epl draft Domain wall motion in thin ferromagnetic nanotubes: Analytic results

Dynamics of magnetization domain walls (DWs) in thin ferromagnetic nanotubes subject to weak longitudinal external fields is addressed analytically in the regimes of strong and weak penalization. Exact solutions for the DW profiles and formulas for the DW propagation velocity are derived in both regimes. In particular, the DW speed is shown to depend nonlinearly on the nanotube radius. The problem of controlled manipulation of magnetization domains in quasi-one-dimensional ferromagnetic nanostructures is of paramount technological importance in designing new generation memory devices [1–3] and of fundamental interest in the vibrant areas of micromagnetics and spintronics. To date, substantial theoretical progress has been achieved in understanding the dynamics of domain walls (DWs) in nanowires and nanostrips under the influence of applied magnetic fields [4–16] and spin-polarized electric currents [16–22]. Nevertheless, the search for schemes and regimes allowing fast and energy efficient DW propagation actively continues. Ferromagnetic nanotubes have been proposed as an alternative device geometry for carrying and manipulating DWs [23,24], and are attracting considerable attention not only for applications [25,26] but also from the point of view of basic theory and numerical simulations [27–32]. A key advantage of the nanotube structure is greater DW stability under strong fields [32] as compared to wire and strip geometries [4, 33], leading to a significant increase in the DW velocity. A striking phenomenon is the dependence on chirality; with the central DW vortex oppositely oriented to the applied field, the DW motion exhibits a high-field Walker-like breakdown, whereas breakdown may be suppressed or even absent when the vortex is aligned with the applied field [28–30]. In this paper, we analytically address the DW dynamics in thin ferromagnetic nanotubes under the action of an external magnetic field and derive an explicit formula for the DW propagation speed in the regimes of strong and weak penalization. Our formula reveals a nonlinear dependence of the propagation speed on the nanotube radius, and may be used as a guide in devising new experiments. Fig. 1: A sketch of a nanotube with an outer radius R and an inner radius R − w. A point on the outer surface of the nanotube is parametrized by the coordinate x along its symmetry axis and the polar angle ψ. The unit vectors ex (parallel to the symmetry axis), eψ (tangential to the surface), and eρ (normal to the surface) form a right-handed triplet. We consider an infinitely long ferromagnetic nanotube with an outer radius R and an inner radius (R − w) (see Fig. 1). The magnetization distribution at a spatial point x and time t is described by M(x, t) = Msm(x, t), where |m(x, t)| = 1 if x ∈ Ω (the point belongs to the nanotube