In this thesis, we study the effects of doping in two-dimensional quantum antiferromagnets. We consider cases where the undoped parent compound is a Mott insulator with long-range antiferromagnetic order and focus on the low-doping situations. The limit of localized impurities is studied in a system consisting of a host magnet and two additional weakly coupled spins. We derive the effective Hamiltonian describing the interaction between these impurities as a function of their distance and show that it exhibits xyz anisotropy, leading to NMR and EPR line broadening. We calculate the magnetization disturbance in the host magnet induced by a single impurity and find that it always enhances Neel order. Relaxing the localization constraint, we investigate the single-hole dynamics of the t-J model on the honeycomb lattice. Using exact diagonalizations, series expansion and the self-consistent Born approximation, we calculate the quasi-particle dispersion, bandwidth and residues and compare our findings with the well-established results for the square lattice. Similar to the latter case, we find an almost flat band along the edges of the magnetic Brillouin zone and well-defined hole pockets around the corners. The most important part of this thesis is devoted to the magnetic properties of lightly doped La2-xSrxCuO4, the simplest and by far most studied cuprate superconductor. Starting from the undoped parent compound, we calculate the spin-wave spectrum and the spin-flop transitions in a uniform magnetic field at zero temperature. We then consider the low-doping regime and derive the effective field theory describing the spin dynamics in insulating La2-xSrxCuO4, x ≤ 0.055, at low temperature. The spin structure resulting from the spiral solution of the extended t-J model, obtained by taking into account the Coulomb trapping of holes by Sr ions, is confined in the copper-oxide planes. Our solution explains why the incommensurate structure is directed along the orthorhombic b axis and allows us to calculate the positions and shapes of the neutron scattering peaks numerically. These results are in perfect agreement with experimental data. We also show that topological defects (spin vortex-antivortex pairs) are an intrinsic property of the spin-glass ground state.

[by] R.J. Harrison. / "This report is based on a Doctoral thesis in the department of Physics, Massachusetts Institute of Technology." / Bibliography: p. 31. / Army Signal Corps Contract No. W-36-039 sc-32037. Dept. of the Army Project No. 3-99-10-022.

Total energy calculations based on density functional theory are generally a good approach to obtain the properties of solids. The local density approximation (LDA) is widely used for calculating the ground state properties of electronic systems; for excited states the errors are in general unknown. The important aspects of LDA pertain to the modeling of the exchange-correlation interaction. If the exchange-correlation potential is approximately the same for the ground and excited states, one expects good results from the LDA calculations for excited states. In this thesis, we utilize the total energy technique for numerical computations of the electronic structure of iron in several magnetic phases and crystalline structures. 1. Body-centered-cubic iron in the ferromagnetic and several antiferromagnetic configurations. We use the total energy results to obtain the parameters in a model Heisenberg Hamiltonian. These include the interaction parameters up to 6-th nearest neighbors. Based on this model Hamiltonian we calculate properties such as the critical (Curie) temperature and spin stiffness constant. We assume that the total exchangecorrelation energy functional is the same in the ferromagnetic ground state and the antiferromagnetic excited states. Our model parameters are based directly on ab initio calculations of the electronic structure. Our calculation yields good results compared with experimental values and earlier work. Some other physical quantities, related to the phase transition, and spin waves are also discussed. 2. Face-centered-tetragonal iron. If iron is grown on a proper substrate ( e.g., Cu(100) ), the crystal structure of the thin film displays a face-centered-tetragonal distortion due to the lattice constant misfit between the film and substrate. Therefore, we performed calculations for fct iron in its ferromagnetic, antiferromagnetic, and nonmagnetic phases for a wide range of values of the lattice parameters. In the ferromagnetic calculations, we found two minima in the total energy: one is close to.the bcc structure and the other ( with a lower energy ) is close to fcc. In the antiferromagnetic and nonmagnetic calculations, we found in each case that there is only one minimum near the fcc structure, providing us clear evidence that the antiferromagnetic and nonmagnetic states are (meta)stable near the fcc region and unstable in bcc region. The antiferromagnetic and nonmagnetic states are almost degenerate near the fcc minimum, but the antiferromagnetic phase has the lowest total energy in the whole fct region. Magnetic moments are also calculated for a variety of fct structures. Near the fcc minimum we found that two ferromagnetic phases co-exist, one with a low spin and one with a high spin. These results are consistent with experimental facts and other earlier calculations. Some structural properties, such as the elastic constants and the bulk modulus, are also studied and compared with experimental data and some earlier calculations. / Graduation date: 1992

Thesis (M.Sc.)--Memorial University of Newfoundland, 2001. / Bibliography: leaves 103-113.

Thesis (M.S.)--West Virginia University, 2003. / Title from document title page. On t.p. "x̲" is subscript. Document formatted into pages; contains viii, 34 p. : ill. Vita. Includes abstract. Includes bibliographical references (p. 30-31).

In this thesis, we study the effects of doping in two-dimensional quantum antiferromagnets. We consider cases where the undoped parent compound is a Mott insulator with long-range antiferromagnetic order and focus on the low-doping situations. The limit of localized impurities is studied in a system consisting of a host magnet and two additional weakly coupled spins. We derive the effective Hamiltonian describing the interaction between these impurities as a function of their distance and show that it exhibits xyz anisotropy, leading to NMR and EPR line broadening. We calculate the magnetization disturbance in the host magnet induced by a single impurity and find that it always enhances Neel order. Relaxing the localization constraint, we investigate the single-hole dynamics of the t-J model on the honeycomb lattice. Using exact diagonalizations, series expansion and the self-consistent Born approximation, we calculate the quasi-particle dispersion, bandwidth and residues and compare our findings with the well-established results for the square lattice. Similar to the latter case, we find an almost flat band along the edges of the magnetic Brillouin zone and well-defined hole pockets around the corners. The most important part of this thesis is devoted to the magnetic properties of lightly doped La2-xSrxCuO4, the simplest and by far most studied cuprate superconductor. Starting from the undoped parent compound, we calculate the spin-wave spectrum and the spin-flop transitions in a uniform magnetic field at zero temperature. We then consider the low-doping regime and derive the effective field theory describing the spin dynamics in insulating La2-xSrxCuO4, x ≤ 0.055, at low temperature. The spin structure resulting from the spiral solution of the extended t-J model, obtained by taking into account the Coulomb trapping of holes by Sr ions, is confined in the copper-oxide planes. Our solution explains why the incommensurate structure is directed along the orthorhombic b axis and allows us to calculate the positions and shapes of the neutron scattering peaks numerically. These results are in perfect agreement with experimental data. We also show that topological defects (spin vortex-antivortex pairs) are an intrinsic property of the spin-glass ground state.

Thesis (Ph. D.)--University of New South Wales, 1999. / Also available online.

Thesis (M.S.)--Oregon State University, 2010. / Printout. Includes bibliographical references (leaves 50-54). Also available on the World Wide Web.

Thesis (Ph. D.)--West Virginia University, 2002. / Title from document title page. On t.p. "x̲" is subscript. Document formatted into pages; contains ix, 93 p. : ill. (some col.). Vita. Includes abstract. Includes bibliographical references (p. 89-92).

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