$W$-type ${\mathrm{SrFe}}_{18}{\mathrm{O}}_{27}$ hexaferrite is emerging as a potential material for permanent magnet applications. Despite this, theoretical modeling on $W$-type hexaferrites is still lacking, leaving only experimental findings to date. Employing density functional theory, we conduct a detailed analysis of pure $W$-type ${\mathrm{SrFe}}_{18}{\mathrm{O}}_{27}$ hexaferrite and its compositions with Ni/Zn substitutions, to explore their intrinsic magnetic properties and assess their viability as potential permanent magnets. We found no significant effect of Ni/Zn substitution on the magnetocrystalline anisotropy energy (MAE); however, Zn substitution is particularly helpful for improving the magnetization ${\mu }_0{M}_s$. The calculated MAE constant $K_u$ values indicate that the compounds are uniaxial with easy axis along the (001) direction. The origin of the predicted MAE is investigated using second-order perturbation theory analysis and the electronic structure. We found that different Fe sublattices contribute differently to the MAE, providing a unique way to enhance the MAE with small site-specific substitutions. The results highlight the challenge of simultaneously enhancing $K_u$ and ${\mu }_0{M}_s$ in $W$-type hexaferrite compounds. However, the compounds show intriguing properties with moderate $K_u$ and high ${\mu }_0{M}_s$, which may outperform the conventional $M$-type ferrite magnets in some applications.

• Received 10 October 2023
• Revised 19 November 2023
• Accepted 22 December 2023

DOI:https://doi.org/10.1103/PhysRevB.109.024414