Theory of the Structure of Ferromagnetic Domains in Films and Small Particles

The theory is developed of the domain structure of ferromagnetic bodies whose smallest dimension is comparable with the thickness of the Weiss domains as found in crystals of ordinary size. Calculations of the domain boundary, magnetic, and anisotropy energies of various domain configurations are given for thin films, small particles, and long needles of ferromagnetic material. For sufficiently small dimensions the optimum structure consists of a single domain magnetized to saturation in one direction. This result implies unusual magnetic characteristics, such as have in fact been reported by a number of experimenters. The critical dimensions for transition from a configuration with domain structure to a saturated configuration are estimated \ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ cm in films and \ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ cm in particles or grains. These estimates are based on typical values of the relevant material constants, and may be increased or decreased by a factor of ten for other values of the constants.