Ferromagnetic liquid crystals for magnetic field visualisation

In this paper, we demonstrate how to apply recently discovered ferromagnetic nematic liquid crystal for visualisation of magnetic fields. The material exhibits strong optical response to both external electric and magnetic fields, which gives us an opportunity to use it for the detection of an area of magnetic vector field in a way that both, the magnitude and the direction of a given field can be simultaneously measured. We discuss the physical model that describes the behaviour of ferromagnetic liquid crystal placed in a liquid crystal cell and demonstrate the method of extracting the information about an arbitrary magnetic field from the combination of magneto-optic and electro-optic response of the sample placed in that field. We have applied the principle to a special case, where magnetic field was visualised on a 2D area near a cylindrical permanent magnet.