms behind level attraction in a coupled magnon-photon system within a microwave cavity, emphasizing the role of diamagnetic responses and specific coupling effects.

## Contribution

It introduces a microscopic framework based on electromagnetic response functions to explain level attraction, highlighting diamagnetic effects and novel coupling mechanisms.

## Key findings

- Diamagnetic response functions enable attractive mode interactions.
- Magneto-optical coupling proportional to photon number contributes to level attraction.
- Aharonov-Casher effect provides a dual mechanism dependent on magnon number.

## Abstract

We discuss various microscopic mechanisms for level attraction in a hybridized magnon-photon system of a ferromagnet in a microwave cavity. The discussion is based upon the electromagnetic theory of continuous media where the effects of the internal magnetization dynamics of the ferromagnet are described using dynamical response functions. This approach is in agreement with quantized multi-oscillator models of coupled photon-magnon dynamics. We demonstrate that to provide the attractive interaction between the modes, the effective response functions should be diamagnetic. Magneto-optical coupling is found to be one mechanism for the effective diamagnetic response, which is proportional to photon number. A dual mechanism based on the Aharonov-Casher effect is also highlighted, which is instead dependent on magnon number.