Fig. 3: The mode hybridization induced by magnon–phonon coupling.

a Transmission amplitude \({S}_{21}\) measured on Sample Z15 as a function of magnetic field applied in the direction of \({{{{{\rm{\theta }}}}}}=54^\circ\). An anticrossing-like feature is observed between the magnon mode and the phonon mode. The field-independent phonon mode is attributed to the high-order (\({k}_{3}\)) excitation from the CPW antenna. The white arrow marks the magnon–phonon hybridized mode (mode X) with strong intensity. The data displayed in the color map is the imaginary part of the transmission spectra, and the color bar denotes the amplitude of the imaginary part, which is in arbitrary units. The data are treated with a background subtraction of the reference spectrum at zero field. b Simulation results on the hybridization of the magnon and phonon dispersions with a fixed applied field of 100 mT at \({{{{{\rm{\theta }}}}}}=45^\circ\). The blue and yellow lines stand for the phonon and magnon branches, respectively. The zoom-in dispersion around the crossing point is shown in the inset where the green color suggests the magnon–phonon hybridization. The wavevector (\(k\)) excitation profile (red dashed line) is calculated by Fourier transformation of the CPW antenna. The amplitude (scales on the right) is normalized to that of the \({k}_{1}\) excitation. The green circle (at \({k}_{3}\) excitation) indicates the hybridization off the crossing point that may lead to the anticrossing-like behavior in (a).