  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.
