Probing the phase diagram of the Ferromagnetic Superconductor UGe2 using high pressure ultrasonic techniques
Kepa, Michal Wawrzyniec
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The main goal of the project was to develop new experimental techniques to further investigate the phase diagram of the ferromagnetic superconductor UGe2 at high pressures. Of particular interest is the metamagnetic transition (FM1-FM2) which is thought to play the key role in the unconventional superconductivity in UGe2. The project attempted to detect experimentally the critical ferromagnetic fluctuations associated with the FM1-FM2 transition. The development of the experimental equipment constitutes a substantial part of the project and includes: (1) a 2-axis Rotation Stage for High Pressures, (2) an Ultrasonic Sapphire Anvil Cell and (3) a High Pressure Pulse Echo Setup. (1) allows transport measurement on single crystal samples with simultaneous two-axis rotation at temperatures down to 2 K, magnetic fields up to 9T and pressures up to 5GPa to be made. (2) employs Resonant Ultrasound Spectroscopy on a sample in the anvil type cell with an optical access at cryogenic temperatures. (3) uses the Pulse Echo Technique inside a cylinder type cell allowing for ultrasonic measurements on samples with a well-defined orientation. The design, technical challenges and tests results are presented and discussed. The existing techniques, used in the project, included Inelastic Neutron Scattering. A single crystal of UGe2 was studied at 12 kbar with a large volume two-layered piston-cylinder cell. No critical fluctuations were detected at Tx associated with the FM1-FM2 transition. Instead, a small inelastic signal below this transition temperature was observed at the threshold of the instrument sensitivity. The fluctuations at TC associated with the paramagnetic-to-ferromagnetic transition (PM-FM) were detected and the energy scale of these fluctuations was found to have decreased, as compared to the ambient pressure case, in proportion to the resistivity - a result supporting recent theory. The elastic constant c11 of a single crystal of UGe2 was measured as a function of temperature using (3) at ambient pressure as well as pressures up to 11 kbar. The elastic constant exhibits clear features associated with the two transitions, PM-FM and FM1-FM2. The temperature dependence of the elastic constant at ambient pressure was modelled with two main contributions (Schottky-like and Wiess-like) to the magnetic heat capacity coming from the two energy scales, Tx and TC, as well as two corresponding Gruneisen parameters, Ωx and ΩC. The values of Gruneisen parameters obtained from the data fitting were in good agreement with the values determined from the slope of the phase transition lines on the phase diagram. The temperature dependence of the elastic constant at high pressures was modelled according to the two-component system with coupled moments. The behaviour of the fitting parameters (including the Ωx and ΩT ) was consistent with the phase diagram of UGe2 and captured important features of c11 temperature evolution. The way forward would be to continue the measurements of c11 at higher pressures but also to repeat the measurements at different ultrasonic frequencies in order to obtain the temperature dependence of the ultrasonic attenuation which will provide more insight on the FM1-FM2 transition.