Micromagnetic modelling - the current state of the art
Josef Fidler and Thomas Schrefl
Journal of Physics D: Applied Physics, 33 (2000) R135-R156.
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
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Feb. 13, 2001