Ultrasonic study of normal-incommensurate-commensurate phase transitions in [N(CH3)4]2MnCl4

The complete set of elastic constants of the single crystal [N(CH3)4]2MnCl4 has been measured at 15 MHz in the temperature range 250-310 K, including the normal-incommensurate transition at TI=292.3 K, the incommensurate-improper ferroelastic lock-in transition at TL=291.7 K, and the improper ferroelastic-improper ferroelastic transition at T1=266.7 K. The Landau theory has been used to explain the experimental data. In addition, the attenuation of the longitudinal wave associated with the C11 mode was measured as a function of temperature and frequency (12.7-71 MHz) around TI and analyzed in terms of a dynamic-scaling model. Above TI the results agree with both three-dimensional-Ising and mean-field theory. In the commensurate phase the critical exponents have values consistent with mean-field theory. The relaxation time of the amplitudon below TI has been determined to be τA=τA0/(TI-T) with τA04×10-10 s K.