The pump-induced magnon mode (PIM) exhibits strong nonlinear coupling with the uniform Kittel mode (KM), offering a novel paradigm for cavity-free hybrid magnonics. However, the fundamental dynamic properties of the PIM, particularly its evolution under varying external magnetic fields, remain largely unexplored. Here, we systematically investigate the magnetic field dependence of the PIM-KM coupling in yttrium iron garnet (YIG) samples. Using the condition of exceptional points, we extract the PIM excitation threshold at different magnetic fields. Through comparative transmission measurements on a single-crystal YIG sphere and an in-plane magnetized YIG thin film, we quantify the field-driven evolution of the effective nonlinear coupling coefficient ($a_0$). We observe distinct field-dependent behaviors of $a_0$ in the two geometries. The evolution of $a_0$ shows a qualitative correlation with the field-dependent KM linewidth, suggesting that magnetic dissipation plays an important role in PIM dynamics.

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• Magnons
• Spin dynamics
• Magnetic insulators
• Magnetic thin films
• Nonlinear waves
• Ferromagnetic resonance
• Holstein-Primakoff method
• Landau-Lifschitz-Gilbert equation