Behaviour of twist-bend nematic structure under a uniform magnetic field

From the elastic point of view, the twist-bend nematic phase, (N-TB), has a ground state characterised by a spontaneous bend with a precession of the director n along the direction of an axis t. The tilt angle formed between the director n and the axis t gives rise to a heliconical structure with a nanometric helical pitch p. Using an elastic continuum theory recently proposed as an extension of the Frank energy for these materials, we investigate the influence of an external magnetic field on the pitch of the N-TB phase. For a material with positive magnetic susceptibility anisotropy, when the magnetic field H is perpendicular to t, it is shown that the pitch of the nematic director n precession increases with H, and at a critical value of it becomes infinite as in a cholesteric liquid crystal, that is, one gets a uniform orientation of n. Our results include the behaviour of a cholesteric under field as a limiting case, and are obtained in the simple case where is assumed as uniform throughout the sample.