First-Principles Prediction of Skyrmionic Phase Behavior in GdFe$_2$ Films Capped by 4$D$ and 5$D$ Transition Metals

In atomic GdFe$_2$ films capped by 4$d$ and 5$d$ 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 5$d$ capping layers which exhibit strong SOC strength. We discover a skyrmion phase by using atomistic spin dynamic simulations at small magnetic fields of $\sim$1 T. In addition, a ground state that a spin spiral phase is remained even at zero magnetic field for both films with 4$d$ and 5$d$ capping layers.