Confinement and magnetic field effect on chiral ferroelectric nematic in Grandjean-Cano wedge cells

We explore the structure and magnetic field response of edge dislocations in Grandjean-Cano wedge cells filled with chiral mixtures of the ferroelectric nematic mesogen DIO. Upon cooling, the ordering changes from paraelectric in the cholesteric phase N* to antiferroelectric in the smectic SmZ_A* and to ferroelectric in the cholesteric N_F*. Dislocations of the Burgers vector b equal the helicoidal pitch P are stable in all three phases, while dislocations with b=P/2 exist only in the N* and SmZ_A*. The b=P/2 dislocations split into pairs of τ(-1/2) λ(+1/2) disclinations, while the thick dislocations b=P are pairs of nonsingular λ(-1/2) λ(+1/2) disclinations. The polar order makes the τ(-1/2) disclinations unstable in the N_F* phase, as they should be connected to singular walls in the polarization field. We propose a model of transformation of the composite τ(-1/2) line-wall defect into a nonsingular λ(-1/2) disclination, which is paired up with a λ(+1/2) line to form a b=P dislocation. The SmZ_A* behavior in the in-plane magnetic field is different from that of the N_F* and N*: the dislocations show no zigzag instability, and the pitch remains unchanged in the magnetic fields up to 1 T. The behavior is associated with the finite compressibility of smectic layers.