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 B_a, = 2K/M_S, in CGS units. The coercive force of single-domain particles is observed to be of this magnitude. Take U_K, = K sin² θ as the anisotropy energy density and U_M = – B_aM 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 ≈ M²_sd³. An arrangement with appreciably less magnetic energy has a single wall in an equatorial plane. The domain wall energy will be πσ_ad²/4, where σ_w 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.