Micromagnetic modelling—the current state of the art

The increasing information density in magnetic recording, the miniaturization in magnetic sensor technology, the trend towards nanocrystalline magnetic materials and the improved availability of large-scale computer power are the main reasons why micromagnetic modelling has been developing extremely rapidly. Computational micromagnetism leads to a deeper understanding of hysteresis effects by visualization of the magnetization reversal process. Recent advances in numerical simulation techniques are reviewed. Higher order finite elements and adaptive meshing have been introduced, in order to reduce the discretization error. The use of a hybrid boundary/finite element method enables accurate stray field computation for arbitrary shaped particles and takes into account the granular microstructure of the material. A dynamic micromagnetic code based on the Gilbert equation of motion to study the time evolution of the magnetization has been developed. Finite element models for different materials and magnet shapes are obtained from a Voronoi construction and subsequent meshing of the polyhedral regions. Adaptive refinement and coarsening of the finite element mesh guarantees accurate solutions near magnetic inhomogeneities or domain walls, while keeping the number of elements small. The polycrystalline microstructure and assumed random magnetocrystalline anisotropy of elongated Co elements decreases the coercive field and the switching time compared to zero anisotropy elements, in which vortices form and move only after a certain waiting time after the application of a reversed field close to the coercive field. NiFe elements with flat, rounded and slanted ends show different hysteresis properties and switching dynamics. Micromagnetic simulations show that the magnetic properties of intergranular regions in nucleation-controlled Nd-Fe-B hard magnetic materials control the coercive field. Exchange interactions between neighbouring soft and hard grains lead to remanence enhancement of isotropically oriented grains in nanocrystalline composite magnets. Upper limits of the coercive field of pinning-controlled Sm-Co magnets for high-temperature applications are predicted from the micromagnetic calculations. Incorporating thermally activated magnetization reversal and micromagnetics we found complex magnetization reversal mechanisms for small spherical magnetic particles. The magnetocrystalline anisotropy and the external field strength determine the switching mechanism. Three different regimes have been identified. For fields, which are smaller than the anisotropy field, magnetization by coherent switching has been observed. Single droplet nucleation occurs, if the external field is comparable to the anisotropy field, and multi-droplet nucleation is the driving reversal process for higher fields.

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