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Understanding the interplay between magnetism and superconductivity is one ofthe central issues in condensed matter physics. Such interplay induced nodalstructure of superconducting gap is widely believed to be a signature of exoticpairing mechanism (not phonon mediated) to achieve unconventionalsuperconductivity, such as in heavy fermion, high $T_c$, and organicsuperconductors. Here we report a new mechanism to drive the interplay betweenmagnetism and superfluidity via the spatially anisotropic interaction. Thisscheme frees up the usual requirement of suppressing long-range magnetic orderto access unconventional superconductivity like through doping or addingpressure in solids. Surprisingly, even for the half-filling case, such schemecan lead the coexistence of superfluidity and antiferromagnetism andinterestingly an unexpected interlayer nodal superfluid emerges, which will bedemonstrated through a cold atom system composed of a pseudospin-$1/2$ dipolarfermi gas in bilayer optical lattices. Our mechanism should pave an alternativeway to unveil exotic pairing scheme resulting from the interplay betweenmagnetism and superconductivity or superfluidity.

Emergent interlayer nodal superfluidity of a dipolar fermi gas in bilayer optical lattices