We experimentally identify coherent spin pumping in the magnon-magnon hybrid modes of permalloy/yttrium iron garnet (Py/YIG) bilayers. Using broadband ferromagnetic resonance, an avoided crossing is observed between the uniform mode of Py and the spin wave mode of YIG due to the fieldlike interfacial exchange coupling. We also identify additional linewidth suppression and enhancement for the in-phase and out-of-phase hybrid modes, respectively, textcolor{black}{which can be interpreted as concerted dampinglike torque from spin pumping}. Our analysis predicts inverse proportionality of both fieldlike and dampinglike torques to the square root of the Py thickness, which quantitatively agrees with experiments.
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