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This work quantifies the impact of dynamical $4f$ valence fluctuations on the magnetic anisotropy of Sm(Co,Cu)$_5$ compounds using self-consistent DFT+$U$(ED). The study reveals that pronounced Sm$^{2+}$--Sm$^{3+}$ valence fluctuations in SmCo$_5$ lead to near compensation of spin and orbital moments, accurately explaining its large uniaxial magnetic anisotropy. Conversely, a shift towards the $f^6$ configuration in SmCu$_5$ due to Cu substitution significantly reduces both total magnetic moment and anisotropy.
Dynamical $4f$ valence fluctuations, not just static configurations, are the critical determinant of magnetic anisotropy in Sm(Co,Cu)$_5$, explaining the stark contrast between Co and Cu substituted compounds.
The magnetic properties of Sm-based intermetallics are governed by a delicate interplay between localized $4f$ states, exchange interactions, and valence fluctuations, yet the role of dynamical $4f$ correlations remains poorly understood. Here we investigate the electronic structure and magnetic anisotropy of SmCo$_5$ and SmCu$_5$ using self-consistent DFT+$U$(ED), which explicitly treats dynamical fluctuations of the Sm $4f$ shell. We find that SmCo$_5$ exhibits pronounced Sm$^{2+}$--Sm$^{3+}$ valence fluctuations, with the $4f$ ground state dominated by $f^5$ and $f^6$ configurations. The resulting dynamical $4f$ correlations yield near compensation of the Sm spin and orbital moments and provide a quantitative description of the electronic structure, magnetic moments, and large uniaxial magnetic anisotropy of SmCo$_5$. Upon replacing Co with Cu, the balance shifts toward the $f^6$ configuration, with substantial changes in the Sm spin and orbital moments. In SmCu$_5$, this evolution of the $4f$ configuration is accompanied by a pronounced reduction of both the total magnetic moment and magnetic anisotropy. These results demonstrate that dynamical $4f$ valence fluctuations are essential for understanding the contrasting magnetic properties of SmCo$_5$ and SmCu$_5$ and provide a microscopic framework for describing magnetic anisotropy upon Co to Cu substitution in Sm(Co,Cu)$_5$.