The magnon-magnon coupling in synthetic antiferromagnets advances it as hybrid magnonic systems to explore the quantum information technologies. To induce the magnon-magnon coupling, the parity symmetry between two magnetization needs to be broken. Here we experimentally demonstrate a convenient method to break the parity symmetry by the asymmetric thickness of two magnetic layers and thus introduce a magnon-magnon coupling in Ir-based synthetic antiferromagnets CoFeB(10 nm)/Ir(tIr=0.6 nm, 1.2 nm)/CoFeB(13 nm). Remarkably, we find that the weakly uniaxial anisotropy field (~ 20 Oe) makes the magnon-magnon coupling anisotropic. The coupling strength presented by a characteristic anticrossing gap varies in the range between 0.54 GHz and 0.90 GHz for tIr =0.6 nm, and between nearly zero to 1.4 GHz for tIr = 1.2 nm, respectively. Our results demonstrate a feasible way to induce the magnon-magnon coupling by an asymmetric structure and tune the coupling strength by varying the direction of in-plane magnetic field. The magnon-magnon coupling in this highly tunable material system could open exciting perspectives for exploring quantum-mechanical coupling phenomena.
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