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It was suggested that the two consecutive metamagnetic transitions and thelarge residual resistivity discovered in Sr$_3$Ru$_2$O$_7$ can be understoodvia the nematic order and its domains in a single layer system. However, arecently reported anisotropy between two longitudinal resistivities induced bytilting the magnetic field away from the c-axis cannot be explained within thesingle layer nematic picture. To fill the gap in our understanding within thenematic order scenario, we investigate the effects of bilayer coupling andin-plane magnetic field on the electronic nematic phases in a bilayer system.We propose that the in-plane magnetic field in the bilayer system modifies theenergetics of the domain formation, since it breaks the degeneracy of twodifferent nematic orientations. Thus the system reveals a pure nematic phasewith a resistivity anisotropy in the presence of an in-plane magnetic field. Inaddition to the nematic phase, the bilayer coupling opens a novel route to ahidden nematic phase that preserves the x-y symmetry of the Fermi surfaces.

Meta-nematic transitions in a bilayer system: Application to the bilayer ruthenate