Anisotropy of Iron-Series Permanent Magnets

Element-strategic considerations have sparked renewed interest in rare-earth-free permanent magnets, but the prediction of the magnetocrystalline anisotropy from the atomic structure is still in its infancy, and there are no rules predicting the $d$ anisotropy as function of the atomic structure. We have obtained tight-binding estimates for a variety of clusters and etxtended structures of different symmetry and $d$-band filling. A expected, the anisotropy strongly oscillates as a function of the $d$-band filling. Our calculations indicate that nearly filled $d$ bands tend to yield anisotropy parallel to the pair axis. Sites with trigonal symmetry support bigger anisotropies than cubic and tetragonal environments, but this is a crystal- field effect similar to that in BaFe$_{12}$O$_{19}$ rather than a band-structure effect. Shape anisotropy is important in alnico- type nanostructured permanent magnets. We find a maximum of the energy product as a function of packing fraction, namely a maximum value of $\mu_{o}M_{s}^{2}$/12 realized at a volume fraction of 2/3. For Fe$_{65}$Co$_{35}$, this yields an upper limit of 390 kJ/m$^{3}$ [49 MGOe].