Domain-wall pinning at inhomogeneities of arbitrary cross-sectional geometry

The coercivity of cellular Sm-Co based permanent magnets is investigated by model calculations. The grain boundaries responsible for the pinning coercivity are modeled as planar inhomogeneities with arbitrary cross-sectional geometry. The calculation yields a physically transparent integral equation for the pinning energy, whose derivative is the pinning force. The theory rationalizes experimental data on a semiquantitative level, but without adjustable parameters, and bridges the gap between smooth concentration gradients and abrupt interfaces. Explicit results are obtained for sinusoidal profiles, for very thin grain boundaries, and for profiles intermediate between attractive and repulsive pinning. The corrections predicted by the present model elucidate the occurrence of coercivity when the main and grain-boundary phases have the same wall energy.