Various experimental and theoretical work indicate that the local structure and chemical ordering play a crucial role in the different physical behaviors of lead-based complex ferroelectrics with the ABO 3 perovskite structure. First-principles linearized augmented plane wave (LAPW) with the local orbital extension method within local density approximation (LDA) are performed on structural models of Pb(Zr1/2Ti1/2 )O3 (PZT), Pb(Sc1/2Ta1/2)O3 (PST), Pb(Sc2/3W1/3)O3 (PSW), and Pb(Mg 1/3Nb2/3)O3 (PMN) to calculate electric field gradients (EFGs). In order to simulate these disordered alloys, various structural models were constructed with different imposed chemical orderings and symmetries. Calculations were carried out as a function of B-site chemical ordering, applied strain, and imposed symmetry. Large changes in the EFGs are seen in PZT as the electric polarization rotates between the tetragonal and rhombohedral directions. The onset of polarization rotation in monoclinic Cm symmetry strongly correlates with the shearing of the TiO6 octahedron, and there is a sharp change in slope in plots of Ti EFGs versus octahedral distortion index. The same changes in EFGs and the BO6 shearing corresponding to the change of off-centering direction are also seen in PST. In PSW and PMN, the calculated B cation EFGs showed more sensitivity to the surrounding nearest B neighboring environments. Calculated B atom EFGs in all alloys are considerably larger than those inferred from the NMR measurements. Based on comparisons with experiments, the calculated results are interpreted in terms of static and dynamic structural models of these materials.

Recent experimental and theoretical work indicates that polarization rotation via a monoclinic phase at the morphotropic phase boundary in PZT is responsible for its large piezoelectric response. We performed Linearized augmented plane wave with the local orbital extension (LAPW+LO) method within local density approximation (LDA) on B-site [001]1:1 ordered Pb(Zr 0.5Ti0.5)O3 (PZT 50/50). We use a tetragonal super-cell and constrain it with monoclinic Cm space group. Atomic forces following the formulation of Yu et al. are calculated, and the conjugate gradient method is implemented to optimize the internal coordinates. Both the tetragonal (P4mm) and monoclinic (Cm) phases are reproduced, when we strain the system while keeping the volume fixed at experimental value. Bulk spontaneous polarization, Born effective charges (Z*) and piezoelectric coefficients are computed from the Berry's phase approach. The polarization rotates between the pseudo-cubic [001] and [nunu1] directions, where nu = 1.27 in the (110) mirror plane. The piezoelectric coefficients are enhanced when polarization rotation is permitted, namely e33 = 12.6 C/m2, e15 = 10.9 C/m 2, and giant absolute values of e13 = -33 C/m 2 and e'11 = 36 C/m2, where e'11, is defined as 0.5 (e11 + e12). It gives an explanation to the big piezoelectric response measured in ceramic PZT 50/50. Furthermore, the calculated internal coordinates of monoclinic phase of PZT 50/50 at experimental value of c/a are in good agreement with the experimental data of Pb(Zr0.52Ti 0.48)O3.

This work is devoted to the study of local order in the ferroelectric PbSc1/2Ta1/2O3 (PST) and relaxor ferroelectric solid solutions (1-x)PbSC2/3W1/3O3-(x)PbTiO 3 (PSW-PT), (1x)PbSC2/3W1/3O3-(x)PbZrO 3 (PSW-PZ). Novel Magic Angle Spinning (MAS) Solid State Nuclear Magnetic Resonance (SS-NMR) experiments, including Multiple Quantum MAS (MQMAS) and Double Quantum Filtered Satellite Transition (DQF-STMAS), have been performed on these materials. A gamma function model is proposed for the distribution of quadrupole coupling constants, based on the Poissonian nature of atomic displacements. Moments for distributions may be subsequently extracted through agreement between experimental spectra and simulations implemented in novel programs. Simple crystal compound scandium oxide provides a reasonable analogue and assists in spectral interpretation. Support is given to the Random Site (RS) model for atomic ordering in Relaxor Ferroelectrics. Based on point charge calculations, significant lead displacement takes place as well as oxygen octahedral tilting. In June 2004, Donghua Zhou proposed an experimental scheme to expedite the interpretation of experimental spectra for materials such as those studied here and a realization with analysis is given.

The internal magnetic field distributions for a type II superconductor (a single crystal YBa2Cu3O7-delta ) with large normal inclusions (YBa2Cu3O 7-delta) are studied. A model based on the London Equations has been successfully developed and applied to the interpretation of the pSR data on this system. In our model, these inclusions are assumed to be cylindrical in shape and infinite in length. Therefore, this model should be especially appropriate for the prediction of field distributions in single crystal superconductors in which columnar defects have been purposely introduced to enhance pinning.;muSR experiments on a large single-crystal sample of YBa2C u3O7-delta with non-conducting YBa2Cu3 O7-delta inclusions show some interesting characteristics, especially the magnetic field distribution in the inclusion regions. In our model, the difference between the field value in the inclusions and the value at the saddle point is sensitive to the penetration depth. Comparing the calculated to observed field differences provides a new method for determining the penetration depth.

One of the most interesting and challenging problems in physics is understanding strongly correlated many-body systems, where strong interactions can yield many remarkable phenomena such as superfluidity in 4He, high-temperature superconductivity, etc. In order to attack these problems, we often need to reduce the complexity of the systems to simple models in hopes of getting better insights into the properties of the systems. The Hubbard model, the focus of this dissertation, is one of the most famous examples of such model, which describes a tunneling of electrons between nearest neighbor sites of a lattice with on-site interactions. This simple model is an important concept in condensed matter physics and provides rich understandings of electronic and magnetic properties of materials. Despite its simplicity, there is no general analytical solution to the Hubbard model beyond 1D.;The discovery of ultracold atoms and optical lattices opens up the possibility of emulating the Hubbard model in experiments. Optical lattices provide an ideal realization of the Hubbard model where relevant parameters can be tuned systematically. It makes theoretical studies of the Hubbard model increasingly attractive since a direct comparison between theoretical calculations and experimental results becomes more and more possible.;In this dissertation, the ground-state properties of the repulsive Hubbard model for weak to intermediate interaction strengths in two, three dimensions and their dimensional crossover are studied within the mean field theory. We show that the system exhibits unidirectional spin-density wave (SDW) order with antiferromagnetic correlations and a long wavelength modulation. The modulating wave is along the [0011-direction at low interaction strength U/t and along the [1111-direction at higher U/t. The evolution of the wavelength of the SDW is determined as a function of U/t, the density, and t⊥/t. With an analysis of the pairing of spins based on nesting and deformation of the Fermi surface, we discuss how these results can be rationalized and how a simple, predictive model can be constructed for the properties of the SDW states.

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