Lifshitz point in the phase diagram of a ferroelectric liquid crystal in an external magnetic field

The Lifshitz point in the (H,T) phase diagram of a ferroelectric liquid crystal in a transverse magnetic field has been determined using photon correlation spectroscopy and linear electrooptic response measurements. The extrapolated Lifshitz magnetic field is $25(1\pm 0.1)\mathrm{T}$ for a smectic-$C^{*}$ material with an unperturbed helical period of ≈6 μm, and the Lifshitz point is located ≈100 mK above the zero-field transition temperature. We have observed the reentrant helical modulated smectic-$C^{*}$ phase just below the λ line. The width of this phase is 100 mK at the low temperature critical field $H_c$ and decreases continuously to zero as we approach the Lifshitz point. The phase boundary between the reentrant phase and the smectic-A phase is of second order, whereas the phase boundary with the unwound smectic-$C^{*}$ phase is of first order far away from the Lifshitz point and becomes of second order close to the Lifshitz point. The order parameter dynamics is discussed within the Landau theory.