Fundamental magnetization processes in nanoscaled composite permanent magnets

Abstract

Excellent candidates for high remanent permanent magnets are nanoscaled composite materials consisting of soft magnetic $\ensuremath{\alpha}$-Fe grains embedded into a hard magnetic ${\mathrm{Nd}}_{2}{\mathrm{Fe}}_{14}\mathrm{B}$ environment. The magnetic properties of such permanent magnets sensitively depend on the prepared grain structure. This can be understood by computational micromagnetism, which reveals the relation between details of the grain structure and intergranular interaction mechanisms like the short-range exchange and the long-range stray field. The main problem of composite materials is to preserve a sufficiently high coercivity. This can be only guaranteed if the soft magnetic inclusions are smaller than twice the domain-wall width ${\ensuremath{\delta}}_{\mathrm{B}}^{\mathrm{hard}}=\ensuremath{\pi}\sqrt{{A/K}_{1}}$ of the hard magnetic environment with the exchange constant $A$ and the first magnetocrystalline anisotropy constant ${K}_{1}.$ Otherwise we obtain a strong decrease of the coercivity following a ${D}_{\mathrm{soft}}^{\mathrm{\ensuremath{-}}\mathrm{const}}$ law, where ${D}_{\mathrm{soft}}$ is the diameter of the soft magnetic inclusion. According to analytical and numerical investigations, the const varies between -2 and -0.5 depending on the dimension and the geometry of the soft magnetic inclusion.