Field driven ferroelectric–ferroelectric transition: Evidence of antiferroelectric Goldstone mode in the SmC  A phase Muklesur Rahman a , A. Mukherjee a , Atsushi Yoshizawa b , B.K. Chaudhuri a, * a Department of Solid State Physics, Indian Association for the Cultivation of Science, Kolkata 700 032, India b Department of Materials Science and Technology, Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan Received 15 May 2007; in final form 8 October 2007 Available online 12 October 2007 Abstract The field (E) driven ferroelectric–ferroelectric (F + –F  ) transition process in ferroelectric SmC * and antiferroelectric SmC  A phases of liquid crystalline material viz. 4 0 -octyloxybiphenyl-4-carboxylate (MOPBIC) has been studied by measuring dielectric permittivity at dif- ferent polarizing states during the transition. It is observed that, the interaction between E and ferroelectric polarization, in the SmC * , phase governs the F–F transition, whereas in the SmC  A phase, the combination of successive coupling of E with antiferroelectric polar- ization and dielectric anisotropy is responsible for the same transition. In the SmC  A phase there exists antiferroelectric Goldstone mode in analogy with the ferroelectric Goldstone mode in the SmC * phase. Ó 2007 Elsevier B.V. All rights reserved. 1. Introduction Fukuda and co-workers [1] discovered antiferroelectric liquid crystal (SmC  A or AFLC) after 14 years of the discov- ery of ferroelectric liquid crystals (SmC * or FLC) made by Mayer [2]. Both the phases possess chiral molecules arranged in layers with directors (n) tilted at an angle (h) with respect to the layer normal. The C 2 symmetry of each smectic layer gives rise to a spontaneous polarization (P S ) along C 2 axis. The only structural difference between these two phases is that in the SmC  A phase, orientations of the molecules in successive layers are almost anti-parallel to each others [1,3,4]. The molecules in both the FLC and AFLC materials, under sufficiently high external electric field (E) applied along the smectic layer are aligned with each other along the applied field maintaining a fixed tilt angle known as the field induced ferroelectric (F + or F  ) state. The tilting direction changes, if the polarity of E changes. Therefore, the molecules as well as the polarization vector (P) can switch between these two high field ferroelectric states (F + M F  ) by changing the polarity of the applied field (±E). Fig. 1 shows the orientation of the molecules at differ- ent polarizing states (±E and E = 0) for the (a) SmC * and (b) SmC  A phases, respectively. The switching current behavior [5,6] shows that in FLCs, the F + –F  transition occurs directly through a zero polarizing state, whereas in AFLCs, the F + –F  transition does not occur directly, but passes through an antiferroelectric state (AF), in other words, the F + –F  transition occurs in two steps: F + –AF (or F–AF) followed by the AF–F transition. Such a field induced F + M F  transition results in characterizing single and double hysteresis loops in the polarization–voltage (P–V) behavior for the FLC and AFLC systems [7–9], respectively. In SmC * phase, the transition occurs due to the coupling between the E and the polarization vector [7]. Presence of an AF state makes the polarization reversal process, in the SmC  A phase, more complicated than that in the SmC * phase. Although there have been a number of reports on the field induced helix unwinding in the SmC  A phase, the mechanism of field driven F + –F  transition is not well understood. From dielectric studies, Moritake 0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.10.027 * Corresponding author. Fax: +91 33 24732805. E-mail address: sspbkc@iacs.res.in (B.K. Chaudhuri). www.elsevier.com/locate/cplett Available online at www.sciencedirect.com Chemical Physics Letters 449 (2007) 92–95