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 extremely reduced diameters of a smaller than 12 nm can occur. 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, they are increased with 5$d$ capping layers compared to films capped by 4$d$ transition metal. We discovered a skyrmion phase by using atomistic spin dynamics simulations at small magnetic fields of $\sim$ 1 T. 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.