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The remanence of an isotropic nanocrystalline exchange-coupled composite system (comprising hard and soft magnetic phases) is investigated analytically within a simple (one-dimensional) micromagnetic model, in which only exchange and anisotropy energies are considered. For a soft grain with size much less than its own Bloch wall width, our analysis shows that the magnetization distribution in the soft phase is linearly dependent upon position, which we show is responsible for the significant enhancement observed in composite systems. Furthermore, we show that a good estimate of the remanence can be provided by a simple formula, which is easily calculated by hand.

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The demagnetization process of a hard/soft/hard sandwich has been investigated systematically within a self-contained micromagnetic model, with particular attention on the cases with small hard layer thickness. The microscopic and macroscopic hysteresis loops, as well as the angular distributions of the magnetization between nucleation and pinning have been obtained numerically, with the formula for the nucleation field derived. It is found that both nucleation and pinning fields, as well as the gap in between decrease as the hard layer thickness reduces. The hard layer thickness has great effect on the hysteresis loops only when the thickness is very small, where the hysteresis loop is nearly square and the dominant coercivity mechanism is the nucleation. The thickness regions at which the theoretical and practical giant energy products can be achieved have been discussed. In most cases, the hard layer can be taken as sufficiently thick so that the magnetization at its surface obeys a simple coherent rotation model. In these cases, the calculation can be simplified significantly, with only the influence of the soft layer thickness accounted.