High Frequency Response Of Ferroelectric 90° Domain Walls And Domain Structures In Multiferroic RMnO₃:A Phase-field Simulation

Domain wall is a type of topological defect that occurs whenever a discrete symmetry is spontaneously broken.In condensed matter physics,variation of lattice symmetry imposes substantial influence on the physical properties and emergence of new phase.Thus,a study of domain structure and domain wall dynamics is important for understanding materials microstructures and also manipulating the performance of materials.In conventional ferroelectrics,domain structure can be directly identified using various microscopies.However,a characterization of domain wall motion in high frequency electric field can only be done indirectly through,such as measuring the dielectric response of a macroscopic sample.The local contribution of domain wall motion to the dielectric response is hard to measure experimentally.On the other hand,in multiferroic materials,the strong coupling between magnetic order and polarization enables complex domain structures.However,due to the low transition temperature and weak polarization,it is extremely hard to observe or study the structure of these domains in these multiferroics.Phase-field approach is an effective mesoscale simulation technique widely used to track microstructure evolution of a range of materials.It assumes that phases transit continuously in space with no singularity.Without any presumption on domain morphology,phase-field model thus can be applied to any materials regardless of details of the underlying interactions.This thesis focuses on using phase-field model to study the domain structures and associated effects on physical properties of different systems,and will illustrate how the 900 ferroelectric domain wall responds to high frequency external field stimulation and the domain structure in multiferroics of cycloidal spin order.In the first chapter,the phase-field model and related computation methods are introduced.As phenomenological theories have been used to study the ferroelectrics for many years,we start our thesis from the basic ferroelectric transition theory to introduce the physics picture of each phenomenological energy term in phase-field model and also the relevant numerical computation methods.After that,we discuss the evolution equations for phase-field model,Monte Carlo method,and TDGL equation.Then the two kinds of parallel computations are also discussed.In the second chapter,the 90° ferroelectric domain wall response under high frequency electric field stimulation is studied.An algorithm calculating the ac dielectric constant and its real-space distribution based on TDGL equation is developed.The anisotropic distribution of dielectric constant is firstly studied.We further demonstrate that regions near domain walls have higher dielectric response due to the domain wall motion in external field.Then the domain wall motion in strained lattice and the corresponding effect on dielectric response are discussed.Our results show that tensile strains suppress domain wall motion and reduce the dielectric response,while slightly compressive strains enhance the dielectric response.In the third chapter,the domain structure in multiferroics of cycloidal spin order is studied.A phase-field model for these multiferroics is proposed.Using this model,we first study the domain structure in thin film RMnO₃.A type of 180° head-to-head/tail-to-tail ferroelectric domain structure is identified.The responses of this domain structure to external electric and magnetic fields are also discussed.Then we study the domain structure in 3D system.The domain structures for different CS planes are simulated.At last,we discuss the underlying mechanism of those domain structures.The magnetic origin of polarization is highlighted.The forth chapter is devoted to the conclusion and perspectives.