Externally-driven transmission and collisions of domain walls in ferromagnetic wires

TL;DR

This paper derives analytical solutions for domain wall dynamics in ferromagnetic wires under external magnetic fields and electric currents, analyzing collisions and velocity control with implications for magnetic memory devices.

Contribution

It introduces a modified Hirota bilinearization method to solve the Landau-Lifshitz-Gilbert equation including dissipation, providing new insights into domain wall behavior under external stimuli.

Findings

Domain walls collide elastically below and above Walker breakdown.

External fields influence domain wall velocity and width.

Analytical relations between parameters and dynamics are established.

Abstract

Analytical multi-domain 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 the 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.