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Register a new userThe structure of electronic polarization and its strain dependence
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The $phi(kpp)sim kpp$ relation is called polarization structure. By density functional calculations, we study the polarization structure in ferroelectric perovskite PbTiO$_3$, revealing (1) the $kpp$ point that contributes most to the electronic polarization, (2) the magnitude of bandwidth, and (3) subtle curvature of polarization dispersion. We also investigate how polarization structure in PbTiO$_3$ is modified by compressive inplane strains. The bandwidth of polarization dispersion in PbTiO$_3$ is shown to exhibit an unusual decline, though the total polarization is enhanced. As another outcome of this study, we formulate an analytical scheme for the purpose of identifying what determine the polarization structure at arbitrary $kpp$ points by means of Wannier functions. We find that $phi(kpp)$ is determined by two competing factors: one is the overlaps between neighboring Wannier functions within the plane {it perpendicular} to the polarization direction, and the other is the localization length {it parallel} to the polarization direction. Inplane strain increases the former while decreases the latter, causing interesting non-monotonous effects on polarization structure. Finally, polarization dispersion in another paradigm ferroelectric BaTiO$_3$ is discussed and compared with that of PbTiO$_3$.
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We present a theory of local electric polarization in crystalline solids and apply it to study the case of wurtzite group-III nitrides. We show that a local value of the electric polarization, evaluated at the atomic sites, can be cast in terms of a summation over nearest-neighbor distances and Born effective charges. Within this model, the local polarization shows a direct relation to internal strain and can be expressed in terms of internal strain parameters. The predictions of the present theory show excellent agreement with a formal Berry phase calculation for random distortions of a test-case CuPt-like InGaN alloy and InGaN supercells with randomly placed cations. While the present level of theory is appropriate for highly ionic compounds, we show that a more complex model is needed for less ionic materials, in which the strain dependence of Born effective charges has to be taken into account. Moreover, we provide ab initio parameters for GaN, InN and AlN, including hybrid functional values for the piezoelectric coefficients and the spontaneous polarization, which we use to accurately implement the local theory expressions. In order to calculate the local polarization potential, we also present a point dipole method. This method overcomes several limitations related to discretization and resolution which arise when obtaining the local potential by solving Poissons equation on an atomic grid. Finally, we perform tight-binding supercell calculations to assess the impact of the local polarization potential arising from alloy fluctuations on the electronic properties of InGaN alloys. In particular, we find that the large upward bowing with composition of the InGaN valence band edge is strongly influenced by local polarization effects. Furthermore, our analysis allows us to extract composition-dependent bowing parameters for the energy gap and valence and conduction band edges.
The renormalization of electronic eigenenergies due to electron-phonon coupling is sizable in many materials with light atoms. This effect, often neglected in ab-initio calculations, can be computed using the perturbation-based Allen-Heine-Cardona theory in the adiabatic or non-adiabatic harmonic approximation. After a short description of the numerous recent progresses in this field, and a brief overview of the theory, we focus on the issue of phonon wavevector sampling convergence, until now poorly understood. Indeed, the renormalization is obtained numerically through a q-point sampling inside the BZ. For q-points close to G, we show that a divergence due to non-zero Born effective charge appears in the electron-phonon matrix elements, leading to a divergence of the integral over the BZ for band extrema. Although it should vanish for non-polar materials, unphysical residual Born effective charges are usually present in ab-initio calculations. Here, we propose a solution that improves the coupled q-point convergence dramatically. For polar materials, the problem is more severe: the divergence of the integral does not disappear in the adiabatic harmonic approximation, but only in the non-adiabatic harmonic approximation. In all cases, we study in detail the convergence behavior of the renormalization as the q-point sampling goes to infinity and the imaginary broadening parameter goes to zero. This allows extrapolation, thus enabling a systematic way to converge the renormalization for both polar and non-polar materials. Finally, the adiabatic and non-adiabatic theory, with corrections for the divergence problem, are applied to the study of five semiconductors and insulators: a-AlN, b-AlN, BN, diamond and silicon. For these five materials, we present the zero-point renormalization, temperature dependence, phonon-induced lifetime broadening and the renormalized electronic bandstructure.
A combined experimental and computational investigation of coupling between polarization and epitaxial strain in highly polar ferroelectric PbZr_0.2Ti_0.8O_3 (PZT) thin films is reported. A comparison of the properties of relaxed (tetragonality c/a = 1.05) and highly-strained (c/a = 1.09) epitaxial films shows that polarization, while being amongst the highest reported for PZT or PbTiO_3 in either film or bulk forms (P_r = 82 microC/cm^2), is almost independent of the epitaxial strain. We attribute this behavior to a suppressed sensitivity of the A-site cations to epitaxial strain in these Pb-based perovskites, where the ferroelectric displacements are already large, contrary to the case of less polar perovskites, such as BaTiO_3. In the latter case, the A-site cation (Ba) and equatorial oxygen displacements can lead to substantial polarization increases.
The effects of tetragonal strain on electronic and magnetic properties of strontium-doped lanthanum manganite, La_{2/3}Sr_{1/3}MnO_3 (LSMO), are investigated by means of density-functional methods. As far as the structural properties are concerned, the comparison between theory and experiments for LSMO strained on the most commonly used substrates, shows an overall good agreement: the slight overestimate (at most of 1-1.5 %) for the equilibrium out-of-plane lattice constants points to possible defects in real samples. The inclusion of a Hubbard-like contribution on the Mn d states, according to the so-called LSDA+U approach, is rather ineffective from the structural point of view, but much more important from the electronic and magnetic point of view. In particular, full half-metallicity, which is missed within a bare density-functional approach, is recovered within LSDA+U, in agreement with experiments. Moreover, the half-metallic behavior, particularly relevant for spin-injection purposes, is independent on the chosen substrate and is achieved for all the considered in-plane lattice constants. More generally, strain effects are not seen to crucially affect the electronic structure: within the considered tetragonalization range, the minority gap is only slightly (i.e. by about 0.1-0.2 eV) affected by a tensile or compressive strain. Nevertheless, we show that the growth on a smaller in-plane lattice constant can stabilize the out-of-plane vs in-plane e_g orbital and significatively change their relative occupancy. Since e_g orbitals are key quantities for the double-exchange mechanism, strain effects are confirmed to be crucial for the resulting magnetic coupling.
We investigated the crystal and electronic structures of ferroelectric Bi4Ti3O12 (BiT) single crystalline thin films site-specifically substituted with LaCoO3 (LCO). The epitaxial films were grown by pulsed laser epitaxy on NdGaO3 and SrTiO3 substrates to vary the degree of strain. With increasing the LCO substitution, we observed a systematic increase in the c-axis lattice constant of the Aurivillius phase related with the modification of pseudo-orthorhombic unit cells. These compositional and structural changes resulted in a systematic decrease in the band gap, i.e., the optical transition energy between the oxygen 2p and transition metal 3d states, based on a spectroscopic ellipsometry study. In particular, the Co 3d state seems to largely overlap with the Ti t2g state, decreasing the band gap. Interestingly, the applied tensile strain facilitates the band gap narrowing, demonstrating that epitaxial strain is a useful tool to tune the electronic structure of ferroelectric transition metal oxides.
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