RKKY interaction in the presence of a charge-density-wave order

Effects of a charge-density-wave (CDW) order on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction has been theoretically investigated. Assuming that the CDW with an incommensurate ordering vector ${\bf Q}_c$ is induced by a Fermi surface nesting, we show that the CDW order suppresses the conventional RKKY interaction and that it can induce a mode coupling between magnetic ordering vectors ${\bf q}_m$ and ${\bf q}_m\pm {\bf Q}_c$. This suggests that below the CDW transition temperature, the correlation between localized spins may develop at both ${\bf q}_m$ and ${\bf q}_m\pm {\bf Q}_c$. Experimental implications of our result to van der Waals materials $R$Te$_3$ are also discussed.