Fig. 2: Experimental confirmation of zero and negative damping in a non-Hermitian sample.

a Line profiles of |S21| and |S12| against frequency (ω/2π) at specific magnetic fields. Narrow linewidths marked in red indicate zero damping, while the blue-colored intermediate region denotes negative damping (anti-damping). b Analysis of the photon-magnon hybrid modes: The top panel shows the refractive index, the middle panel details real eigenvalues, and the bottom panel focuses on imaginary eigenvalues for \({\kappa }_{c}=0.0296+0.0088i\) (left) and \({{\kappa }^{*}}_{c}=0.0296-0.0088i\) (right), according to Eq. 1. Solid and dashed lines trace the eigenvalues of the higher- and lower-branch modes, respectively. Red dash lines denote zero linewidths, and the blue area represents regions of negative linewidth (indicative of negative damping). The vertical lines at field strengths, denoted as \({H}_{-}\) and \({H}_{+}\), highlight the points of zero damping and delineate the range within which NRI is observable.