A.S. SGibbs 1, J. Farrell 1, J.-F. Mercure, R.S. Perry 2, A.W. Rost 1, A.P. Mackenzie 1 1 University of St Andrews, St. Andrews (Scotland) 2 University of Edinburgh (CSEC), Edinburgh (Scotland) Summer Project 2007 University of St Andrews Scottish Universities Physics Alliance Alexandra Gibbs 5 th Year Masters Student Prof. Andy Mackenzie Supervisor For further information please contact References Gold plated ellipsoidal mirrors (focus radiation to ≈1cm 3 hot zone) Feed Rod (polycrystalline) Quartz tube (pressures of up to ≈10atm) Seed Rod (single crystal) RuO 2 octahedra SrO layer To grow the crystals, an infra-red image furnace was used (figure, left). This can be used to grow materials with melting temperatures less than about 2300 °C that also absorb infra-red radiation. The powder used to form the crystal is prepared by solid state reaction (see equation below) and then compressed into a rod and hung from wires at the top of the setup (this is the ‘feed’ rod). A piece of pre-grown crystal is used as a seed crystal for the molten zone. The IR radiation is absorbed by the feed rod as it is lowered into the hot zone (≈1cm 3 ) and the rod melts and is joined to the seed Both rods move downwards and with careful adjustment of parameters during growth, the crystal grows over a few hours, dependent on the material being grown e-e- Impurity atom The effect of impurities on conduction electrons: the impurity atom scatters the conduction electron, shortening the mean free path and therefore increasing the resistivity. Figure 1: The resistivity data for the Sr 2 RuO 4 crystal grown. The fit was extrapolated to T=0 to allow determination of ρ o. One of the main research efforts in condensed matter physics is concentrating on transition metal oxides whose properties are dominated by the d-level electrons of the transition metal ions. In these materials the electrons are not independent of each other but highly correlated leading to many interesting novel states such as strange metals, novel magnets and unconventional superconductivity. These properties are highly sensitive to disorder and much research is done in optimising the growth processes for each system making a comprehensive knowledge in chemistry indispensable in this field of physics. The aim of this particular project was to grow high quality single crystals of Sr 2 RuO 4 and investigate its physical properties. In this material the electron correlations lead to a highly unusual superconducting state in which the electrons pair with spins aligned parallel, something that in almost all other superconductors is energetically unfavourable. The physical properties of particular interest were residual resistivity and the superconducting transition temperature, both being important quantities for establishing the quality of the crystals. We measured the residual resistivity with a 4-point measurement (see figure 1) in a helium flow cryostat. It was found to be ρ o ≈0.12μΩcm (figure 1) which means the crystal is ‘ultra clean’ (has a residual resistivity of <1μΩcm). The estimated mean free path is of the order of 10 4 Å. We furthermore investigated the superconducting transition by using an AC susceptibility measurement (inset figure 3) in an adiabatic demagnetization cryostat working between 100mK and 1.5K. The superconducting transition midpoint (midpoint of peak in figure 2) was found to be 1.49K with the onset of superconductivity being at 1.52K (figure 3). Both values are the same as the best published ones [2] and confirm the ρ o measurement (inset figure 2). These excellent results allowed more complicated measurements of the electronic structure of the material by de Haas van Alphen experiments (figure 4). The very high amplitude of the oscillations observed further confirmed the exceptional quality of the sample. Figure 2: The midpoint of the transition to superconductivity is measured as the peak in χ’’, the imaginary part of the AC susceptibility. Inset: The relationship between residual resistivity and critical temperature for Sr 2 RuO 4 [3] Figure 3: The real component of the AC susceptibility showing the onset of superconductivity. Inset: AC susceptibility coil setup (courtesy of J-F Mercure). Figure 4: The quantum oscillations seen in the de Haas van Alphen experiment. Alexandra Gibbs or Prof. A P Mackenzie [1] S.I. Ikeda et al., Journal of Crystal Growth 237–239 (2002), 787–791 [2] Z Q Mao, Y Maeno, H Fukazawa, Materials Research Bulletin 35 (2000), [3]??????? Above : The crystal structure of Sr 2 RuO 4 [1] Below : Example of a single crystal grown in the project. Above : The infra-red Image Furnace used for growth (picture courtesy of N. Kikugawa) Below : Solid State reaction the initial materials undergo Resistivity is the resistance, R, multiplied by a geometric factor for the sample. The residual resistivity ρ o (at T=0K) is only dependent on the concentration of defects and impurities. These atomic defects act as scattering centers for conduction electrons (see figure), impeding their path through the lattice and thereforeincreasing the resistivity of the material. Therefore the lower the residual resistivity the better the quality of the crystal. A superconducting state is one for which the material has no electrical resistance, so a current set up in such a state will circulate indefinitely without decaying. Sr 2 RuO 4 is a superconductor below a critical temperature, theoretically predicted to be ≈1.5K in an ideal crystal. Impurities lower this temperature dramatically. The project overall therefore required both knowledge of crystal chemistry to allow preparation of high purity materials and estimate the effects of impurities or dopants as well as knowledge in materials physics to be able to relate the low temperature measurement results to the microscopic physics of the crystal. 1cm