  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, boundary conditions and the coupling between the magnetic
nanoparticles and the host nematic medium. Our most striking observations
pertain to domain walls in the magnetization profile whose location can be
manipulated by the coupling and material properties, and stable interior and
boundary nematic defects, whose location and multiplicity can be tailored by
the coupling too. These novel morphologies are not accessible in uncoupled
systems and can be used for new multistable systems with singularities and
stable interfaces.
