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Ultrathin L1$_0$ films with different $c$-axis orientations relative to thefilm plane are promising candidates for data storage materials. In this work,within the framework of density functional theory, we calculated the magneticproperties of ultrathin L1$_0$ (111) and (010) films with thicknesses rangingfrom 4 to 16 atomic monolayers (from about 0.8 to 3.5~nm). The highest averagemagnetic moments are observed for the thinnest films considered, and withincreasing film thickness, the values converge towards the magnetic moment forbulk. The observed increase comes mainly from enhanced moments in the twoatomic monolayers closest to the surface of the films. The easy axis ofmagnetization of (111) films prefers an alignment close to the tetragonal axis,an example of tilted magnetic anisotropy. The 6-monolayer (111) film (about1.3~nm thick) inclines the easy axis of magnetization of about 45{\deg} to thefilm plane, which can find use in applications. The (010) films show anin-plane easy magnetization axis in a unique L1$_0$ tetragonal direction. Thisis an unusual type of in-plane anisotropy, as the particular directionpreference is very strong. The computational results encourage furtherexperimental studies of L1$_0$ systems with tilted and in-plane fixed magneticanisotropy.

L1$_0$ FePt thin films with tilted and in-plane magnetic anisotropy: first-principles study