Remanence and coercivity in isotropic nanocrystalline permanent magnets

Numerical micromagnetic calculations rigorously describe the correlation between the microstructure and the magnetic properties of nanocrystalline permanent magnets. In isotropic nanocrystalline permanent magnets exchange interactions override the anisotropy of the individual grains. Therefore the spontaneous magnetic polarization deviates from the easy axes in a region along the grain boundaries. For a fine grain structure with a mean grain size d20 nm the remanence is considerably enhanced, since the volume fraction of the boundary regions where the spontaneous magnetic polarization points towards the direction of the applied field becomes significantly high. The inhomogeneous ground state, however, favors the nucleation of reversed domains leading to a reduction of the coercive field with decreasing grain size. A uniform grain structure with a very small range in grain size avoids large demagnetizing fields and thus preserves a high coercivity. For a grain size of 10 nm isotropic two-phase permanent magnets based on ${\mathrm{Fe}}_{14}$${\mathrm{Nd}}_{2}$B and \ensuremath{\alpha}-Fe show remarkable high-energy products, because the volume fraction of the magnetically soft phase can be increased up to 50% without a significant loss of coercivity.