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 $R\mathrm{Te}{}_3$ are also discussed.

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• Charge density waves
• Magnetic interactions
• Rare-earth magnetic materials
• Transition metal dichalcogenides
• Feynman diagrams
• Green's function methods
• Kondo lattice model
• Mean field theory