Computer simulation of single-phase nanocrystalline permanent magnets

Demagnetizing curves have been calculated numerically for three-dimensional micromagnetic model assemblies of randomly oriented, magnetically hard, exchange coupled, uniaxial nanocrystals as typified by rapidly quenched Nd2Fe14B. The curves were obtained as a sequence of static equilibrium states in an incrementally changing applied field. The magnetization distribution in each state was obtained by minimizing the sum of the exchange, anisotropy and Zeeman energies of the assembly, using a modified LaBonte method, with computational elements as small as 1.11 nm (roughly 1/4 the domain wall thickness in Nd2Fe14B]. For computational economy, internal dipolar interactions were ignored in the energy minimization. For a material with the magnetic constants of stoichiometric Nd2Fe14B. tests showed that these interactions contribute less than 3% to the energy. On increasing the model grain size from 4.4 to 36 nm, the reduced remanence fell from 76 to 54% and the reduced intrinsic coercivity mu(0i)H(C)M(S)/K-U increased from 0.16 to 0.46 (just under half the Stoner-Wohlfarth value); both sets of results are in reasonable agreement with experimental values. The energy product, evaluated for Nd2Fe14B, ranged from similar to 224 kJ/m(3) for 10 nm grains to similar to 128 kJ/m(3) for 36 nm grains. For grain sizes greater than or equal to 20 run, spatial magnetization variation was confined to domain walls centred on the grain boundaries, For grain sizes decreasing below about twice the domain wall thickness, spatial magnetization variation extended to the interior of the grains and exhibited increasingly long-range correlations. (C) 1998 Elsevier Science B.V. All rights reserved.