Quasicoherent nucleation mode in two-phase nanomagnets

Magnetization processes in advanced magnetic nanostructures are investigated. For the case of spherical soft or semihard grains surrounded by a very hard matrix a bulging nucleation mode is discovered. The bulging mode exhibits the radial angular symmetry of the coherent mode, but it is incoherent due to its radial variation. The radial dependence of the bulging mode is obtained by solving a spherical Bessel equation which is subject to appropriate boundary conditions. In contrast to the coherent mode, the bulging mode yields a nucleationfield coercivity which depends on the exchange stiffness and on the size of the grain. There is a critical grain radius 7.869√A/μ0Ms2 above which the bulging mode is replaced by a modified curling mode. The nucleation modes realized in nanostructures affect the demagnetizing-field corrections necessary to account for the external shape of magnetic samples. Since strong but short-range exchange and weak but long-range magnetostatic interactions compete on nanostructural length scales, the sample-shape dependence of the hysteresis loops cannot be mapped onto a purely magnetostatic demagnetizing factor