## 1 Introduction  
In the sphere of magnetic memory storage (especially in spintronics), magnetic skyrmions, which are localized topologically protected spin structures, are promising candidates due to their unique properties [1; 2; 3]. Even though skyrmions have long been investigated by simulations such as micromagnetic and phenomenological model calculations [4; 5; 6], the experimental discovery of skyrmions was came about very recently in bulk MnSi [7]. Since then, researchers have focused on observing stabilized skyrmions experimentally in not only bulk crystals [8; 9], but also thin films and multilayers [10; 11; 12; 13; 14].  
At room temperature, Neel-type skyrmions with a diameter of \(\sim\)50 nm are found in multilayer stacks, such as Pt/Co/Ta and Ir/Fe/Co/Pt [15; 16]. However, to use them in memory and logic devices, a further reduction in skyrmion sizes is necessary. As a result of the decreasing stability of small skyrmions at room temperature, thicker magnetic layers are required to increase stability [17; 18]. For multilayer systems consisting of ferromagnet and heavy metals, interfacial anisotropy and the strength of Dzyaloshinskii-Moriya interaction (DMI) reduces as the thickness of ferromagnetic layer increases. Moreover, the skyrmion Hall effect is a challenge when it comes to moving skyrmions in electronics devices [19; 20; 21]. Amorphous rare-earth-transition-metal (RE-TM) ferrimagnets are one of the potential materials to overcome these challenges. Their Intrinsic perpendicular magnetocrystalline anisotropy (MCA) gives an advantage in stabilizing skyrmions by using relatively thick magnetic layers (\(\sim\)5 nm) [22]. Another advantage of RE-TM alloys is that the skyrmion Hall effect is largely reduced by the near zero magnetization of RE-TM alloys [23]. Furthermore, in perspective of the applications, all-optical helicity-dependent switching (AO-HDS) has been shown in RE-TM alloys due to its ultrafast switching. Recently, AO-HDS has been demonstrated in RE-TM alloys using a circularly polarized laser. As a result, RE-TM alloys have drawn interest in the field of skyrmions research.  
In recent, large skyrmions with diameter of \(\sim\)150 nm have been observed in Pt/GdFeCo/MgO [24], and skyrmion bound pairs are found in Gd/Fe multilayers [25]. However, further tuning is essential to reduce the size of skyrmions in RE-TM alloys.  
In the present paper, magnetic properties such as DMI, MCA, and magnetic phase transition are investigated in atomic GdFe\({}_{2}\) films capped by 4\(d\) and 5\(d\) transition metals (TMs) using first principles density functional theory (DFT) calculations and atomistic spin dynamics simulations. We recognize that the 5\(d\) TMs give rise to a large DMI and strong MCA due to their large spin-orbit coupling (SOC) and orbital hybridization with 3\(d\) bands of Fe atom. Firstly, an extended Heisenberg model is studied by using atomistic spin dynamics. Then, we parameterize an extended Heisenberg model from DFT calculations. According to the phase diagram observed at zero temperature, there are phase transitions under externally applied magnetic fields of the order of \(\sim\)1 T. The magnetic phase changes from the spin spiral state to the ferromagnetic state via skyrmion lattice, the diameters of isolated skyrmions amount to 6 to 15 nm depending on the capping layers.