Fluctuations and Instabilities of Ferromagnetic Domain Wall pairs in an External Magnetic Field

TL;DR

This paper analytically studies the stability and fluctuations of ferromagnetic domain wall pairs under external magnetic fields, revealing their stability conditions, instability thresholds, and potential for experimental detection in thin films.

Contribution

It provides a detailed analytical analysis of soliton pair stability in ferromagnets, connecting domain wall configurations to nonlinear sigma and sine-Gordon models, and predicts experimental signatures.

Findings

Soliton-antisoliton pairs have one unstable mode, acting as critical nuclei for magnetization reversal.

Soliton-soliton pairs are stable at low fields but become unstable at high fields.

The model's static properties align with a nonlinear sigma-model, reducible to a double sine-Gordon model under certain conditions.

Abstract

Soliton excitations and their stability in anisotropic quasi-1D ferromagnets are analyzed analytically. In the presence of an external magnetic field, the lowest lying topological excitations are shown to be either soliton-soliton or soliton-antisoliton pairs. In ferromagnetic samples of macro- or mesoscopic size, these configurations correspond to twisted or untwisted pairs of Bloch walls. It is shown that the fluctuations around these configurations are governed by the same set of operators. The soliton-antisoliton pair has exactly one unstable mode and thus represents a critical nucleus for thermally activated magnetization reversal in effectively one-dimensional systems. The soliton-soliton pair is stable for small external fields but becomes unstable for large magnetic fields. From the detailed expression of this instability threshold and an analysis of nonlocal demagnetizing effects it is shown that the relative chirality of domain walls can be detected experimentally in thin ferromagnetic films. The static properties of the present model are equivalent to those of a nonlinear sigma-model with anisotropies. In the limit of large hard-axis anisotropy the model reduces to a double sine-Gordon model.