Bloch and Néel disclination lines in a small-anisotropy ferromagnet

Bloch and Néel lines are, from a topological point of view, disclinations in a spin lattice. They are described in a small-anisotropy ferromagnet ($K\ll 2\pi M_S^2$) for two different situations. First one considers Bloch lines at the limit of vanishing anisotropy: A complete calculation shows that cross and circular Bloch lines have no core singularity, which fact decreases exchange energy, and that stray fields control the size of cross Bloch lines, while magnetostriction controls the size of circular Bloch lines. Second one considers Néel lines in a situation inspired by recent experimental results on amorphous ferromagnets. Here it is shown that the interactions between lines, whose size is controlled by the existence of a small anisotropy, are mainly due to stray-field effects and magnetostriction effects. Topologically Bloch lines are wedge disclinations and Néel lines are twist disclinations. The importance of magnetostriction is emphasized throughout the article and original methods are given in an Appendix to calculate the internal magnetostrictive stresses due to singularities. Although the theoretical results do not coincide fully with the experimental ones, especially because a strictly two-dimensional calculation is used, we are confident that the analysis is true in the main. Qualitatively, this analysis differs drastically from the case $K\gg 2\pi M_S^2$.