Soft anchoring effect and magnetic field induced transitions in homeotropic cholesteric liquid crystal layer

We study the influence of anchoring energy on the orientational structure of a cholesteric liquid crystal in a layer with soft homeotropic anchoring on the boundaries. We consider magnetic field induced transition from the uniform homeotropic nematic phase to the cholesteric phase. We show that this phase transition can occur due to the change of external magnetic field, oriented normally to the cell walls, or due to the change of the layer thickness, and can be either the first- or the second order transition. We determine the conditions of the phase transition hysteresis. We show that the variation of anchoring energy causes the change of the phase transition order, and can also lead to occurrence of the planar alignment in the layer. We also propose the method for measurement of the polar anchoring energy. We show that for some values of polar anchoring energy and the layer thickness, the initial uniform homeotropic state becomes unstable relative to small long-wave perturbations periodical along the layer.