Magneto-optical response of liquid-crystal suspensions of ferromagnetic Carbon nanotubes

Purpose. To theoretically investigate the optical response of compensated suspensions of ferromagnetic carbon nanotubes in a nematic liquid crystal induced by an external magnetic field.Methods. The problem was solved within the framework of the continuum theory, which is based on the free energy functional. To describe the orientational structure of the liquid crystal and the impurity ferromagnetic carbon nanotubes, two vector quantities were used, i.e. directors, which specify the directions of the preferred orientation of the long axes of the molecules and nanotubes. Since the work considered a compensated suspension, which is a liquid crystal analogue of an antiferromagnet, two equal volume fractions of nanotubes with magnetic moments directed parallel and antiparallel to the director of the liquid crystal were additionally taken into account. Thus, the free energy of the suspension is a functional with respect to two vector and two scalar quantities. The equilibrium states of the system were determined from the condition of minimum free energy, as a result of which a system of integro-differential equations was obtained, which could be integrated. The numerical solution of the final system of equations was carried out using the multidimensional secant method. Integration was carried out using the Simpson method.Results. A system of integral equations of orientational and magnetic equilibrium of a compensated liquid-crystal suspension of ferromagnetic carbon nanotubes was obtained. For different values of the magnetic field, the optical phase difference (phase lag) between ordinary and extraordinary beams of monochromatic light passed through a planeparallel cell with the suspension was calculated.Conclusion. Impurity carbon nanotubes, which are additionally filled or covalently functionalized with magnetic particles, are capable of significantly enhancing the magneto-orientational response of the nematic matrix compared to a pure liquid crystal. This allows us to make a prediction about the potential use of liquid crystal suspensions of ferromagnetic carbon nanotubes in magneto-optical devices.