The order parameter for the superconducting phases of UPt3

I review the principal theories that have been proposed for the superconducting phases of UPt₃. The detailed H-T phase diagram places constraints on any theory for the multiple superconducting phases. Much attention has been given to the Ginzberg-Landau region of the phase diagram where the phase boundaries of three phases appear to meet at a tetracritical point. It has been argued that the existence of a tetracritical point for all field orientations eliminates the two-dimensional (2D) orbital representations coupled to a symmetry-breaking field (SBF) as a viable theory of these phases and favours either a theory based on two primary order parameters belonging to different irreducible representations that are accidentally degenerate, as described by Chen and Garg 1993, or a spin-triplet, orbital one-dimensional representation with non spin-orbit coupling in the pairing channel, as described by Machida and Ozaki 1991. I comment on the limitations of the models proposed so far for the superconducting phases of UPt₃. I also find that a theory in which the order parameter belongs to an orbital 2D representation coupled to a SBF is a viable model for the phases of UPt₃, based on the existing body of experimental data. Specifically, I show that the existing phase diagram (including an apparent tetracritical point for all field orientations), the anisotropy of the upper critical field over the full temperature range, the correlation between superconductivity and basal plane antiferromagnetism and the low-temperature power laws in the transport and thermodynamic properties can be explained qualitatively, and in many respects quantitatively, by an odd-parity E_2u order parameter with a pair spin projection of zero along the ?c axis. The coupling of an antiferromagnetic moment to the superconducting order parameter acts as a SBF which is responsible for the apparent tetracritical point, in addition to the zero-field double transition. The new results presented here for the E_2u representation are based on an analysis of the material parameters calculated within the Bardeen-Cooper-Schrieffer theory for the 2D representations, and a refinement of the SBF model given by Hess et al. (1989). I also discuss possible experiments to test the symmetry of the order parameter.     

Multiple gap symmetries for the order parameter of cuprate superconductors from penetration depth measurements

The temperature dependence of the London penetration depth lambda was measured for an untwinned single crystal of YBa_{2}Cu_{3}O_{7-delta} along the three principal crystallographic directions (a, b, and c). Both in-plane components (lambda_{a};{-2} and lambda_{b};{-2}) show an inflection point in their temperature dependence which is absent in the component along the c direction (lambda_{c};{-2}). The data provide convincing evidence that the in-plane superconducting order parameter is a mixture of (s+d)-wave symmetry whereas it is mainly s wave along the c direction. In conjunction with previous results it is concluded that coupled s+d-order parameters are universal and intrinsic to cuprate superconductors.     

Emulsion droplet sizing using low-field NMR with chemical shift resolution and the block gradient pulse method

Pulsed Field Gradient (PFG) measurements are commonly used to determine emulsion droplet size distributions based on restricted self-diffusion within the emulsion droplets. Such measurement capability is readily available on commercial NMR bench-top apparatus. A significant limitation is the requirement to selectively detect signal from the liquid phase within the emulsion droplets; this is currently achieved using either relaxation or self-diffusion contrast. Here we demonstrate the use of a 1.1 T bench-top NMR magnet, which when coupled with an rf micro-coil, is able to provide sufficient chemical shift resolution such that unambiguous signal selection is achieved from the dispersed droplet phase. We also improve the accuracy of the numerical inversion process required to produce the emulsion droplet size distribution, by employing the Block Gradient Pulse (bgp) method, which partially relaxes the assumptions of a Gaussian phase distribution or infinitely short gradient pulse application inherent in current application. The techniques are successfully applied to size 3 different emulsions.     

Random textures of the order parameter of superfluid 3He-B in aerogel

A phenomenological scheme of the observed properties of superfluid ³He in aerogel is proposed in the spirit of the Ginzburg-Landau theory. The effect of the aerogel on the order parameter is described by the random tensor field η_jl(r). The tensor field exerts a considerable disorienting effect on the order parameter in the A phase of ³He, but virtually unaffects the orientation of the order parameter in the B phase in zero magnetic field. The change in the texture of the order parameter emerging in the B phase in aerogel in a magnetic field is considered. It is shown that the mean square of the angle between the magnetic field direction and the anisotropy axis of the B phase is proportional to the third power of the magnetic field strength. The fluctuations of the direction of the magnetic anisotropy axis of ³He-B are correlated over the familiar “healing length”, which is inversely proportional to the field strength and has a macroscopic scale.     

Third order nonlinear optical characterization using focal shift measurements

We report on third order optical nonlinear experimental characterization using Z-scan method through focal shift measurements of a converging lens. The sample is fixed in front of a lens and is illuminated by a collimated beam. The shift of the geometrical focus in the nonlinear regime using input Gaussian beams is related to the nonlinear induced dephasing owing to a simple linear relation. Numerical calculations based on the Helmholtz wave equation are performed. Good agreement is obtained between experimental and theoretical results.     

Fast NMR flow measurements in plants using FLASH imaging

A fast method for quantitative NMR imaging of flow velocities in intact plants is described. The purpose of this method is to observe dynamic changes of flow velocity in the xylem of plants after fast changes of environmental conditions. The spatial image resolution is 47 x 188 micrometer(2) in-plane. The method applies a fast gradient echo sequence (FLASH). Compared to other flow NMR imaging sequences, the imaging time was reduced by a factor of 6 with comparable signal-to-noise ratio. A complete flow measurement consists of a set of 8 different flow weighted images with a total acquisition time of 3.5 min.     

Temperature dependence of the order parameter of the two dimensional antiferroelectric squaric acid as determined from birefringence measurements

The temperature dependence of the partial birefringence Δn is measured on single crystals of squaric acid. In contrast to previous results a phase transition of the first order is detected. The temperature dependence of Δn close to T_c supports the validity of a classical Landau expansion which also has been suggested recently in order to account for the behaviour of the specific heat. The results are discussed in relation to those of previous works.     

Calculating order parameter profiles utilizing magnetically aligned phospholipid bilayers for 2H solid-state NMR studies

Solid-state deuterium NMR spectroscopy was used to study the structural and dynamic properties of stearic acid-d(35) in magnetically aligned phospholipid bilayers as a function of temperature. Magnetically aligned phospholipid bilayers or bicelles are model systems, which mimic biological membranes for magnetic resonance studies. Paramagnetic lanthanide ions (Yb(3+)) were added to align the bicelles such that the bilayer normal is colinear with the direction of the static magnetic field. The corresponding order parameters of the stearic acid-d(35) probe were calculated and compared with values obtained from unoriented samples in the literature. The addition of cholesterol to the bicelle system decreases the fluidity of the phospholipid bilayers and increases the ordering of the acyl chains of stearic acid-d(35). This study demonstrates the feasibility of utilizing magnetically aligned bicelles for calculating 2H order parameter profiles for non-biological systems such as polymer-grafted membranes and Schiff's base complexes.     

Temperature behavior of the order parameter in Pb5Ge3O11

The temperature dependence of the spontaneous polarization in the Pb₅Ge₃O₁₁ lead germanate (PGO) is experimentally investigated using optical, magnetic resonance, and conventional electrical measurements. The deviations from the temperature dependence typical of second-order phase transitions at temperatures below 420 K are explained in terms of incomplete polarization switching and polarization induced by a residual depolarization field. The low-temperature anomalies are interpreted without consideration of additional structural transformations. The internal bias field is determined from the experimental temperature dependence of the perfect polarization of PGO single crystals in an electric field.