An induced nonlinear phase shift of spin waves excited in an yttrium iron garnet film waveguide has been studied. Experiments were performed with two microwave magnonic signals, being operating and pumping waves, co-propagated at different frequencies. The results show that a nonlinear phase shift up to 180° for the low-power operating wave is induced when increasing the pump-wave power. A theory describing the induced nonlinear phase shift is developed taking into account four-wave parametric coupling and nonlinear damping of two waves. The observed phenomenon paves the way to elaborate different types of nonlinear magnonic logic circuits.
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