Abstract
High performance magnetic materials are characterized by the combination of outstanding magnetic properties and optimized microstructures, e.g., nanocrystalline composites of multilayers and small particle systems. The characteristic parameters of the hysteresis loops of these materials vary over more than a factor of $10^{6}$ with optimum values for the coercive field of several Tesla and permeabilities of $10^{6}$. Within the framework of the computational micromagnetism (nanomagnetism) using the finite element method the upper and lower bounds of the coercive field of different types of grain ensembles and multilayers have been determined. For the case of nanocrystalline composites the role of grain size, exchange and dipolar coupling between grains and the degree of grain alignment will be discusses in detail. It is shown that the largest coercivities are obtained for exchange decoupled grains, whereas remanence enhancing requires exchange coupled grains below 20 nm. For composite permanent magnets based on $Nd_{2}Fe_{14}B$ with an amount of ~ 50% soft $\alpha$-Fe-phase coercivities of ${\mu}_{0}H_{c}=0.75\;T$, a remanence of 1.5 T and an energy product of $400\;kJ/m^{3}$ is expected. In nanocrystalline systems the temperature dependence of the coercivity is well described by the relation ${\mu}_{0}H_{c}=(2\;K_{1}/M_{s}){\alpha}-N_{eff}{\mu}_{0}M_{s}$, where the microstructural parameters $\alpha$ and $N_{eff}$ take care of the short-range perturbations of the anisotropy and $N_{eff}$ is related to the long-range dipolar interactions. $N_{eff}$ is found to follow a logarithmic grain size size dependence ${\mu}_{0}H_{c}=(2\;K_{1}/M_{s}){\alpha}-N_{eff}(\beta1nD){\mu}_{0}M_{s}$. Several trends how to achieve the ideal situation $\alpha$->1 and $N_{eff}$->1->0 will be discussed.