Magnetization configurations and reversal of magnetic nanotubes with opposite chiralities of the end domains

For thick soft magnetic nanotubes with an anisotropy axis directed along the nanotube length the equilibrium energy ground states present magnetization configurations with opposite rotating senses in two tube ends (B-state), referring as antiparallel chiralities of the end vortex domains. For nanotubes with outer radius R of 50 nm, 100 nm and 150 nm, and length L =(2.5-20) R the B-state remanent magnetization and the reversal field dependence on tube thickness and anisotropy strength are studied by using both two-dimensional simulation and analytic methods. The equilibrium states, the hysteresis loops and the switching field values calculated numerically are presented as the functions of tube size and material parameters. For the short nanotubes the domain walls patterns, such as transverse walls and vortex walls, nucleating in the tube center, as well as the hysteresis loops of the nanotubes with transverse walls are presented. The numerical results are interpreted by a simple analytical model in which the equilibrium state of nanotube is described by θ , the angle of the magnetization M deviation from the intrinsic tube easy axis. θ as a function of the tube aspect ratio L/R , tube thickness ΔR , and uniaxial anisotropy constant K u , obtained by minimizing the total magnetic energy, well describes dependences of the shape of hysteresis loops and switching field values on the tube geometric and material parameters in the B-state.