Magnetic interactions in an antiferromagnet govern the spin moment carried by magnons and the strength of multimagnon interactions that lead to magnetization relaxation. We present a numerical method to generate a four-magnon interactions Hamiltonian by fourth-rank tensor and apply it to an antiferromagnetic insulator NiO, where magnetic dipolar interactions (MDIs) have non-negligible effects on the magnon states, for investigating four-magnon interactions-induced magnon decay rates, by taking into account intra- and intermode interactions. First, we confirmed the suppressed magnon spin moment of two magnon modes, labeled as $\alpha$ and $\beta$ modes, owing to non-spin-conserving interactions of the MDIs. An applied magnetizing field $B^z$ enhanced the magnon spin moment of each magnon mode by increasing the spin moment contribution from one Ni sublattice, while decreasing it from another sublattice. Second, by expressing the four-magnon scattering probability in the fourth-rank tensor form, we found that the low magnon decay rates of both magnon modes are mainly caused by the suppressed magnon spin moment. The applied magnetizing field promotes the intermode and suppresses the intramode interactions contribution to the magnon decay rates.

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• Bosons
• Dipolar interaction
• Exchange interaction
• Magnetic anisotropy
• Magnons