In atomic GdFe₂ films capped by 4d and 5d transition metals, we show that skyrmions with diameters smaller than 12 nm can emerge. The Dzyaloshinskii-Moriya interaction (DMI), exchange energy, and the magnetocrystalline anisotropy (MCA) energy were investigated based on density functional theory. Since DMI and MCA are caused by spin-orbit coupling (SOC), they are increased with 5d capping layers which exhibit strong SOC strength. We discover a skyrmion phase by using atomistic spin dynamic simulations at small magnetic fields of ~1 T. In addition, a ground state that a spin spiral phase is remained even at zero magnetic field for both films with 4d and 5d capping layers.