3D and 1D micromagnetic calculation for hard/soft bilayers with in-plane easy axes

Macroscopic hysteresis loops and microscopic magnetic moment distributions have been determined by three-dimensional (3D) as well as one-dimensional (1D) micromagnetic models for exchange-coupled Nd₂Fe₁₄B/α–Fe bilayers and carefully compared with each other. It is found that the results obtained from the two methods are consistent with each other, where the nucleation and coercive fields decrease monotonically as the soft layer thickness L^s increases whilst the largest maximum energy products (roughly 600 kJ/m³) occur at L^s=5 nm. Moreover, the calculated angular distributions in the thickness direction for the magnetic moments are similar. Nevertheless, the calculated critical fields and energy products by 3D OOMMF are systematically smaller than those given by the 1D model, mainly due to the local demagnetization fields, which are taken into account in the 3D calculation and ignored in the 1D calculation. It is demonstrated by the 3D calculation that the large demagnetization fields in the corners of the soft layers reduce the nucleation fields and thus facilitate the magnetic reversal. Such an effect enhances as L^s increases. When L^s=20 nm, the differences between the coercivity is as large as 30%, while the nucleation fields obtained by the two methods have opposite signs.