  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.
