Site-selective cobalt substitution in La-Co co-substituted magnetoplumbite-type ferrites: $^{59}$Co-NMR and DFT calculation study

Abstract: The La-Co co-substituted magnetoplumbite-type (M-type) ferrites $A$Fe${12}$O${19}$ ($A$ = Ca, Sr and Ba, ion sizes Ca$^{2+}$ $<$ Sr$^{2+}$ $<$ Ba$^{2+}$) with Co compositions around 0.2 have been subjected to $^{59}$Co-NMR. The results show that Co occupies the 4f$1$, 2a and 12k sites, and that the smaller the $A$ ion, the more Co tends to occupy the 4f$_1$ minority spin site, which is effective in enhancing both uniaxial anisotropy and magnetisation. First-principles total energy calculations based on density functional theory (DFT) of undoped $A$Fe${12}$O$_{19}$ and a supercell ($2 \times 2 \times 1$ of the unit cell) in which 1/96 of Fe$^{3+}$ is replaced by Co$^{2+}$ were performed to predict the stable structure and Co occupancy sites. The results show that regardless of $A$, Co is most stable when it occupies the 4f$_1$ site, followed by the 2a and 12k sites with energy differences on the order of 100 meV, and Co practically does not occupy the 2b and 4f$_2$ sites. As the $A$ ion becomes smaller, the energy difference when Co occupies each Fe site tends to increase, and the Co occupancy of the 4f$_1$ site also increases. The site selectivity of Co can be roughly explained as a result of the difference in uniaxial strain along the $c$-axis associated with the difference in $A$. However, the influence of the $A$ ion differs between the R and S blocks and the local strain also has a secondary effect on the Co distribution. Based on these results, the guidelines for improving the performance (anisotropy and magnetisation) of La-Co co-substituted M-type ferrite magnets with a limited amount of Co can be summarised as follows: It is effective to select as small $A$ ions as possible and to post-anneal at low temperature or cool slowly to concentrate Co at the 4f$_1$ site in tetrahedral coordination.