Effect of magnetic hysteresis on magnon-magnon coupling induced by interlayer Dzyaloshinskii-Moriya interaction

Based on the Smit-Suhl formula, we propose a universal approach for solving the magnon-magnon coupling problem in bilayer coupled systems (e.g., antiferromagnets). This method requires only the energy expression, enabling the automatic derivation of analytical expressions for the eigenmatrix elements via symbolic computation, eliminating the need for tedious manual calculations. Using this approach, we investigate the impact of magnetic hysteresis on magnon-magnon coupling in a system with interlayer Dzyaloshinskii-Moriya interaction (DMI). The magnetic hysteresis leads to an asymmetric magnetic field dependence of the resonance frequency and alters the number of degeneracy points between the pure optical and acoustic modes. Moreover, it can result in the coupling strength at the gap of the f-H phase diagram being nearly vanishing, contrary to the conventionally expected maximum. These results deepen the understanding of the effect of interlayer DMI on magnon-magnon coupling and the proposed universal method significantly streamlines the solving process of magnon-magnon coupling problems.