The QCD axion or axion-like particles are candidates of dark matter of the universe. On the other hand, axion-like excitations exist in certain condensed matter systems, which implies that there can be interactions of dark matter particles with condensed matter axions. We discuss the relationship between the condensed matter axion and a collective spin-wave excitation in an anti-ferromagnetic insulator at the quantum level. The conversion rate of the light dark matter, such as the elementary particle axion or hidden photon, into the condensed matter axion is estimated for the discovery of the dark matter signals.
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