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We focus on a dilute uniform suspension of magnetic nanoparticles in a nematic-filled micron-sized shallow well with tangent boundary conditions as a paradigm system with two coupled order parameters. This system exhibits spontaneous magnetization without magnetic fields. We numerically obtain the stable nematic and associated magnetization morphologies, induced purely by the geometry, the boundary conditions, and the coupling between the magnetic nanoparticles and the host nematic medium. Our most striking observations pertain to doma
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