Effects of local lattice deformation on magnetic anisotropy of W-type ferrites

We calculate the magnetic anisotropy (MA) energy of W-type ferrites, Ba(Sr)Me ₂Fe ₁₆O ₂₇, where Me is Mg, Co, and Ni, using a cluster model and L S coupling on magnetic ions, along with the structural data obtained via x-ray and neutron diffractions. We show that the local MA energy of Fe ^3＋ and Me 2 + on each non-equivalent site depends strongly on the local lattice structure around the magnetic ions. The bulk MA energy calculated for W-type ferrite with Me=Mg is found to be weakly dependent on the details of local lattice structures, and the calculated result is consistent with that observed for SrMg ₂Fe ₁₆O ₂₇. Results for W-type ferrite with Me=Co suggest the appearance of a cone-type magnetic structure; however, c − plane MA may appear when a small amount of Co 2 + resides on 12k sites. The finding could resolve the experimental controversy for the magnetic structure of W-type ferrite with Me=Co. Based on the results, we discuss site-selective substitution of Me 2 + (Me = Fe, Co, and Ni) to enhance the performance of permanent magnets.