Magnetic field induced bistability in distorted nematic ground states

Abstract

Previous theoretical studies are extended to consider bistability of director orientations induced by changing the tilt of a magnetic field applied to a nematic sample. The ground state configuration which is assumed to be twisted, with the director tilted at the sample planes, can be one of two kinds—S ₁ and S ₂. The rigid anchoring hypothesis is employed throughout. When the field is sufficiently strong there occur two independent branches over which the distortion varies as the magnetic tilt is changed and these branches generally overlap over the bistable region. When the ground state twist is high enough, the bistable region can disappear altogether leaving a gap of no overlap between the two branches. Linear stability analysis shows that the static orientation tends to become unstable against linear perturbations when the magnetic tilt crosses the edges of the gap. It is possible that the distortion changes irreversibly from the S ₁ type (or S ₂ type) to one of S ₂ type (or S ₁ type) causing a considerable lowering of the overall twist. Results for positive diamagnetic anisotropy materials (χ _A > 0) are compared with those for negative χ _A materials. When the ground state is of the S ₂ type, a sufficiently strong field applied along certain directions can produce a transition at a threshold above which the distortion becomes asymmetric relative to the sample centre. The case of chiral nematics and that of weak anchoring are briefly reviewed.