Linear birefringence behavior of-type ferroic crystals in the normal-incommensurate phase transition

Critical behavior of linear birefringence was studied in the normal-incommensurate phase transition of various (Formula presented)-type crystals. We considered the fluctuation effect in the scaling analysis so that we could obtain a precise value of the critical exponent (Formula presented) from linear birefringence measurements. The numerical values of (Formula presented) obtained from our experiment were (Formula presented). These results are in agreement with the previous theoretical prediction which suggests that the normal-incommensurate phase transition of (Formula presented)-type crystals belongs to the universality class of the three-dimensional (3D) (Formula presented) model. Beyond the critical region, we observed crossover from 3D (Formula presented)-like behavior into classical Landau-like behavior, (Formula presented), in (Formula presented) and (Formula presented).