Theoretical study of current induced domain wall motion in magnetic nanotubes with azimuthal magnetization

Abstract

Nanowires and nanotubes are one-dimensional conduits, providing an ideal playground to investigate the fundamentals of domain-wall motion and spin-wave propagation. While simulations have been dominating for two decades, the first experiments are emerging. In particular, a peculiar class of domains were observed recently in nanotubes – domains with azimuthal (flux-closure) magnetization [1] (CoNiB, 400nm diameter). Azimuthal magnetization relates to the curvature-induced magnetic anisotropy resulting from the anisotropy of the granular structure, combined with inverse magnetostriction and/or inter-grain interface anisotropy. Interestingly, besides the conventional spin-transfer torques, a significant OErsted field directly coupled to the azimuthal magnetization through Zeeman energy may exist in a tubular geometry. This opens new possibilities for the manipulation of the domain walls in such geometries. Curvature-induced anisotropy together with OErsted field effects suggest that according to the domain wall type their dynamical features may be very different from the case of thin flat strips, now well established theoretically and experimentally.Given that, we report a theoretical overview [2] of the magnetic domain wall behavior under an electric current in infinitely long nanotubes with azimuthal magnetization, combining the one-dimensional analytic model and micromagnetic simulations. We derive a phase diagram predicting the stable azimuthal domains versus the anisotropy strength and the tube geometry, see Fig. 1. In addition, we predict the types of stable walls, either Néel or Bloch, pictured in Fig. 2, resulting from the competition between the curvature induced exchange energy, the demagnetization energy and the anisotropy energy. We also draw the panorama of the impact of the OErsted field on wall motion in tubes with azimuthal domains, pointing at curiosities such as opposite directions of motion below and above the Walker current and dramatic contrast between Néel and Bloch walls. In particular, we show the existence of spin-transfer torque and/or Oersted dominated regime for both domain wall structures and we predict large domain wall speeds reaching potentially 800 m/s, before the occurrence of a so-called Walker breakdown, see Fig. 2. We show how the domain wall speed and the walker field depend on the anisotropy and the geometrical parameter of the magnetic tubes and highlight the most suitable parameters to achieve high domain wall speed. Our study may guide the experimental realization of magnetic tubes, targeting the optimal parameters to get the desired properties. **