Coping with Brown's paradox: The pinning and nucleation of magnetic domain walls at antiphase boundaries

The critical field for unpinning or nucleation of a domain wall in a ferromagnetic crystal at an antiphase boundary (APB) is calculated as a function of the magnetic coupling constant η across the APB. It turns out that for positive values of η pinning occurs and that for negative values there is very strong pinning and also nucleation.