Relaxation process in the photoinduced neutral-ionic paraelectric-ferroelectric phase transition in tetrathiafulvalene-p-chloranil

To find characteristic properties of relaxation process in the neutral-ionic, paraelectric-ferroelectric phase transition in the charge-transfer complex, tetrathiafulvalene-p-chloranil, we investigate stochastic process in the spin 1 anisotropic Blume-Emery-Griffith model [Phys. Rev. A 4, 1071 (1971)]. We assume that spins obey the Markov process which is described by the master equation with the transfer probability 1/tau exp[-(beta/2)Delta H], where Delta H is the energy difference for the transfer. We derive time-evolution equations from two standpoints. One is the mean-field approximation (MFA) and the other is an extension of the Saito-Kubo treatment to the spin 1 and anisotropic case, which improves MFA. Solving the equations numerically, we have found highly anisotropic relaxations during the neutral-ionic phase transition: the interchain ordering develops much more slowly than the intrachain one. In contrast, the ionic-neutral phase transition proceeds rather isotropically.