Magnonics of time-varying media: Giant amplification via phase-transition-driven temporal interfaces

Gilbert damping-the primary obstacle limiting spin-wave propagation in magnonic devices-can be transformed from an adversary into an asset. Here we demonstrate 175-fold spin-wave amplitude amplification in ultrathin films with perpendicular magnetic anisotropy at temporal interfaces associated with a field-driven transition between a uniform in-plane state and a stripe-domain state, exceeding existing parametric and spin-torque schemes (10-50-fold) without a continuous power supply. When the in-plane bias field is swept through a critical value in the presence of finite Gilbert damping, the spin-wave dispersion undergoes dramatic softening, and the eigenfrequency crosses zero and acquires a positive imaginary part that drives exponential growth. We identify this as a damping-induced instability operating near an exceptional point-a non-Hermitian degeneracy where, counterintuitively, increased Gilbert damping enhances amplification. This mechanism exploits ingredients specific to these magnetic films: the interplay of Gilbert damping, Dzyaloshinskii-Moriya-interaction-induced nonreciprocity, and field-driven phase transitions-a combination that, to our knowledge, has no direct counterpart in photonic or acoustic time-varying platforms. Our analytical framework provides explicit design rules, while micromagnetic simulations capture the full nonlinear dynamics, including stripe-domain formation. This work establishes temporal magnonics as a new paradigm for reconfigurable, lithography-free spin-wave control.