  We report dissipative magnon-photon coupling caused by cavity Lenz effect,
where the magnons in a magnet induce a rf current in the cavity, leading to a
cavity back action that impedes the magnetization dynamics. This effect is
revealed in our experiment as level attraction with a coalescence of hybridized
magnon-photon modes, which is distinctly different from level repulsion with
mode anticrossing caused by coherent magnon-photon coupling. We develop a
method to control the in- terpolation of coherent and dissipative magnon-photon
coupling, and observe a matching condition where the two effects cancel. Our
work sheds light on the so-far hidden side of magnon-photon coupling, opening a
new avenue for controlling and utilizing light-matter interactions.
