Nucleation field of a soft magnetic nanotube with uniaxial anisotropy

We have performed both one-dimensional variational and two-dimensional numerical calculations of the magnetic curling structure near the ends of soft magnetic nanotubes whose axes are magnetically favored, and compared the two. The variational calculation is based on the observation that the numerical simulation results for ending curling structure are similar to those for head-to-head domain walls. Except for magnetic fields opposing the average magnetization and larger than a critical value, the wall centers are outside the tube, and there is an appreciable energy barrier against penetration of the tube by the wall. The two calculations are in reasonable agreement for a range of tube dimensions and material parameters. Both predict critical fields lower than those for infinite tubes.