Critical exponent β of A₂BX₄-type crystals at the normal-incommensurate phase transition

The normal-incommensurate phase transition of K₂Z_nCl₄, Rb₂ZnCl₄ and [N(CH₃)₄]₂ZnCl₄ were studied by the linear birefringence method for determining the critical exponent, β. 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 β 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, 2β = 1.