Joint Hamiltonian and Stochastic Dynamics of Ferroelectric Polarization
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Аннотация
Symmetry breaking models for structural phase instability in ferroelectrics takes as the lowest level starting point if going to the limits of thermodynamics at which the time evolution and relaxation to equilibrium is affected by the uncontrollable, thermalized degrees of freedom so emerging stochastic dynamics in the system. Top challenges motivated by its fundamental and technological importance include dynamics of phase separations and the behavior of ferroelectrics at mesoscopic scale. Objective is reconciliation the Hamiltonian and stochastic dynamics by incorporating a lattice of microscopically large and macroscopically small interacting blocks each obeying Langevin dynamics so constituting a spatial mesh and capturing dynamics of temperature and field controlled polarization and electroelastic response. The regular behaviour of a single block is given by Ginzburg-Landau model Hamiltonian 1 derived, however, from density-functional theory 2 whereas the stochastic behaviour emerges by block thermal bath coupling 3.
The resulting dynamics is determined by kinetic and diffusion coefficients as well as the block block interaction. Unlike the equilibrium Ginzburg-Landau model with temperature dependent expansion coefficient(s), temperature in the block model is introduced by diffusion coefficient allowing a systematic nonequilibrium approach. The mathematical technique includes Fokker-Planck equation for model Hamiltonian 2, mapping to imaginary time Schrodinger equation and symplectic integration 4. Representative examples concern nucleation and sideway growth of a domain at reducing the temperature under the transition one (Fig. 1) and domain switching associated with motion of the domain walls and the growth of new domains with essential details revealing of the impact of electric and coupled electro-elastic fields and demonstrated in movies. Calculations are made in physical units for PbTiO3 2, 5 with kinetic and diffusion coefficients as the fitting parameters. Microscopic interpretation of these parameters is discussed.\\
1) S. Nambu, A. Sagala, Phys. Rev. B, 50, 5838 (1994).\noindent
2) N. Sai, K. M. Rabe, D. Vanderbilt, Phys. Rev. B 66 104108 (2002).\noindent
3) M.Shiino, Phys. Rev. A 36, 2393 (1987).\noindent
4) E. Klotins, Eur. Phys. J. B 50, 315-320 (2006).\noindent
5) Y.L. Li, S.Y. Hu, Z.K. Liu, L.Q. Chen, Acta Materialia 50 (2002) 395-411.\noindent
6) M. Dawber, K. M. Rabe , J. F. Scott, Rev. Mod. Phys, Vol 77, (2005).