Hall resistivity and torque magnetometry studies of the ferromagnetic superconductors UGe2 and URhGe

Abstract

Ferromagnetism (FM) and superconductivity (SC) are traditionally thought of as competing states of matter, since the opposite-spin electron pairing mechanism required for conventional SC is rendered impossible by FM spin alignment. However, recently discovered heavy-fermion compounds UGe2 and URhGe are examples where SC and FM are cooperative, and rather than antagonistic the presence of FM is actually necessary for the occurrence of the SC phase. A cooperative state of FM and SC is a topic of interest because it presents a possible solution to one of the two main problems with present superconductors: technology inhibiting limits on the highest temperature and highest magnetic field to which the SC phase can exist. Although both UGe2 and URhGe cease to be superconductors before even reaching 1 K, unlike the various `high temperature' superconductors currently known that easily surpass 100 K, it is their magnetic properties that are interesting, the inherent FM ordering allowing them to exceed conventional limits on the maximum magnetic field that SC can withstand. For example, URhGe remains superconducting above 35 T and the upper limit is so high that it is still experimentally undetermined. How exactly the FM SC phase arises in these compounds is as yet unknown. The necessary opposite-spin pairing mechanism is theoretically provided by magnetic fluctuations in an easily polarizable system right on the edge of a magnetic phase transition, and indeed SC emerges in UGe2 and URhGe around a first-order quantum critical point (QCP) where the temperature of the transition to an FM phase is reduced to absolute zero, by application of pressure in the case of UGe2 and by application of a magnetic field for URhGe. The aim of the research detailed in this thesis is to probe the FM phase transition and the associated QCP related to the emergence of SC in these compounds, to gather more information about the precise nature of the phases either side of the transition and exactly what changes occur in the system crossing the QCP. Specifically, the main objective is to characterise the magnetic fluctuations at the phase boundary and determine whether, by current FM SC theory, these fluctuations could be responsible for SC or if instead other, modified, unconventional theories are required to explain the unconventional electron pairing. The probes of choice for this PhD were Hall effect and magnetoresistance measurements of UGe2, and capacitive torque magnetometry and simultaneous magnetoresistance measurements of URhGe. The main result of the UGe2 project is an observed order-of-magnitude change in the Hall coefficient crossing the FM transition as a function of temperature and a dramatic change, similar in magnitude but also accompanied by a sign reversal, crossing the QCP as a function of pressure. Furthermore, the sign reversal at the critical pressure persists up to roughly 12 K, far beyond the 7 K critical end point of the phase transition, suggesting that in fact three different phases converge at the QCP where fluctuations between them presumably lead to the emergence of SC. Further investigation of the Fermi surface, either by deeper analysis of the Hall effect results or by other experimental methods, will be required to complete the main objective and determine exactly what the differences are between these newly identified phases. The main result of the URhGe project is actually the successful development of the capacitive torque magnetometry technique itself and the proof of operation for simultaneous measurement of all the individual components of both the magnetization and differential susceptibility tensors in a high magnetic field, which is currently not possible by any other technique. Completing the main objective was hampered by the extremely high susceptibility components encountered in the vicinity of the QCP, which in itself could be considered evidence for the theoretical relationship between strong FM fluctuations and the emergence of SC in URhGe. A number of results incidental to the main aim of the URhGe project are also summarised in this thesis, including the characterisation of quantum oscillations frequencies not previously reported in scientific literature and a variety of subtle features in resistivity measurements, which could, in conjunction with evidence from the susceptibility measurements, suggest the presence of another superconducting state such as surface or domain wall SC.