  Anticrossing behavior between magnons in a non-collinear chiral magnet
Cu$_2$OSeO$_3$ and a two-mode X-band microwave resonator was studied in the
temperature range 5-100K. In the field-induced ferrimagnetic phase, we observed
a strong coupling regime between magnons and two microwave cavity modes with a
cooperativity reaching 3600. In the conical phase, cavity modes are
dispersively coupled to a fundamental helimagnon mode, and we demonstrate that
the magnetic phase diagram of Cu$_2$OSeO$_3$ can be reconstructed from the
measurements of the cavity resonance frequency. In the helical phase, a
hybridized state of a higher-order helimagnon mode and a cavity mode - a
helimagnon polariton - was found. Our results reveal a new class of magnetic
systems where strong coupling of microwave photons to non-trivial spin textures
can be observed.
