First-principles study of intrinsic magnetic properties of hexagonal and orthorhombic (Fe$_{1-x}$Co$_x$)$_2$P alloys*

(Fe$_{1-x}$Co$_x$)$_2$P is a candidate rare-earth-free alloy for permanent-magnet applications, which is hexagonal ($h$) up to $x\approx0.12$ and orthorhombic ($o$) at larger $x$. The Curie temperature $T_C$, which is only 270 K in Fe$_2$P, raises sharply with $x$, peaking above 450 K in the $o$-phase [1]. The measurement [2] of magnetocrystalline anisotropy (MCA) in the $o$-phase is inconsistent with M\"ossbauer data suggesting a spin reorientation transition (SRT) at $x\approx0.3$ [1]. Here we report the results of $ab\ initio$ calculations of the magnetization, mean-field $T_C$, and MCA in $h$- and $o$-phases as a function of $x$, addressing the role of unequal site occupation, which is confirmed by total-energy calculations. The trends in the magnetization are reproduced, as well as MCA in the $h$-phase, and so is the SRT near $x\approx0.3$ (at odds with the results of Ref. 2). The trends in the mean-field $T_C$, obtained using the disordered-local-moment method, agree with experimental data. [1] R. Fruchart \emph{et al.}, J. Appl. Phys. 40, 1250 (1969). [2] T. Hokabe \emph{et al.}, J. Phys. Soc. Japan 36, 1704 (1974).