Interactions, disorder and spin waves in quantum Hall ferromagnets near integer filling

The interplay between exchange interactions and disorder is studied in quantum Hall ferromagnets near integer filling. Both analytical and numerical methods are used to investigate a non-linear sigma model of these systems in the limit of vanishing Zeeman coupling and at zero temperature. Chapter 1 gives an introduction to the quantum Hall effect and to quantum Hall ferromagnets in particular. A brief review of existing work on disordered quantum Hall systems is included. In chapters 2-4, the static properties of quantum Hall ferromagnets are investigated. Analytical results are obtained for simple, non-random background potentials. To study randomly disordered systems numerically, the Monte Carlo method is employed together with the concept of simulated annealing in order to find ground states. This method is presented in chapter 3 and applied to quantum Hall ferromagnets in chapter 4. A disorder-driven transition to a disordered phase is studied numerically and explained by an analytical model. Various response functions of the system are investigated both numerically and analytically. The information gained on the disordered phase is used to identify this phase as a quantum Hall spin glass. In addition, the influence of a net charge density on the quantum Hall ferromagnet is studied and the phase diagram of the system is calculated. The remaining chapters of this thesis concentrate on the dynamical properties of the disordered phase. A formalism to deal with these dynamics is discussed in chapter 5 and employed to study spin waves in a domain wall structure. A hydrodynamic theory of spin waves is used to treat long-wavelength excitations of randomly disordered quantum Hall ferromagnets. Finally, the contribution of spin waves to the optical conductivity is studied in chapter 6. Predictions are made for the experimental signatures of spin waves in disordered quantum Hall systems. The observability of these signatures is discussed both for transport measurements and NMR experiments. (author)SIGLEAvailable from British Library Document Supply Centre-DSC:D216802 / BLDSC - British Library Document Supply CentreGBUnited Kingdo