Magnetism and superconductivity are intimately connected in many so-called heavy fermion metals. A particularly dramatic case is URhGe, where two distinct superconducting regions exist - one coexisting with ferromagnetism, and the other at extremely strong applied magnetic fields that are sufficient to destroy conventional forms of superconductivity. This project will involve developing sensitive heat capacity and magnetic measurement apparatus that will operate at extremes of low-temperature an high-magnetic field, and apply them to study URhGe and other related materials. The aims are both to gain a deeper understanding of how magnetic pairing may lead to superconductivity and to drive the search for new superconducting materials. The project is an integral part of a major research effort to study quantum criticality and unusual quantum ordered phases using a variety of magnetic, electrical and thermal measurement techniques. The apparatus in St Andrews includes a state-of-the-art dilution refrigerator (commissioned December 2007) with a base temperature 10 millikelvin and equipped with a 17 tesla magnet. The focus for the project is on magnetic measurements including heat capacity, torque magnetometry, field gradient magnetometry and a.c. susceptibility. By combining torque and field-gradient results, the vector magnetic moment can be determined as a function of magnetic field. This will give a complete phenomenological (Ginzburg-Landau) description of the magnetism in the region superconductivity occurs, and will provide detailed information about the nature of the magnetic interactions that are important for superconductivity. Another important component of the work will be to use quantum oscillations in the different measurements to study the Fermi surface and how it changes approaching and crossing quantum phase transitions.
Transition metal oxide (TMO) materials exhibit a wide variety of exotic ground states from unconventional superconductivity to orbital-ordered magnetic metals with potential for novel technological development. Progress in the field is dependent on the production of high-quality single crystal samples although this is remarkably difficult due to challenging chemical issues. Notably, many interesting systems for example, vanadates, molybdates and niobates have transition metal ions in unusual or intermediate oxidation states whereas current crystal growth technology is restricted to growing compounds in which the ions are in 'standard' oxidation states. A particular goal of this project is to develop technology that will allow the synthesis of crystals containing non-standard oxidation states. The project will involve first, identifying and synthesising novel TMO materials using a newly installed optical light furnace. Once crystals are synthesised, they will be fully characterised with in-house facilities with further physical measurements being made with international collaborators to elucidate their properties. The research naturally straddles both physics and chemistry and would be suitable for students starting from either background.
A magneto-Kerr microscope will be built to work at progressively lower temperatures, ulimately down to 0.1 K. The microscope will then be used to image domain structures in ferromagnetic superconductors (URhGe and UCoGe). The images will be used to position contacts to make transport measurements across single domain walls and to test for the presence of Josephson currents (Shapiro steps etc). The microscope will also be used to look for surface currents around domain edges that are signatures of topologically protected states associated with some non-conventional order parameters (with applications in quantum computing). The microscope will also be used to image vortices to look for new behaviours predicted at domain walls. The above project will be based in Edinburgh but with some measurements making use of facilities in St Andrews.
The possibility of magnetic spin-crystals formed by the superposition of helical spin modulations with different wave-vectors has been a subject of much recent experimental and theoretical work. Signatures of phases with this property have been found in an array of materials including MnSi and Sr3Ru2O7. On the theoretical side, there are several ways in which such states might form. These include the formation of spiral modulation due to a Dzyalosinskii-Moriya spin-orbit interaction in itinerant magnets, residual, small-wavevector nesting due to the electron dispersion in a lattice [1,2] and from competing interactions that can give rise to a series of transitions forming a Devil's Staircase [3]. Perhaps the most intriguing suggestion - and one that has most captured the imagination of condensed matter theorists of late - is that an itinerant system on the brink of a quantum phase transition might possess an intrinsic instability to the formation of modulated magnetic phases [4]. In any particular material, one or more of these effects may operate with the possibility of a complicated interplay between them. This project aims to investigate the phenomenon of spatially modulated magnetism from both an experimental and theoretical perspective. We will use techniques of quantum many-body physics and field theory to investigate the possibility of spatially modulated magnetism in real systems. These investigations will be carried out in concert with neutron scattering experiments to provide inspiration for and validate this theory. The experimental part will include growing the crystals for these experiments as well as performing the measurements. We anticipate that a student will spend approximately 2/3 of their time on theory and 1/3 on experimental work, working both in Edinburgh and St Andrews as well as at international facilities.
[1] A. M. Berridge, A. G. Green, S. A. Grigera and B. D. Simons A Magnetic Analogue of the of the FFLO state: Inhomogeneous Instabilities Near to Tricritical Points, Physical Review Letters 102, 149903 (2009).
[2] G. J. Conduit, A. G. Green, and B. D. Simons, Inhomogeneous phase formation on the border of itinerant ferromagnetism, Physical Review Letters 103, 207201 (2009) [spotlighted in Physics 2, 93 (2009)]
[3] P. Bak & J. von Boehm, "Ising model with solitons, phasons, and 'the devil's staircase'", Phys Rev B 21 5297 (1980)
[4] J. Rech C.Pépin, V.Chubukov, "Quantum critical behaviour in intinerant electron systems: Eliashberg theory and instability of a ferromagentic quantum critical point", Phys Rev B 74 195126 (2006)
High pressures are often needed to tune materials to quantum critical points at which new state formation occurs. The application of magentic field and the rotation of pressurised samples in the field can provide additional tuning. Rotation in a field is also essential for quantum oscillation studies to map out Fermi-surfaces. The project will develop pressure cells and instrumentation for these measurements and use this to study various quantum critical phenomena. It will build on (i) further development of miniature turnbuckle diamond anvil cells to be used on our low-temperature high-field rotatable platform and (ii) new designs for the piezo-electric rotators to rotate the cells at very low temperature. The emphasis here will be on developing apparatus and making measurements such as Hall resistivity and susceptibility. The use of designer diamonds will be explored. The project affords the possibility of making exciting discoveries probing materials where new state formation is expected to be induced withpressure and field as well as acquiring valuable transferrable skills in CAD (computer aided design) and FEA (finite element analysis) calculations. The project would be based in the new CSEC building and PhD registration could be in either physics or engineering schools depending on the preference of the candidate.
Charge Ordering, a long range order of different metal oxidation states, is implicated in many interesting electronic phenomena, for example, the low temperature Verwey state in magnetite, Fe3O4, colossal magnetoresistances and phase separation phenomena in magnanese oxide perovskites, and superconductivity in doped BaBiO3 and the layered cuprates. Although charge order is an apparently simple phenomenon, there is little theoretical understanding in comparison to the descriptions that have been developed for phenomena such as magnetism and superconductivity. Recently, Monthoux and Attfield (manuscript in preparation) proposed a model Hamiltonian which at the Hartree-Fock level of approximation reproduces the salient features of both the observed charge disproportionated (e.g BaBiO3) and semivalent (e.g La0.5Ca0.5MnO3) charge order in oxides. These result from the interplay between electron-electron correlations and local electron-lattice softening. The model predicts competing magnetic, charge ordered, and magnetic charge ordered ground states.This project aims to see whether this model can also lead to superconducting instabilities, and whether it can describe the salient features of superconductivity on the border of charge ordering as experimentally observed in potassium doped BaBiO3 for example. The insights provided by this theoretical study study could be used to guide the search for new materials with interesting electronic properties, in collaboration with the group of Prof. J.P. Attfield.
