| Summary: | We study a model system with nematic and magnetic order, within a channel geometry modeled by an interval, $[-D, D]$. The system is characterized by a tensor-valued nematic order parameter ${{Q}}$ and a vector-valued magnetization ${{M}}$, and the observable states are modeled as stable critical points of an appropriately defined free energy which includes a nemato-magnetic coupling term, characterized by a parameter $c$. We (i) derive $L^\infty$ bounds for ${{Q}}$ and ${{M}}$; (ii) prove a uniqueness result in specified parameter regimes; (iii) analyze 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.
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