The dissipative light-matter coupling can cause the attraction of two energy levels, i.e., level attraction, when competing with the coherent coupling that induces usual Rabi-level splitting. The level attraction shows attractive potential for topological information processing. However, the underlying microscopic quantum mechanism of dissipative coupling still remains unclear although the behavior has been understood to root in the non-Hermitian physics, which brings difficulties in quantifying and manipulating the competition between coherence and dissipation and thereby the flexible control of level attraction. Here, by coupling a magnon mode to a cavity supporting both standing and traveling waves, we identify the traveling-wave state to be responsible for magnon-photon dissipative coupling. By characterizing the radiative broadening of a magnon linewidth, we quantify the coherent and dissipative coupling strengths and their competition. The effective magnon-photon coupling strength, as a net result of competition, is analytically presented using quantum theory to show good agreement with measurements. In this manner, we extend the control dimension of level attraction by tuning field torque on magnetization or global cavity geometry. Our findings provide insights on engineered coupled harmonic oscillator systems.

A magnon, the collective excitation of ordered spins, can spontaneously radiate a travelling photon to an open system when decaying to the ground state. However, in contrast to electric dipoles, magnetic dipoles by magnons are more isolated from the environment, limiting their radiation and coherent communication with photons. The recent progresses in strongly coupled magnon-photon system have stimulated the manipulation of magnon radiation via tailoring the photon states. Here, by loading an yttrium iron garnet sphere in a one-dimensional waveguide cavity supporting both the travelling and standing photon modes, we demonstrate a significant magnon radiative damping that is proportional to the local density of photon states (LDOS). By modulating the magnitude and/or polarization of LDOS, we can flexibly tune the photon emission and magnon radiative damping. Our findings provide a way to manipulate photon emission from magnon radiation, which could help harness angular momentum generation, transfer, and storage in magnonics.