Nematic liquid crystals in high magnetic field: Quenching of the transverse fluctuations

The partial quenching of the fluctuations of orientation of nematic layers by very large magnetic fields predicted by de Gennes and leading to increased birefringence has received a first experimental verification by Poggi and Filippini. In this paper a detailed account of this effect is given: the progressive disappearance of the induced-excess-birefringence (IEB) effect near a second-order smectic transition is connected quantitatively with the divergence of the bend elastic constant. As the isotropic phase is approached from below, the increase of IEB is connected with the decrease of the elastic constants. The IEB varies with field as ${\mathrm{}\left|H\right|\mathrm{}}^u$ with $u=1\mathrm{}\pm 0.02$ over the whole nematic range. This critical-exponent determination is closely connected with the problem of the divergence of the longitudinal susceptibility in magnetic systems where both "semiclassical" and renormalization-group approaches predict a divergence in $H^{-\frac{1}{2}}$ in three dimensions. As no data seem to be available for the magnetic problem, the linear form obtained here provides a first experimental test of the validity of both approaches based on the quenching of transverse magnetization fluctuations by a field. Departures from the de Gennes model observed near $T_{\mathrm{NI}}$, as well as deviations of the induced birefringence, observed in the same experiments, from the mean-field behavior in the isotropic phase above the nematic transition, emphasize the need for new theoretical description of this weakly first-order phase transition.