Modelling of exchange-spring permanent magnets

Micromagnetic modelling using the finite-element method reveals the correlation between the local arrangement of the magnetic moments on a length scale of several nanometers and the magnetic properties of nanocomposite permanent magnets. Theoretical limits for remanence and coercivity are derived for Nd2Fe14B/Fe3B/alpha-Fe nanocrystalline permanent magnets. The coercive field shows a maximum at an average grain size of D = 20 nm. Intergrain exchange interactions override the magneto-crystalline anisotropy of the Nd2Fe14B grains for smaller grains, whereas exchange hardening of the soft phases becomes less effective for larger grains. The calculations show a linear trade off of remanence and coercivity as a function of the alpha-Fe to Fe3B ratio. The coercive field H-c and the remanence J(r) cover the range (H-c, J(r)) = (340 kA/m, 1.4 T) to (610 kA/m, 1.1 T) for a composite magnet containing 40% Nd2Fe14B, (60 - x)% Fe3B, and x% alpha-Fe. The numerical integration of the Gilbert equation yields the transient magnetic states during irreversible switching and thus reveal how reversed domains nucleate and expand. (C) 1998 Elsevier Science B.V. All rights reserved.