Coercive force of a small particle

(a) Consider a small spherical single-domain particle of a uniaxial Ferro-magnet. Show that the reverse field along the axis required to reverse the magnetization is Ba, = 2K/MS, in CGS units. The coercive force of single-domain particles is observed to be of this magnitude. Take UK, = K sin2 θ as the anisotropy energy density and UM = – BaM cos θ as the interaction energy density with the external field; here θ is the angle between B, and M.

(b) Show that the magnetic energy of a saturated sphere of diameter d is ≈ M2sd3. An arrangement with appreciably less magnetic energy has a single wall in an equatorial plane. The domain wall energy will be πσad2/4, where σw is the wall energy per unit area. Estimate for cobalt the critical radius below which the particles are stable as single domains, taking the value of JS2/n as for iron.