Coexistence and Competition of Superconductivity and Magnetism

Abstract

This dissertation studies the coexistence and competition of superconductivity and magnetism. Initially, an overview of the subject is given with descriptions of various compounds which show unusual forms of both phenomena. This is followed by an analysis of the basic theoretical concepts behind both superconductivity and magnetism. The accepted microscopic model of conventional superconductivity is studied and its equivalence to the established phenomenological theory is shown. Various models of quantum magnetism are also discussed. A brief survey of previous models that have been used to describe coexistence is given, including both microscopic and phenomenological theories. A microscopic Hamiltonian is then introduced to model the presence of both isotropic superconductivity and itinerant antiferromagnetism. Firstly, a free energy approximation is derived to study the behaviour near the critical temperatures of the two phenomena. This is followed by an examination of the phase diagram at lower temperatures. A novel phase is found which shows the coexistence of both forms of ordering. The temperature range over which this phase exists is seen to depend on the amount of nesting present in the Fermi surface and the relative strength of the magnetic interaction. The introduction of an anomolous term in the free energy leads to a new phase which consists of a constant superconducting order parameter and an antiferromagnetic spin-wave with a shifted wave-vector. The possibility of multiple superconducting states is studied using group theory. Initially, the fundamental properties of groups are established and their application to superconductivity discussed, including representation theory, the classification of gap structures and the formation of free energies through symmetry considerations. Following this, phase diagrams are derived for various combinations of representations leading to the presence of helically ordered phases. The dissertation ccncludes by summarising the results obtained and discussing possible future work.