Critical Size and Nucleation Field of Ideal Ferromagnetic Particles

Abstract

The field at which the spins of a previously saturated ideal ferromagnetic particle cease to be aligned is defined as the nucleation field. This field is calculated, using calculus of variation, for an infinite cylinder and a sphere, assuming three mechanisms of magnetization reversal: spin rotation in unison, magnetization curling, and magnetization buckling. Theoretical treatment shows that, in fact, only curling and rotation in unison need be considered.The critical size for single-domain behavior, defined as the largest size at which magnetization reversal proceeds by rotation in unison, is calculated for the prolate ellipsoid and is found to be practically independent of magnetocrystalline anisotropy and elongation and approximately equal to $\frac{{A}^{\frac{1}{2}}}{{I}_{s}}$. Here $A$ is the exchange constant and ${I}_{s}$ is the saturation magnetization.For cylinders larger than the critical size, the coercive force, for a field applied in the direction of the long axis, is found to be equal to the nucleation field, when magnetocrystalline anisotropy is neglected. The coercive force thus calculated decreases with the radius of the cylinder, $R$, according to ${H}_{c}=\frac{6.78A}{{I}_{s}{R}^{2}}$.Available experimental data are discussed and are generally found to be in a better agreement with this than with previous theory.