# Inhomogeneous domain walls in spintronic nanowires

## TL;DR

This paper investigates the existence and characteristics of inhomogeneous domain walls in spintronic nanowires under spin-polarized currents, revealing new types and mechanisms through bifurcation theory and numerical analysis.

## Contribution

It introduces the concept of non-flat, inhomogeneous domain walls and provides a bifurcation-based existence proof alongside numerical continuation results.

## Key findings

- Existence of inhomogeneous domain walls with non-trivial azimuthal profiles.
- Identification of a new non-flat domain wall with oscillatory magnetization.
- Parameter mechanisms for flat and non-flat domain wall solutions below a threshold.

## Abstract

In case of a spin-polarized current, the magnetization dynamics in nanowires are governed by the classical Landau-Lifschitz equation with Gilbert damping term, augmented by a typically non-variational Slonczewski term. Taking axial symmetry into account, we study the existence of domain wall type coherent structure solutions, with focus on one space dimension and spin-polarization, but our results also apply to vanishing spin-torque term. Using methods from bifurcation theory for arbitrary constant applied fields, we prove the existence of domain walls with non-trivial azimuthal profile, referred to as inhomogeneous. We present an apparently new type of domain wall, referred to as non-flat, whose approach of the axial magnetization has a certain oscillatory character. Additionally, we present the leading order mechanism for the parameter selection of flat and non-flat inhomogeneous domain walls for an applied field below a threshold, which depends on anisotropy, damping, and spin-transfer. Moreover, numerical continuation results of all these domain wall solutions are presented.