Title: Towards tailored magnetic anisotropy: A first-principles study of L1$_0$ FeNi ultrathin films

Abstract: In previous experiments, thin films of L1$\mathrm{_0}$ FeNi with different surfaces, including (001), (110) and (111), were produced and studied. Each surface defines a different alignment of the crystallographic tetragonal axis with respect to the film's plane, resulting in different magnetic anisotropies. In this study, we use density functional theory calculations to examine three series of L1$\mathrm{_0}$ FeNi films with surfaces (001), (010), and (111), and with thicknesses ranging from 0.5 to 3 nm (from 4 to 16 atomic monolayers). Our results show that films (001) have perpendicular magnetic anisotropy, while (010) favor in-plane magnetization, with a clear preference for the tetragonal axis [001]. We propose calling this type of in-plane anisotropy fixed in plane. A film with surface (111) and a thickness of four atomic monolayers has the magnetization easy axis almost perpendicular to the plane of the film. As the thickness of the (111) film increases, the direction of magnetization rotates towards a tetragonal axis [001], positioned at an angle of about 45$^{o}$ to the plane of the film. Furthermore, the magnetic moment of ultrathin films increases by a maximum of 5%, and the most significant changes in spin and orbital magnetic moments occur at a depth of about three near-surface atomic monolayers. The presented results could be useful for experimental efforts to synthesize ultrathin L1$\mathrm{_0}$ FeNi films with different surfaces. Ultrathin L1$\mathrm{_0}$ FeNi films with varying magnetic anisotropies may find applications in spintronic devices.