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 ${\mathbf{q}}_{m}\ifmmode\pm\else\textpm\fi{}{\mathbf{Q}}_{c}$. This suggests that, below the CDW transition temperature, the correlation between localized spins may develop at both ${\mathbf{q}}_{m}$ and ${\mathbf{q}}_{m}\ifmmode\pm\else\textpm\fi{}{\mathbf{Q}}_{c}$. Experimental implications of our result to van der Waals materials $R\mathrm{Te}{}_{3}$ are also discussed.