Magnetic anisotropy and intermediate valence in CeCo${}_5$ ferromagnet

The intermediate valence of Ce in CeCo${}_5$ challenges standard density functional theory (DFT) and static DFT+$U$ approaches, which fail to capture its magnetic properties. By combining DFT+$U$ with exact diagonalization of the Anderson impurity model for the Ce 4$f$ shell, we find a substantial reduction of Ce spin and orbital moments, consistent with DFT+DMFT, arising from Ce${}^{4+}$ - Ce${}^{3+}$ valence fluctuations. The total magnetic moment of 6.70 ${\mu }_B$ agrees with experiment, and the calculated $4f$ density of states reproduces photoemission and Bremsstrahlung isochromat spectra. The uniaxial magnetic anisotropy energy reaches 4.8 meV/f.u. when Coulomb correlations on both Ce 4$f$ and Co 3$d$ shells are included, in very good agreement with experimental data. These results highlight the importance of dynamical correlations and provide guidance for exploring high-performance, low-rare-earth-content permanent magnets.