Simple Model for Nucleation around Dislocations

The effect of the mechanical stresses at a dislocation, via magnetostriction, on the theoretical nucleation field for magnetization reversal is approached by assuming a cylindrical region in which the magneto-crystalline anisotropy vanishes. The complete spectrum of eigenvalues is studied for this model, and it is found that the buckling mode yields the lowest eigenvalues for hard materials with reasonable size for the defective region. The turnover to the curling mode is at a radius of about 300 Å for MnBi and 550 Å for Ba${\mathrm{Fe}}_{12}$ ${\mathrm{O}}_{19}$. To obtain the observed value of nucleation field in Ba${\mathrm{Fe}}_{12}$ ${\mathrm{O}}_{19}$, the radius of the cylinder with $K=0\mathrm{}$, should be about 350 Å, which seems plausible for a dislocation.