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Gain-driven magnon-polariton dynamics in the ultrastrong coupling regime: Effective circuit approach for coherence versus nonlinearity

We theoretically study the dynamics of gain-driven magnon-polaritons (MPs), which characterizes auto-oscillation of MPs, across the strong coupling (SC) and ultrastrong coupling (USC) regimes. Taking into account the magnon dynamics via the magnetic flux, we present an effective circuit model of gain-driven MPs, which allows to manipulate the coupling strength of MPs by tuning the size of a ferromagnet and incorporates the self-Kerr nonlinearity of magnons due to the shape magnetic anisotropy. In the SC regime, we find that the self-Kerr nonlinearity generates a frequency shift and reduces the coherent magnon-photon coupling. In contrast, in the USC regime, we find that the coherent magnon-photon coupling not only overcomes the self-Kerr nonlinearity but also effectively couples to gain via the imaginary part of complex eigenfrequencies, resulting in magnon-like auto-oscillations. Subsequently, the USC enables one to widely tune the auto-oscillation frequency by means of an external magnetic field. These findings indicate that there is a trade-off relation between the coupling strength of MPs and the self-Kerr nonlinearity of magnons. This work is attributed to understanding of the interplay between gain-loss and USC in nonlinear polariton dynamics, offering a novel principle for frequency tunable maser-like devices based on gain-driven MPs.