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Register a new userSelf-consistent DFT+$U$+$V$ study of oxygen vacancies in SrTiO$_3$
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Contradictory theoretical results for oxygen vacancies in SrTiO$_3$ (STO) were often related to the peculiar properties of STO, which is a $d^0$ transition metal oxide with mixed ionic-covalent bonding. Here, we apply, for the first time, density functional theory (DFT) within the extended Hubbard DFT+$U$+$V$ approach, including on-site as well as inter-site electronic interactions, to study oxygen-deficient STO with Hubbard $U$ and $V$ parameters computed self-consistently via density-functional perturbation theory. Our results demonstrate that the extended Hubbard functional is a promising approach to study defects in materials with electronic properties similar to STO. Indeed, DFT+$U$+$V$ provides a better description of stoichiometric STO compared to standard DFT or DFT+$U$, the band gap and crystal field splitting being in good agreement with experiments. In turn, also the description of the electronic properties of oxygen vacancies in STO is improved, with formation energies in excellent agreement with experiments as well as results obtained with the most frequently used hybrid functionals, however at a fraction of the computational cost. While our results do not fully resolve the contradictory findings reported in literature, our systematic approach leads to a deeper understanding of their origin, which stems from different cell sizes, STO phases, the exchange-correlation functional, and the treatment of structural relaxations and spin-polarization.
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We propose a self-consistent site-dependent Hubbard $U$ approach for DFT+$U$ calculations of defects in complex transition-metal oxides, using Hubbard parameters computed via linear-response theory. The formation of a defect locally perturbs the chemical environment of Hubbard sites in its vicinity, resulting in different Hubbard $U$ parameters for different sites. Using oxygen vacancies in SrMnO$_3$ as a model system, we investigate the dependence of $U$ on the chemical environment and study its influence on the structural, electronic, and magnetic properties of defective bulk and strained thin-film structures. Our results show that a self-consistent $U$ improves the description of stoichiometric bulk SrMnO$_3$ with respect to GGA or GGA+$U$ calculations using an empirical $U$. For defective systems, $U$ changes as a function of the distance of the Hubbard site from the defect, its oxidation state and the magnetic phase of the bulk structure. Taking into account this dependence, in turn, affects the computed defect formation energies and the predicted strain- and/or defect-induced magnetic phase transitions, especially when occupied localized states appear in the band gap of the material upon defect creation.
We present a first-principles investigation of the structural, electronic, and magnetic properties of pyrolusite ($beta$-MnO$_2$) using conventional and extended Hubbard-corrected density-functional theory (DFT+$U$ and DFT+$U$+$V$). The onsite $U$ and intersite $V$ Hubbard parameters are computed using linear-response theory in the framework of density-functional perturbation theory. We show that while the inclusion of the onsite $U$ is crucial to describe the localized nature of the Mn($3d$) states, the intersite $V$ is key to capture accurately the strong hybridization between neighboring Mn($3d$) and O($2p$) states. In this framework, we stabilize the simplified collinear antiferromagnetic (AFM) ordering (suggested by the Goodenough-Kanamori rule) that is commonly used as an approximation to the experimentally-observed noncollinear screw-type spiral magnetic ordering. A detailed investigation of the ferromagnetic and of other three collinear AFM spin configurations is also presented. The findings from Hubbard-corrected DFT are discussed using two kinds of Hubbard manifolds - nonorthogonalized and orthogonalized atomic orbitals - showing that special attention must be given to the choice of the Hubbard projectors, with orthogonalized manifolds providing more accurate results than nonorthogonalized ones within DFT+$U$+$V$. This work paves the way for future studies of complex transition-metal compounds containing strongly localized electrons in the presence of pronounced covalent interactions.
We report on the observation of metallic behavior in thin films of oxygen-deficient SrTiO$_3$ - down to 9 unit cells - when coherently strained on (001) SrTiO$_3$ or DyScO$_3$-buffered (001) SrTiO$_3$ substrates. These films have carrier concentrations of up to 2$times10^{22}$ cm$^{-3}$ and mobilities of up to 19,000 cm$^2$/V-s at 2 K. There exists a non-conducting layer in our SrTiO$_{3-delta}$ films that is larger in films with lower carrier concentrations. This non-conducting layer can be attributed to a surface depletion layer due to a Fermi level pinning potential. The depletion width, transport, and structural properties are not greatly affected by the insertion of a DyScO$_3$ buffer between the SrTiO$_3$ film and SrTiO$_3$ substrate.
The electronic band structure of SrTiO$_3$ is investigated in the all-electron QS$GW$ approximation. Unlike previous pseudopotential based QS$GW$ or single-shot $G_0W_0$ calculations, the gap is found to be significantly overestimated compared to experiment. After putting in a correction for the underestimate of the screening by the random phase approximation in terms of a 0.8$Sigma$ approach, the gap is still overestimated. The 0.8$Sigma$ approach is discussed and justified in terms of various recent literature results including electron-hole corrections. Adding a lattice polarization correction (LPC) in the ${bf q}rightarrow0$ limit for the screening of $W$, agreement with experiment is recovered. The LPC is alternatively estimated using a polaron model. We apply our approach to the cubic and tetragonal phases as well as a hypothetical layered post-perovskite structure and find that the LDA (local density approximation) to $GW$ gap correction is almost independent of structure.
The origin of the 2-dimensional electron system (2DES) appearing at the (001) interface of band insulators $rm SrTiO_3$ and $rm LaAlO_3$ has been rationalized in the framework of a polar catastrophe scenario. This implies the existence of a critical thickness of polar $rm LaAlO_3$ overlayer ($4~rm u.c.$) for the appearance of the 2DES: polar catastrophe for thick $rm LaAlO_3$ overlayer is avoided either through a Zener breakdown or a stabilization of donor defects at the $rm LaAlO_3$ surface, both providing electrons to dope the substrate. The observation of a critical thickness is observed in experiments, supporting these hypotheses. Yet, there remains an open debate about which of these possible mechanisms actually occurs first. Using hybrid functional Density Functional Theory, we re-examine these mechanisms at the same level of approximation. Particularly, we clarify the role of donor defects in these heterostructures, and argue that, under usual growth conditions, electric-field driven stabilization of oxygen vacancies and hydrogen adsorbates at the LAO surface occur at a smaller LAO thickness than required for Zener breakdown.
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