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Spin dynamical phase and anti-resonance in a strongly coupled magnon-photon system

We experimentally studied a strongly coupled magnon-photon system via microwave transmission measurements. An anti-resonance, i.e. the suppression of the microwave transmission, is observed, indicating a relative phase change between the magnon response and the driving microwave field. We show that this anti-resonance feature can be used to interpret the phase evolution of the coupled magnon-microwave system and apply this technique to reveal the phase evolution of magnon dark modes. Our work provides a standard procedure for the phase analysis of strongly coupled systems, enabling the phase characterization of each subsystem, and can be generally applied to other strongly coupled systems.