# PHASE-FIELD SIMULATIONS OF TOPOLOGICAL STRUCTURES AND TOPOLOGICAL PHASE TRANSITIONS IN FERROELECTRIC OXIDE HETEROSTRUCTURES

Open Access

- Graduate Program:
- Materials Science and Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- May 08, 2017
- Committee Members:
- Long-Qing Chen, Dissertation Advisor
- Long-Qing Chen, Committee Chair
- Venkatraman Gopalan, Committee Member
- Clive A Randall, Committee Member
- Michael T Lanagan, Outside Member

- Keywords:
- Phase-field simulation
- Ferroelectrics
- Topological structure and topological phase transition
- Oxide thin films and superlattices
- Materials by design

- Abstract:
- Ferroelectrics are materials that exhibit spontaneous electric polarization which can be switched between energy-degenerated states by external stimuli (e.g., mechanical force and electric field) that exceeds a critical value. They have wide potential applications in memories, capacitors, piezoelectric and pyroelectric sensors, and nanomechanical systems. Topological structures and topological phase transitions have been introduced to the condensed matter physics in the past few decades and have attracted broad attentions in various disciplines due to the rich physical insights and broad potential applications. Ferromagnetic topological structures such as vortex and skyrmion are known to be stabilized by the antisymmetric chiral interaction (e.g., Dzyaloshinskii-Moriya interaction). Without such interaction, ferroelectric topological structures (i.e., vortex, flux-closure, skyrmions, and merons) have been studied only recently with other designing strategies, such as reducing the dimension of the ferroelectrics. The overarching goal of this dissertation is to investigate the topological structures in ferroelectric oxide perovskites as well as the topological phase transitions under external applied forces. Pb(Zr,Ti)O3 (PZT) with morphotropic phase boundary is widely explored for high piezoelectric and dielectric properties. The domain structure of PZT tetragonal/rhombohedral (T/R) bilayer is investigated. Strong interfacial coupling is shown, with large polarization rotation to a lower symmetry phase near the T/R interface. Interlayer domain growth can also be captured, with T-domains in the R layer and R-domains in the T layer. For thin PZT bilayer with 5nm of T-layer and 20 nm of R-layer, the a1/a2 twin domain structure is formed in the top T layer, which could be fully switched to R domains under applied bias. While a unique flux-closure pattern is observed both theoretically and experimentally in the thick bilayer film with 50 nm of thickness for both T and R layers. It is revealed that the bilayer system could facilitate the motion of the ferroelastic a-domain in the top T-layer since the a-domain is not directly embedded in the substrate with high density of defects which can pin the domain wall. Excellent dielectric and piezoelectric responses are demonstrated due to the large polarization rotation and the highly mobile domain walls in both the thick and thin bilayer systems. The long-range ordered polar vortex array is observed in the (PbTiO3)n/(SrTiO3)n (PTOn/STOn with n=10~20) superlattices with combined experimental and theoretical studies. Phase-field simulations reveal the three-dimensional textures of the polar vortex arrays. The neighboring vortices rotate in the opposite directions, which extended into tube-like vortex lines perpendicular to the vortex plane. The thickness-dependent phase diagram is predicted and verified by experimental observations. The energetics (the contributions from elastic, electrostatic, gradient and Landau chemical energies) accompanying the phase transitions are analyzed in details. The dominating depolarization energy at short periodicity (n<10) favors a1/ a2 twin domain, while the large elastic relaxation and Landau energy reduction at large periodicity (n>20) leads to the formation of flux-closure domain with both 90o a/c domain walls and 180o c+/c- domain walls, counterbalancing of the individual energies at intermediate periodicities (n=10~20) gives rise to the formation of exotic vortex structure with continuous polarization rotation surrounding a singularity-like vortex core. Analytical calculations are performed, showing that the stability of the polar vortex structure is directly related to the length of Pi times bulk domain wall width, where vortex structure can be expected when the geometric length scale of the ferroelectrics is close to this value. The role of insulating STO is further revealed, which shows that a rich phase diagram can be formed by simply tuning the thickness of this layer. Wave-like polar spiral phase is simulated by substituting part of the PTO with BiFeO3 (BFO) in the PTO/STO superlattice (i.e., in a (PTO)4/(BFO)4/(PTO)4/(STO)12 tricolor system) which has demonstrate ordered polar vortex lattice. This spiral phase is made up of semi-vortex cores that are floating up-down in the ferroelectric PTO layers, giving rise to a net in-plane polarization. An increase of Curie temperature and topological to regular domain transition temperature (over 200 K) is observed, due to the higher Curie temperature and larger spontaneous polarization in BFO layers. This unidirectional spiral state can be reversibly switched by experimentally feasible in-plane field, which evolves into a metastable vortex structure in-between two spiral phases with opposite in-plane directions. The switching of polar vortex lattice under capacitor field for the (PTO)16/(STO)16 superlattice is studied, which reveals the existence of polar skyrmion state at intermediate applied bias. This is akin to the Rayleigh-Plateau instability in the fluid mechanics. A similar phenomenon is experimentally observed in the ferromagnetic system recently. The skyrmion-like structure will shrink with the further increasing of applied bias after saturation and eventually disappear given sufficiently large bias, leading to the formation of ferroelectric/ferroelastic twin domains with distinct 90o domain walls. Dimensionality cross-over is demonstrated, where a 1-D vortex core structure can be switched to the 2-D domain wall by the joint of two vortices with opposite curls. Electric-field phase diagram is plotted, showing a wide electric field region which could stabilize the metastable polar skyrmion state. This could serve as a road map for the experimental observation of the ferroelectric skyrmion state.