Domain-Wall Motion in Ferromagnetic Nanowires Driven by Arbitrary Time-Dependent Fields: An Exact Result

Abstract

We address the dynamics of magnetic domain walls in ferromagnetic nanowires under the influence of external time-dependent magnetic fields. We report a new exact spatiotemporal solution of the Landau-Lifshitz-Gilbert equation for the case of soft ferromagnetic wires and nanostructures with uniaxial anisotropy. The solution holds for applied fields with arbitrary strength and time dependence. We further extend this solution to applied fields slowly varying in space and to multiple domain walls. 75.78.Fg Introduction.-The motion of magnetic domain walls (DWs) in ferromagnetic nanowires has recently become a subject of intensive research in the condensed matter physics community [1]. Manipulation of DWs by external magnetic fields, and in particular, the question of how the DW propagation velocity depends on the applied field have drawn considerable attention [2][3][4].In ferromagnetic nanowires, the dynamics of the orientation of the magnetization distribution, m(x, t) (normalized so that |m| = 1), is described by the LandauLifshitz-Gilbert (LLG) equation [5]

Domain wall motion in magnetic nanowires: an asymptotic approach

“…Equation (2.4) then reduces to as studied by [15,16]. Here, x * (τ ) is a function representing the time-dependent position of the DW centre.…”

“…It is straightforward to show that exact solutions of the LLG equation (1.1) can be found in two distinct regimes of j and k 2 . When k 2 = 0, there is a solution for arbitrary j analogous to the precessing solution of field-driven motion [16] given by 15) where θ 0 is the profile given in equation (2.7). When k 2 > 0, there is a TW solution for constant j up to a certain critical value j W , analogous to the Walker solution, given by 16) where γ = (1 + K 2 cos 2 ϕ) −1/2 is the usual Walker scaling factor.…”

Inhomogeneous domain walls in spintronic nanowires

“…It is known from [13] in case β = 0 and from [12] in case c cp = 0 (and arbitrary β) that (7) admits for µ < 0 a family of explicit homogeneous DWs m 0 given by …”

Current-induced instability of domain walls in cylindrical nanowires

“…Hence, the Walker limit is the maximum velocity that a transverse DW can reach in thin strips (similar relativistic velocity limit can be found for antiferromagnetic DWs as well [11]). Interestingly, a transverse (head-tohead or tail-to-tail) DW does not suffer the Walker limit in cylindrical nanowires [3,12]; this is because the transverse DW in cylindrical nanowires can rotate freely due to the absence of easy-plane anisotropy. Therefore, we ask if there is a similar physical limit which determines the maximum velocity of the transverse DWs in cylindrical nanowires.…”