Permanent magnetism of dense-packed nanostructures

The effect of nanostructuring on magnetostatic interactions in permanent magnets is investigated by model calculations. Emphasis is on the energy product as a function of packing fraction of the magnetic phase, of the magnet’s macroscopic shape, and of the nanoscale feature size. The main difference between nanostructured and macroscopic magnetic bodies, namely, the transition between coherent and incoherent reversal, has a far-reaching impact on demagnetizing field and energy product. For small magnet sizes, the energy product is substantially enlarged, up to μ0Ms24 for soft magnetic materials, but this effect is difficult to exploit in real devices. In bulk magnets, the energy product depends on the packing fraction f of the soft phase and exhibits a maximum μ0Ms212 for f =23. Nanoscale magnetization processes involve demagnetizing factors different from the macroscopic ones used to determine the optimum shape of permanent magnets. Confusion of these two types of demagnetizing fields yields unphysical mechanisms, such as hysteresis-loop overskewing and the addition of self-interaction fields to the external field