Strong coupling between magnons and cavity photons was studied extensively for quantum electrodynamics in the past few years. Recently, the strong magnon-magnon coupling between adjacent layers in magnetic multilayers has been reported. However, the strongly coupled magnons confined in a single nanomagnet remains to be revealed. Here, we report the interaction between different magnon modes in a single magnonic cavity. The intermodel coupling between edge and center magnon modes in the strong coupling regime was approached with a maximum coupling strength of 0.494 GHz and cooperativity of 60.1 with a damping of 1X10-3. Furthermore, it is found that the coupling strength is highly dependent on the geometric parameters of the magnonic cavity. Our findings could greatly enrich the still evolving field of quantum magnonics.
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