Threshold magnetic fields and Fréedericksz transition in a ferronematic

Continuum theory is used to analyze the effect of an applied magnetic field on a ferronematic (i.e. dilute suspension of needle-like magnetic particles in nematic liquid crystal) with soft homeotropic anchoring between the ferroparticles and the director, and positive diamagnetic anisotropy of the liquid-crystalline matrix. It is shown that in infinite ferronematic a peculiar Freedericksz-like transition takes place, at which by a threshold way the conditions of coupling on magnetic particles vary from homeotropic anchoring to planar one. The Freedericksz transition field and saturation field are found as a functions of material parameters of a suspension. The continuum theory predicts the existence of three ferronematic phase (homeotropic, angular, and planar) with different relative orientations of the director and magnetization. The orientational structure of these ferronematic phases is studied.