  Due to its strong magnetocrystalline anisotropy, FePt L1$\mathrm{_0}$ phase
is considered as a promising magnetic recording media material. Although the
magnetic properties of this phase have already been analyzed many times using
density functional theory (DFT), we decided to study it again, emphasizing on
full potential methods, including spin-polarized relativistic
Korringa-Kohn-Rostoker (SPR-KKR) and full-potential local-orbital (FPLO)
scheme. In addition to the determination of exact values of the
magnetocrystalline anisotropy constants K$\mathrm{_1}$ and K$\mathrm{_2}$, the
magnetic moments (m), the Curie temperature, and the magnetostriction
coefficient, we focused on the investigation of the magnetocrystalline
anisotropy energy (MAE) dependence on the magnetic moment values using the
fully relativistic fixed spin moment (FSM) method with various
exchange-correlation potentials. We present nearly identical MAE(m) curves near
the equilibrium point, along with different equilibrium values of MAE and
magnetic moments. For a magnetic moment reduced by about 10%, we determined a
theoretical MAE maximum in the ground state (0 K) equal to about 20.3 MJ
m$\mathrm{^{-3}}$ and independent of the choice of the exchange-correlation
potential form. These calculations allow us to understand the discrepancies
between the previous MAE results for different exchange-correlation potentials.
