Theoretical Aspects of Electric Field Gradients in Relation to Nuclear Magnetic Resonance

The electric field gradient (EFG) is a physical quantity which reveals a wealth of infor- mation about the properties of materials. Arising from the local electronic environment in a material, its interaction with a quadrupolar nucleus results in energy level splitting, the transition frequencies of which can be measured by way of nuclear magnetic resonance (NMR). This dissertation is primarily concerned with the calculation of EFGs from first-principles for a variety of purposes, both theoretical and experimental. First, the NMR theory of spin 3/2 particles in a magnetic field is developed in a novel, exact, and analytical way using fictitious spin-1/2 formalism. From derived closed-form expressions of the spectrum, it is shown precisely how the EFG affects the spectrum for different materials. Next, the ability of density functional theory (DFT) to accurately predict EFGs, which has been a central question since the advent of DFT, is quantitatively evaluated. Calculations from different projector- augmented wave potentials are compared and contrasted to each other, and compared again to experimental values as well as to other all-electron calculations, in a first-of-its kind holistic study. We discuss the limits and bounds on how accurate the calculations can be compared to experiment. Next, we show how these calculations have led to the development of the first DFT-based EFG database, in collaboration with the JARVIS database developers at the National Institute of Standards and Technology. Statistics of the database and comparisons to experiment, which are largely favorable, are discussed. Finally, a case study of how the EFG can be used as a probe into both electric and magnetic effects in Fe-based superconductors is presented. This study includes DFT calculations of the EFG in Ba(Fe1–xCox)2As2 and how it is influenced by spin fluctuations of the Fe magnetic moments. An argument is presented which proposes the presence of anomalously low frequency spin fluctuations in the paramagnetic phase that can be detected on the NMR timescale. This is an indication of residual magnetism making its way into the paramagnetic phase. Finally, it is shown how the EFG from NMR can be a direct probe of these fluctuations and the potential implications into the theory of superconductivity for these materials is discussed.

Author

• Ansari, Jaafar Nather

• density functional theory
• electric field gradient
• iron based superconductors
• nuclear magnetic resonance

Identifier

hdl:1920/14416

OAI identifier oai:identifier

oai:MARS:1920/14416