Fig. 2: Coherent propagation of magnon-polaritons and phonon-polaritons.

a The spatiotemporal waveform observed in the pump-probe imaging measurement. The colors in the heat map, ranging from red to blue, represent the ellipticity change of the circularly polarized probe pulse induced at each point of the sample. The black dashed frame delineates the region of the Fourier transform for (d). b, c shows the same waveform as (a) with different Fourier transform regions for (e, f), respectively. g–i are distributions in (d–f) integrated in the wavenumber direction within the region delimited by the red lines in (d–f). The red dashed line in (g–i) represents 0.56 THz. j represents the time evolution of the power of the components around the (anti-)crossing point. k illustrates the temperature dependence of the frequency, which exhibited anomalous behavior in (j), along with the eigenfrequency of the magnon \({\Psi }_{1}^{(1)}\) mode²⁸. The error bars are defined by the frequency resolutions.