Saddle-splay and periodic instability in a hybrid aligned nematic layer subjected to a normal magnetic field

-A nematic layer with opposite boundary conditions (unidirectional planar and homeotropic) is considered, having strong anchoring at the planar wall. It is known that a periodic deformation of splay-type can intervene between the aperiodic hybrid alignment and undistorted planar state as one decreases the film thickness. This periodic state occurs due to the fact that the energetic cost for a mixed twist-splay can be lower than the surface energetic cost at the homeotropic wall in the case of undistorted planar alignment. Such a situation