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We study a model system with nematic and magnetic orders, within a channelgeometry modelled by an interval, $[-D, D]$. The system is characterised by atensor-valued nematic order parameter $\mathbf{Q}$ and a vector-valuedmagnetisation $\mathbf{M}$, and the observable states are modelled as stablecritical points of an appropriately defined free energy. In particular, thefull energy includes a nemato-magnetic coupling term characterised by aparameter $c$. 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 theirstabilities as a function of $D$ and $c$ and (iv) perform numerical studiesthat elucidate the interplay of $c$ and $D$ for multistability.

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