Origin and tuning of the magnetic anisotropy in Fe$_2$P-based alloys*

Fe$_2$P-based alloys have been studied for years due to their potential magnetocaloric applications. In addition, Fe$_2$P demonstrates record-high magnetocrystalline anisotropy (MCA) for systems with no heavy elements. While the Curie temperature $T_C$ in pure Fe$_2$P is too low for applications, this system appears to be highly tunable, and its $T_C$ can be greatly increased by alloying with many other $d$ and $p$ elements. Here we present the electronic structure analysis of magnetic properties of these alloys, searching for systems with higher $T_C$ while preserving high MCA. The microscopic origin of the dominant contribution to MCA and its concentration dependence is revealed. We further find that co-alloying with Co or Ni and Si is a promising strategy for achieving high Curie temperature and MCA, which is more favorable compared to individual alloying by Co/Ni or Si due to the compensation of their effects on the band occupation.