Pump-induced magnon anticrossing due to three-magnon splitting and confluence

We present a plausible mechanism for achieving a magnon-magnon level repulsion spectrum originating from the oscillation between the splitting and confluence in a three-magnon scattering process. When a magnetostatic mode on a YIG sphere is pumped by a microwave signal near the magnon resonance frequency with an increasing amplitude, the generated magnon condensate at half of the pumping frequency exerts a backaction to the original magnon mode. Such a strong nonlinear coupling manifests a striking feature of a ``bending effect'' of the magnetostatic mode spectra, akin to the anticrossing observed in a strongly coupled magnon-photon system.