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 ${\mathbf{Q}}_c$ 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 ${\mathbf{q}}_m$ and ${\mathbf{q}}_m\pm {\mathbf{Q}}_c$. This suggests that below the CDW transition temperature, the correlation between localized spins may develop at both ${\mathbf{q}}_m$ and ${\mathbf{q}}_m\pm {\mathbf{Q}}_c$. Experimental implications of our result to van der Waals materials $R$Te${}_3$ are also discussed.