Dynamics of ferromagnetic domain walls under extreme fields

Abstract

We report the existence of a new regime for domain wall motion in uniaxial and near-uniaxial ferromagnetic nanowires, characterised by applied magnetic fields sufficiently strong that one of the domains becomes unstable. There appears a new stable solution of the Landau-Lifshitz-Gilbert equation, describing a nonplanar domain wall moving with constant velocity and precessing with constant frequency. Even in the presence of thermal noise, the new solution can propagate for distances on the order of 500 times the field-free domain wall width before fluctuations in the unstable domain become appreciable. arXiv:1902.04968v3 [cond-mat.mes-hall]

Domain wall motion in axially symmetric spintronic nanowires

“…Our results match the prediction from [28] when c cp = 0, i.e., for (LLG), which is based on the so-called saddle-point approximation [15,42,54]. Our more general approach is based on weighted L 2 -spaces, the explicit expression of the absolute spectrum associated to the unstable states, and its relation to the pointwise Green's function.…”

“…Within the bistable regime, DWs can be orbitally asymptotically stable, i.e., perturbations relax back to a translate of the DW. This occurs for stable point spectrum (up to translation as well as rotation modes), which has been proven in [28] for field strength h below a threshold. Here, we slightly improve this threshold analytically and show that stability is robust for 0 < |c cp | 1.…”

“…The study of interfaces invading an unstable state, also in the context of ferromagnetic dynamics, has a long history, see e.g. [4,15,16,17,21,23,28,30,36,54]. The most accurate method for predicting the asymptotic behavior in systems of parabolic equations is based on the so-called pointwise Green's function associated with the unstable state [7,30,31], rather than the saddle-point analysis that is sufficient for the classical scalar case [15,54].…”

“…In case Ω = Ω lin , it was proven (see [49,Theorem 2] for full statement) that if |c cp | 1 then a family of inhomogeneous DWs (flat as well as non-flat ones) co-exist. We again note that the linear spreading speed and linear spreading frequency of DWs in the monostable parameter regime were determined in [28] for the case c cp = 0 utilizing a saddle-point approximation. While this is generally valid for scalar reaction-diffusion equations and the (CGL) equation, the saddle-point approach may fail for systems of PDEs, as already conjectured in [15].…”

“…In the monostable case, one expects that DWs propagate towards the unstable state [14,30,54] and thus invade it, as studied in case c cp = 0 for m 0 in [28].…”