Merons in strained PbZr0.2Ti0.8O3 thin films: Insights from phase-field simulations

Materials exhibiting nontrivial topological spin textures known as merons attract considerable interest for their fascinating underlying physics and promising device applications. The ${\mathrm{PbTiO}}_{3}$ family of compounds is known to host ferroelectric, ferroelastic, and piezoelectric polar orders and possess topological domain structures that are sensitive to external conditions. Here, we examine the polar states in ${\mathrm{PbZr}}_{0.2}{\mathrm{Ti}}_{0.8}{\mathrm{O}}_{3}$ (PZT) thin films and explore the influence of film thickness and epitaxial strain via phase-field modeling under short-circuit (sc) and open-circuit (oc) boundary conditions. In this paper, we uncovered four distinct meron states in ultrathin films with tensile strains. Under the sc boundary condition, there is an intermediate meron bubble texture comprising a twisted N\'eel-like and Bloch-like meron texture with a distinct helicity and a meron bubble pair texture combining two intermediate merons along the $z$ axis. Under the oc boundary condition, there is an antimeron bubble texture with negative winding numbers and an achiral topology, and a trimeron bubble texture with two antimeron bubbles and one meron bubble. These simulation results show that strain and film thickness have a major impact on the polarization strength and topology to dictate the formation and transition of meron phases in PZT thin films. The insights obtained in this paper may help elucidate and design materials with tailored and tunable microscopic and mesoscopic polar topological structures.