Critical exponent beta of A(2)BX(4)-type crystals at the normal-incommensurate phase transition

The normal-incommensurate phase transition of K2ZnCl4, Rb2ZnCl4 and [N(CH3)(4)]2ZnCl4 were studied by the linear birefringence method for determining the critical exponent, P. Critical linear birefringence behavior can be well described by the standard 3-d XY model over the temperature range 10(-2.5) < (T-i-T)/T-i < 10(-1.5). The effect of symmetry breaking proposed by Regis et. al. was not found in our LB experiments. Therefore we could determine the critical exponent beta directly from linear birefringence data by scaling analysis. As the temperature was decreased in K2ZnCl4, the critical linear birefringence behavior asymptotically approached to the value predicted by the classical mean field theory, 2 beta = 1.