Magnetic order in the Hubbard model in three dimensions and the crossover to two dimensions.

Systems of fermions described by the three-dimensional (3D) repulsive Hubbard model on a cubic lattice have recently attracted considerable attention due to their possible experimental realization via cold atoms in an optical lattice. Analytical and numerical results are limited away from half-filling. We study the ground state of the doped system from weak to intermediate interaction strengths within the generalized Hartree-Fock approximation. The exact solution to the self-consistent-field equations in the thermodynamic limit is obtained and the ground state is shown to exhibit antiferromagnetic order and incommensurate spin-density waves (SDW). At low interaction strengths, the SDW has unidirectional character with a leading wavevector along the [100]-direction, and the system is metallic. As the interaction increases, the system undergoes a simultaneous structural and metal-to-insulator transition to a unidirectional SDW state along the [111]-direction, with a different wavelength. We systematically determine the real and momentum space properties of these states. The crossover from 3D to two dimensions (2D) is then studied by varying the inter-plane hopping amplitude, which can be experimentally realized by tuning the distance between a stack of square-lattice layers. Detailed comparisons are made between the exact numerical results and predictions from the pairing model, a variational ansatz based on the pairing of spins in the vicinity of the Fermi surface. Most of the numerical results can be understood quantitatively from the ansatz, which provides a simple picture for the nature of the SDW states.

Finite-temperature properties of Ba(Zr,Ti)O3 relaxors from first principles.

A first-principles-based technique is developed to investigate the properties of Ba(Zr,Ti)O(3) relaxor ferroelectrics as a function of temperature. The use of this scheme provides answers to important, unresolved and/or controversial questions such as the following. What do the different critical temperatures usually found in relaxors correspond to? Do polar nanoregions really exist in relaxors? If yes, do they only form inside chemically ordered regions? Is it necessary that antiferroelectricity develop in order for the relaxor behavior to occur? Are random fields and random strains really the mechanisms responsible for relaxor behavior? If not, what are these mechanisms? These ab initio based calculations also lead to deep microscopic insight into relaxors.

Spin- and charge-density waves in the Hartree-Fock ground state of the two-dimensional Hubbard model.

The ground states of the two-dimensional repulsive Hubbard model are studied within the unrestricted Hartree-Fock (UHF) theory. Magnetic and charge properties are determined by systematic, large-scale, exact numerical calculations, and quantified as a function of electron doping, h. In the solution of the self-consistent UHF equations, multiple initial configurations and simulated annealing are used to facilitate convergence to the global minimum. New approaches are employed to minimize finite-size effects in order to reach the thermodynamic limit. At low to moderate interacting strengths and low doping, the UHF ground state is a linear spin-density wave (l-SDW), with antiferromagnetic order and a modulating wave. The wavelength of the modulating wave is 2/h. Corresponding charge order exists but is substantially weaker than the spin order, hence holes are mobile. As the interaction is increased, the l-SDW states evolve into several different phases, with the holes eventually becoming localized. A simple pairing model is presented with analytic calculations for low interaction strength and small doping, to help understand the numerical results and provide a physical picture for the properties of the SDW ground state. By comparison with recent many-body calculations, it is shown that, for intermediate interactions, the UHF solution provides a good description of the magnetic correlations in the true ground state of the Hubbard model.

First-principles calculations of 17O nuclear magnetic resonance chemical shielding in Pb(Zr(1/2)Ti(1/2))O3 and Pb(Mg(1/3)Nb(2/3))O3: linear dependence on transition-metal/oxygen bond lengths.

First-principles density functional theory oxygen chemical shift tensors were calculated for A(B,B')O(3) perovskite alloys Pb(Zr(1/2)Ti(1/2))O(3) (PZT) and Pb(Mg(1/3)Nb(2/3))O(3) (PMN). Quantum chemistry methods for embedded clusters and the gauge including projector augmented waves (GIPAW) method [C. J. Pickard and F. Mauri, Phys. Rev. B 63, 245101 (2001)] for periodic boundary conditions were used. Results from both methods are in good agreement for PZT and prototypical perovskites. PMN results were obtained using only GIPAW. Both isotropic δ(iso) and axial δ(ax) chemical shifts were found to vary approximately linearly as a function of the nearest-distance transition-metal/oxygen bond length, r(s). Using these results, we argue against Ti clustering in PZT, as conjectured from recent (17)O NMR magic-angle-spinning measurements. Our findings indicate that (17)O NMR measurements, coupled with first-principles calculations, can be an important probe of local structure in complex perovskite solid solutions.

High sensitivity of 17O NMR to p-d hybridization in transition metal perovskites: first principles calculations of large anisotropic chemical shielding.

A first principles embedded cluster approach is used to calculate O chemical shielding tensors, sigma, in prototypical transition metal oxide ABO(3) perovskite crystals. Our principal findings are (1) a large anisotropy of sigma between deshielded sigma(x) approximately sigma(y) and shielded sigma(z) components (z along the Ti-O bond); (2) a nearly linear variation, across all the systems studied, of the isotropic sigma(iso) and uniaxial sigma(ax) components, as a function of the B-O-B bond asymmetry. We show that the anisotropy and linear variation arise from large paramagnetic contributions to sigma(x) and sigma(y) due to virtual transitions between O(2p) and unoccupied B(nd) states. The calculated isotropic delta(iso) and uniaxial delta(ax) chemical shifts are in good agreement with recent BaTiO(3) and SrTiO(3) single crystal (17)O NMR measurements. In PbTiO(3) and PbZrO(3), calculated delta(iso) are also in good agreement with NMR powder spectrum measurements. In PbZrO(3), delta(iso) calculations of the five chemically distinct sites indicate a correction of the experimental assignments. The strong dependence of sigma on covalent O(2p)-B(nd) interactions seen in our calculations indicates that (17)O NMR spectroscopy, coupled with first principles calculations, can be an especially useful tool to study the local structure in complex perovskite alloys.

Strained hexagonal ScN: a material with unusual structural and optical properties.

Local-density approximation calculations are performed to predict properties of compressively strained hexagonal ScN. This material is found to exhibit a large electromechanical response, a structural phase transition from a nonpolar to a polar structure, and a variation of the band gap in the entire visible light range when continuously changing the compressive strain. Microscopic effects responsible for these anomalies are revealed and discussed. Suggestions on how to practically grow ScN-based materials having such unusual properties are also provided.