  By using the stripline Microwave Vector Network Analyzer Ferromagnetic
Resonance and Pulsed Inductive Microwave Magnetometry spectroscopy techniques,
we study a strong coupling regime of magnons to microwave photons in the planar
geometry of a lithographically formed split-ring resonator (SRR) loaded by a
single-crystal epitaxial yttrium-iron garnet (YIG) film. Strong anti-crossing
of the photon modes of SRR and of the magnon modes of the YIG film is observed
in the applied-magnetic-field resolved measurements. The coupling strength
extracted from the experimental data reaches 9 percent at 3 GHz.
  Theoretically, we propose an equivalent circuit model of an SRR loaded by a
magnetic film. This model follows from the results of our numerical simulations
of the microwave field structure of the SRR and of the magnetization dynamics
in the YIG film driven by the microwave currents in the SRR. The equivalent
circuit model is in good agreement with the experiment. It provides a simple
physical explanation of the process of mode anti-crossing.
  Our findings are important for future applications in microwave quantum
photonic devices as well as in magnetically tunable metamaterials exploiting
the strong coupling of magnons to microwave photons.
