We investigate spacer-mediated long-range Dzyaloshinskii-Moriya interaction (LR-DMI) in $\mathrm{Co}/\mathrm{Cu}\left(n\right)/\text{HM}$ multilayers $(\text{HM}=\text{Pt}, \mathrm{Pd}, \mathrm{Ir}, \mathrm{W}, \mathrm{Mo})$ using first-principles calculations and micromagnetic simulations. LR-DMI shows a pronounced nonmonotonic, oscillatory dependence on Cu thickness, demonstrating that the intralayer DMI within Co can be tuned through a nonmagnetic spacer and a remote heavy-metal (HM) spin-orbit source. Atomic layer decomposition reveals that the LR-DMI signal is carried predominantly by the Co planes, and the heavy-metal overlayer acts as the spin-orbit source whose influence is transmitted through the Cu spacer and weakens with increasing $n$. Thickness-dependent electronic structure and charge density difference analyses link the oscillatory LR-DMI to spacer-tuned Co-Pt coupling and interface to interface charge redistribution that becomes progressively localized at larger $n$. Extending to different heavy-metal overlayers, all systems retain the same thickness-driven oscillatory backbone, while the amplitude and phase depend strongly on the heavy-metal species, consistent with $d$ band filling and relativistic character. Micromagnetic simulations for Pt and Ir stacks demonstrate that these first-principles LR-DMI trends translate into distinct field tunable skyrmion diameters and hysteresis behavior. These results establish a Co/HM1/HM2-type route for engineering single-layer DMI through nonmagnetic spacer and spin-orbit layers.

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• Density of states
• Dzyaloshinskii-Moriya interaction
• Micromagnetism
• Skyrmions
• Magnetic thin films
• First-principles calculations
• Micromagnetic modeling