From the Ising model to mesoscopic studies of multiferroics containing crystal defects

CIC nanoGUNE Seminars

Roman Gröger, Institute of Physics of Materials, Brno, Czech Republic
nanoGUNE seminar room, Tolosa Hiribidea 76, Donostia - San Sebastian
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From the Ising model to mesoscopic studies of multiferroics containing crystal defects The Landau theory of phase transitions has been enormously successful at describing phase transitions in systems close to their critical points. It postulates that the free energy of a system has to be analytical and possess the symmetry of the underlying Hamiltonian. In the vicinity of the critical temperature, the free energy is then written as an expansion in terms of a well-defined order parameter that serves to map the broken symmetry phase. Many seemingly disparate problems were thus found to belong into the universal class of a simple Ising model. At present, the Landau theory continues to serve as a template for models of structural phase transitions in ferroic materials. One example is the free energy functional for ferroelastic materials developed by Barsch and Krumhansl, where the order parameter is written in terms of elastic strains. This allows for sorting the systems into universality classes for materials undergoing the same type of phase change (cubic-tetragonal, cubic-monoclinic, etc.) In this talk, we demonstrate that the concept of the Landau free energy functional can be rigorously coupled with continuum models of crystal defects. Within this novel formulation, the crystal lattice is viewed as an elastic template that is distorted by the presence of defects. In ferroelastic martensites this disorder is responsible for emergence of a complex microstructure. In piezoelectrics and piezomagnets, the presence of defects induces local depolarization (demagnetization) and thus deterioration of the ferroelectric (ferromagnetic) properties. This formulation allows for studies of the physical properties of materials with defects at the length and time scales that are not amenable to atomistic models.