One-dimensional ferronematics in a channel: order reconstruction, bifurcations and multistability

TL;DR

This paper investigates the complex behaviors of one-dimensional ferronematics in a channel, focusing on order reconstruction, bifurcations, and multistability through analytical and numerical methods.

Contribution

It provides new analytical bounds, uniqueness results, and stability analysis for coupled nematic and magnetic order parameters in a channel geometry.

Findings

Derives $L^ abla$ bounds for $ extbf{Q}$ and $ extbf{M}$

Establishes uniqueness regimes based on parameters

Identifies conditions for multistability and domain wall stability

Abstract

We study a model system with nematic and magnetic orders, within a channel geometry modelled by an interval, $[-D, D]$. The system is characterised by a tensor-valued nematic order parameter $\mathbf{Q}$ and a vector-valued magnetisation $\mathbf{M}$, and the observable states are modelled as stable critical points of an appropriately defined free energy. In particular, the full energy includes a nemato-magnetic coupling term characterised by a parameter $c$. We (i) derive $L^\infty$ bounds for $\mathbf{Q}$ and $\mathbf{M}$; (ii) prove a uniqueness result in parameter regimes defined by $c$, $D$ and material- and temperature-dependent correlation lengths; (iii) analyse order reconstruction solutions, possessing domain walls, and their stabilities as a function of $D$ and $c$ and (iv) perform numerical studies that elucidate the interplay of $c$ and $D$ for multistability.