Topological Defects in Hexagonal Manganites: Inner Structure and Emergent Electrostatics

Abstract

Diverse topological defects arise in hexagonal manganites, such as ferroelectric vortices, as well as neutral and charged domain walls. The topological defects are intriguing because their low symmetry enables unusual couplings between structural, charge, and spin degrees of freedom, holding great potential for novel types of functional 2D and 1D systems. Despite the considerable advances in analyzing the different topological defects in hexagonal manganites, the understanding of their key intrinsic properties is still rather limited and disconnected. In particular, a rapidly increasing number of structural variants is reported without clarifying their relation, leading to a zoo of seemingly unrelated topological textures. Here, we combine picometer-precise scanning-transmission-electron microscopy with Landau theory modeling to clarify the inner structure of topological defects in ErZrMnO. By performing a comprehensive parametrization of the inner atomic defect structure, we demonstrate that one primary length scale drives the morphology of both vortices and domain walls. Our findings lead to a unifying general picture of this type of structural topological defects. We further derive novel fundamental and universal properties, such as unusual bound-charge distributions and electrostatics at the ferroelectric vortex cores with emergent U(1) symmetry.

Charged domain walls in improper ferroelectric hexagonal manganites and gallates

“…S1 [36]). These findings are consistent with experimental TEM studies [23], and are important for switching dynamics as high energy DWs can only occur transiently. We note that due to the electrostatic potential across the cell model, the DW energy is inherently cell size dependent as discussed later.…”

“…Here the order parameter amplitude Q and phase Φ describe the amplitude and angle of the tilt as shown in gradient terms lead to a broadening. The DW width is quantified by the evolution of Φ through the approximate analytical solution derived by Holtz et al [23]:…”

Electrical half-wave rectification at ferroelectric domain walls

“…5a shows a neutral domain wall, visible as a deviation from the displacement patterns of the erbium ions in P and P domains as explained, e.g., in ref. 34. Density functional calculations show that the electronic structure and band gap at such walls are very similar to the bulk when considering a defect free sample ( Supplementary Fig.…”

“…36. The latter is expected to also apply to charged domain walls in hexagonal manganites due to their local strain field 34 , providing an additional handle for controlling their transport properties beyond the previously discussed electrostatics-driven electronic reconstruction phenomena 4,16 . In summary, DFT reveals that the formation of oxygen interstitials is energetically favored at neutral domain walls, while vacancies show no tendency to accumulate (not shown).…”

Electrostatic potential mapping at ferroelectric domain walls by low-temperature photoemission electron microscopy

“…In order to simulate the X-PEEM response shown in the manuscript, we developed a numerical model implementing the finite-element method similar to Ref. 29. First, we minimize the Landau potential describing the space evolution of the trimerization order parameter = ( cos Φ , sin Φ): = 2 2 + 4 4 + 1 6 ( + ′ cos 3Φ) 6 + 2 ((∇ ) 2 + 2 (∇Φ) 2 ), (S. 1)…”