Externally driven transmission and collisions of domain walls in ferromagnetic wires

Abstract

Analytical multidomain solutions to the dynamical (Landau-Lifshitz-Gilbert) equation of a one-dimensional ferromagnet including an external magnetic field and spin-polarized electric current are found using the Hirota bilinearization method. A standard approach to solve the Landau-Lifshitz equation (without the Gilbert term) is modified in order to treat the dissipative dynamics. I establish the relations between the spin interaction parameters (the constants of exchange, anisotropy, dissipation, external-field intensity, and electric-current intensity) and the domain-wall parameters (width and velocity) and compare them to the results of the Walker approximation and micromagnetic simulations. The domain-wall motion driven by a longitudinal external field is analyzed with especial relevance to the field-induced collision of two domain walls. I determine the result of such a collision (which is found to be an elastic one) on the domain-wall parameters below and above the Walker breakdown (in weak- and strong-field regimes). Single-domain-wall dynamics in the presence of an external transverse field is studied with relevance to the challenge of increasing the domain-wall velocity below the breakdown.

Domain-wall-assisted giant magnetoimpedance of thin-wall ferromagnetic nanotubes

“…Since the in-plane anisotropy field is dominated by the stray-field contribution; H M = M s −H K ≈ M s , for a thinwall Co nanotube, with α = 0.05, one estimates τ 1D = 0.4ns. Note that, in relevant evaluations for soft-magnetic nanostripes [28,37,38], H M = 2H W /α, where H W denotes the critical field of the Walker breakdown, while, following [39], for simple DWs (without vortex-like singularities), H W = αM s /2, thus, the relation H M ≈ M s is valid, (in the presence of singularities inside DW; H W < αM s /2, [28]). When inducing MI in long nanotubes via oscillations of the DW position (the interaction of DW with the tube ends is negligible), the relaxation rate Γ must be smaller than the circular frequency, (the underdamped oscillations regime), which gives the lower bound on the AC frequency ν > Γ/2π = 2.5GHz.…”

“…For a Co tube of the length of 3µm and of the DW width ∆ ≈ 15nm, (∆ ≈ l K ≡ A ex /|K| following Appendix A, while A ex = 3.3 · 10 −11 J/m, K = −1.5 · 10 5 J/m 3 ), in the limit of thick-wall tube (a nanowire); δ → 1, the critical frequencies ν c2 = 6.2GHz and ν c1 = 3.9GHz are the minimum and maximum frequencies of the regimes of stable "in-phase" oscillations of the DW position, respectively. Note that the presence of the external longitudinal field influences the DW width [38], thus, shifting the eigenfrequency of the oscillator ω 0 and the critical frequencies ν c1 , ν c2 upward. In the limit of thin-wall tube; δ → 0, one finds ν c1 = 0 and ν c2 = Γ/2π = 2.5GHz, which result is almost independent of the tube length.…”

Study of the single domain‐wall structure in glass‐coated microwires

“…One possible explanation could be given in terms of the domain wall width variation with an applied transversal field. The transversal field drives widening or shrinking of the transverse domain wall (with dependence on whether the field is parallel or antiparallel to the domain-wall magnetization), thus, influencing the domain-wall mobility [39,40]. This is also confirmed by measurements of domain-wall dynamics in different directions of a transversal field for two types of domain walls (head-to-head or tailto-tail), see Fig.…”

Externally driven transformations of vortex textures in flat submicrometer magnets

“…39,40 Defining θ ≡ arctan(q /k ), via (6), one finds k = −q tan(θ ) and k 2 − q 2 = β 1 /{J [1 + tan 2 (θ )]}. Also, I assume the magnetization orderings on both the stripe edges to be similar; thus, the phase factor on the right-hand side of (7a) changes by nπ along the DW line k x + q z = 0 between its ends, where n = 1,2, .…”