RESUMEN
Controlled interaction between localized and delocalized solid-state spin systems offers a compelling platform for on-chip quantum information processing with quantum spintronics. Hybrid quantum systems (HQSs) of localized nitrogen-vacancy (NV) centers in diamond and delocalized magnon modes in ferrimagnets-systems with naturally commensurate energies-have recently attracted significant attention, especially for interconnecting isolated spin qubits at length-scales far beyond those set by the dipolar coupling. However, despite extensive theoretical efforts, there is a lack of experimental characterization of the magnon-mediated interaction between NV centers, which is necessary to develop such hybrid quantum architectures. Here, we experimentally determine the magnon-mediated NV-NV coupling from the magnon-induced self-energy of NV centers. Our results are quantitatively consistent with a model in which the NV center is coupled to magnons by dipolar interactions. This work provides a versatile tool to characterize HQSs in the absence of strong coupling, informing future efforts to engineer entangled solid-state systems.