Defect chemistry and ferroelectric domain walls in hexagonal manganites
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The hexagonal manganites h-RMnO3 (R=Y, In, Sc, Ho-Lu) have been studied the last two decades for their exotic and diverse functional properties. Their large chemical flexibility makes this material class an ideal chemical playground for finetuning the functional properties with respect to doping and thermoatmospheric history. The principal goal of this work is to investigate the coupling between the defect chemistry, the electronic properties, and the ferroelectric domain structure in this material class, by combining first-principles density functional theory (DFT) calculations, and bulk measurements on polycrystalline samples. From first principles calculations and bulk measurements, Y-deficiency is found to give a decrease in the unit cell volume, while Y-excess gives an increase in the unit cell volume. The unit cell volumes for the Y-deficient systems also tend to increase for oxygen poor conditions during heat treatment, attributed to the chemical expansion associated with the formation of oxygen vacancies. Cation vacancies are found to be charge compensated by oxidation of manganese, giving rise to p-type conductivity. Fromthe experimental results, solid solubility for cation non-stoichiometry of x ∼ 0.05 for the compositions Y1–xMnO3 and YMn1–xO3 is reported. An extensive defect chemistry model for donor and acceptor doping of YMnO3 with respect to oxygen content is presented, and confirmed by first principles calculations. Donor doping is predicted to give rise to n-type conductivity in oxygen poor conditions, where the donor dopants are found to reduce manganese. In oxidizing atmospheres, donor doped systems are predicted to switch to p-type conducting for sufficiently high oxygen interstitial concentrations, where the p-type conductivity is governed by the charge compensation of the negatively charged oxygen interstitials. Oppositely, acceptor doping is predicted to give rise to p-type conductivity in oxygen rich conditions, where the acceptor dopants are found to oxidize manganese. In reducing atmospheres, acceptor doped systems are predicted to switch to n-type conducting for sufficiently high oxygen vacancy concentrations, where the n-type conductivity is governed by the charge compensation of the positively charged oxygen vacancies. The theoretical predictions are corroborated by bulk measurements on polycrystalline samples during heating and cooling in different atmospheres. The intrinsic energetics, local crystal structure, and electronic properties for the two fundamental types of ferroelectric domain walls in the hexagonal manganites, namely neutral and charged domain walls, are elaborated. A change in the ferroelectric mode phase, Φ, of ΔΦ = 60° across the walls display lower formation energies than ΔΦ = 180°, in agreement with the free-energy expansion for the hexagonal manganites. Both type of domain walls show asymmetric crystal structure behaviour with respect to R-cation termination, attributed to the resulting local chemical environment at the walls. The domain wall widths are found to be correlated with the ionic or covalent nature of the R-O bond. The conductivity for the charged walls are discussed with respect to inherent differences in bulk polarization and electronic band gap for three different material systems, using a Zener-like electrostatic breakdown model. Conducting walls are observed for small band gaps, large bulk polarizations, and large domains, while the opposite gives insulating walls. Compared to the charged domain walls, the neutral domain walls show similar electronic structure as bulk. Hence, the reported differences in the conductivity at the neutral domain walls cannot be explained from their intrinsic electronic properties. Building on the elaborated intrinsic properties for the two types of fundamental domain walls, the coupling between domain wall mobility and cation doping is discussed. The charged and neutral domain walls show similar migration energy barriers, comparable to that reported for conventional ferroelectrics. The differences in the ratio between the domain wall migration energy barriers and the formation energies imply that the field required to move the neutral walls are significantly higher than that of the charged walls. For the charged domain walls, the electrostatic potential profile between the walls change during the migration, which implies that the electronic properties for dynamic charged domain walls might differ to that of the stationary walls. The negatively charged tail-to-tail domain wall shows a strong affinity to form at donor dopants, while the positively charged head-to-head domain wall shows a strong affinity to form at acceptor dopants. This is reasoned from the electrostatic potential between the walls, where the aliovalent dopants can screen the bound charges at the charged walls reducing the electrostatic energy. The neutral domain walls show an affinity to from at different aliovalent R-cation dopants, rationalised by how the dopants and the local strain fields in the vicinity of the walls perturb the R-O bond lengths. The neutral domain wall migration energy barriers are also found to be strongly dependent on the cation defect chemistry. In the hexagonal manganites, where the domain state is governed by the R-O bonds, dopants that give shorter, and hence stronger, R-O bonds were found to increase the domain switching energy, and pin the walls. These results imply that the microscopic origin for ferroelectric domain wall pinning by defects can be predicted from any crystallographic changes that give an increased robustness of the ferroelectric domain state, and is expected to be universal for all ferroelectrics. As an approach towards large scale first principles calculations of the ferroelectric domain structure in the hexagonal manganites, a computational efficient pseudoatomic orbital basis set for YGaO3 was constructed for the large-scale first principles density functional theory code CONQUEST. The basis set was carefully tested, and was found to give satisfying materials properties compared to those obtained by using conventional first principles calculations. The crystal structure evolution and energetics for different domain wall configurations were also found to be comparable to those obtained from conventional first principles calculations. Geometry optimization for supercells with 3000+ atoms and different domain wall configurations were performed, with satisfying crystal structure evolutions even for configurations with large interface–interface interactions. This opens the possibility to model the local crystal structure and local electronic properties for complex ferroelectric domain structures, such as the topologically protected vortices, not captured by the system sizes accessible using conventional first principle calculation methods. These results reveal an intricate coupling between the defect chemistry, the electronic properties, and the ferroelectric domain structure in the hexagonal manganites. The electronic properties are mainly governed by the multivalency of manganese, where the electronic properties are determined by the balance between the cation and anion stoichiometry. The ferroelectric domain state, on the other hand, is mainly governed by the R-O bonds, where the ionic or covalent nature of the R-O bonds, as well as any perturbations in the R-O bond lengths in defect systems, determine the resulting ferroelectric domain structure. Understanding this intricate coupling between the defect chemistry, electronic properties, and ferroelectric domain state is crucial for the further development of hexagonal manganite based electronics and electrochemical devices.