Wave-type dynamics in ferromagnetic thin films and the motion of Néel walls

Abstract

We investigate the magnetization dynamics in soft ferromagnetic films with small damping. In this case, the gyrotropic nature of Landau-Lifshitz-Gilbert dynamics and the shape anisotropy effects from stray-field interactions effectively lead to a wave-type dynamics for the in plane magnetization. We apply this result to study the motion of Néel walls in thin films and prove the existence of a traveling wave solution under a small constant forcing.

One-dimensional Néel walls under applied external fields

“…x (0) < 0 employing the same argument as in [23]. Since ϑ (0) ∈ C 2 (R) is a classical solution of (58), if we assume that ϑ (0) (0) = π 2 and ϑ (0)…”

“…Stability of geometrically constrained one-dimensional Néel walls with respect to large two-dimensional perturbations in soft materials was demonstrated asymptotically in [24]. More recently, Γ-convergence studies of the one-dimensional wall energy in the limit of very soft films and in the presence of an applied in-plane field normal to the easy axis were undertaken in [25,26], and a rigorous derivation of the effective magnetization dynamics driven by the reduced thin film energy introduced in [23] from the full three-dimensional Landau-Lifshitz-Gilbert equation was presented in [27].…”

“…It is clear that in view of the translational invariance the function ϑ (x0) (x) = ϑ (0) (x − x 0 ) with any x 0 ∈ R still belongs to A and satisfies ϑ (x0) (x 0 ) = π 2 . To conclude, we have to show that every minimizers of E in A is of the form ϑ (0) (x − x 0 ) for some x 0 ∈ R. Our argument is related to the strict convexity of the integrand in (6) written as a function of u = sin ϑ and its derivative noted in [23].…”

Reduced model for precessional switching of thin-film nanomagnets under the influence of spin torque

“…[8] for vanishing spin-current density in an infinite sample. This constitutes our reduced PDE model for magnetization dynamics in thin-film elements under the influence of out-of-plane spin currents.…”

“…Here we consider a weakly damped asymptotic regime of the Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation for a thin-film ferromagnet, in which the oscillatory nature of the in-plane dynamics is highlighted. In this regime, we derive a reduced partial differential equation (PDE) for the in-plane magnetization dynamics under applied spin-torque, which is a generalization of the underdamped wave-like model due to Capella, Melcher and Otto 8 . We then analyze the solutions of this equation under the macrospin (spatially uniform) approximation, and discuss the predictions of such a model in the context of previous numerical studies of the full LLGS equation 16 .…”