Fig. 3: Enhanced magnon–magnon coupling strength.

a Enhancement of the anticrossing gap by by rotating the external magnetic field by an oblique angle Θ along the out-of-plane direction at \(45^\circ\) to the in-plane principal a-axis as indicated. b \(\Theta\) dependence of the coupling strength \({g}_{c}\) and the dissipation rates for the upper and lower magnonic branches, \({\kappa }_{U}\) and \({\kappa }_{L}\) derived from the frequency-field dependence of resonance spectra presented in (c). The dotted red line is the fitted curve for the coupling strength following a quadratic behavior. The insets in (c) highlight the resonance spectra under an adjusted color scale, showing the increased DMI-induced nonzero gap, \({f}_{g}\) of the ‘dark’ mode as \(\Theta\) increases.