Influence of a Realistic Multiorbital Band Structure on Conducting Domain Walls in Perovskite Ferroelectrics

TL;DR

This study demonstrates that the morphology of conducting domain walls in ferroelectrics is significantly influenced by the multiorbital band structure, affecting domain wall shape and electron distribution at various doping levels.

Contribution

It introduces a coupled modeling approach combining LGD, tight-binding, and Gauss' law to analyze how multiorbital band structures affect domain wall morphologies in doped perovskite ferroelectrics.

Findings

Low electron densities pin electron gas to surfaces with Kittel-like domains.

Increased electron density leads to zigzag and flat domain wall structures.

Multiorbital band structure enhances screening and alters domain wall morphology.

Abstract

Domain wall morphologies in ferroelectrics are believed to be largely shaped by electrostatic forces. Here, we show that for conducting domain walls, the morphology also depends on the details of the charge-carrier band structure. For concreteness, we focus on transition-metal perovskites like BaTiO$_3$ and SrTiO$_3$. These have a triplet of $t_{2g}$ orbitals attached to the Ti atoms that form the conduction bands when electron doped. We solve a set of coupled equations -- Landau-Ginzburg-Devonshire (LGD) equations for the polarization, tight-binding Schr\"odinger equations for the electron bands, and Gauss' law for the electric potential -- to obtain polarization and electron density profiles as a function of electron density. We find that at low electron densities, the electron gas is pinned to the surfaces of the ferroelectric by a Kittel-like domain structure. As the electron density increases, the domain wall evolves smoothly through a zigzag head-to-head structure, eventually becoming a flat head-to-head domain wall at high density. We find that the Kittel-like morphology is protected by orbital asymmetry at low electron densities, while at large electron densities the high density of states of the multiorbital band structure provides effective screening of depolarizing fields and flattens the domain wall relative to single-orbital models. Finally, we show that in the zigzag phase, the electron gas develops tails that extend away from the domain wall, in contrast to na\"{i}ve expectations.