Aspects of quantum criticality in itinerant electron ferromagnetic systems

Fermi-liquid theory is one of the standard models of condensed matter physics, supplying a valid explanation of the low temperature properties of many metals. However, non-Fermi-liquid behaviours arise in many itinerant systems that exhibit a zero temperature magnetic phase transition. This thesis is mainly concerned with such quantum critical points and is an investigation into the various phenomena seen in the phase diagram of itinerant ferromagnetic systems. We apply a standard theory of itinerant quantum criticality to a quantum-critical end-point in a three-dimensional ferromagnet, before speculating on ZrZn\(_2\) being a test-bed of our results. Then we consider two explanations for the appearance of a first-order phase transition at low temperatures and attempt to reconcile them with ZrZn\(_2\). Finally we concentrate on the wide range of novel states that appear instead of a pure quantum critical point. Such exotic phases are superconducting or magnetic in nature and we investigate whether the onset of ferromagnetic quantum critical fluctuations can give rise to a certain class of such states