We have investigated the microwave non-reciprocity for a non-centrosymmetric antiferromagnet Ba$_2$MnGe$_2$O$_7$. The magnon modes expected by the conventional spin wave theory for staggered antiferromagnets are certainly observed. The magnitudes of exchange interaction and magnetic anisotropy are obtained by the comparison with the theory. The microwave non-reciprocity is identified for one of these mode. The relative magnitude of microwave non-reciprocity can be explained with use of spin wave theory and Kubo formula.
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