Performance of adiabatic melting as a method to pursue the lowest possible temperature in 3^3He and 3^3He-4^4He mixture at the 4^4He crystallization pressure

We studied a novel cooling method, in which $^3$He and $^4$He are mixed at the $^4$He crystallization pressure at temperatures below $0.5\,\mathrm{mK}$. We describe the experimental setup in detail, and present an analysis of its performance under varying isotope contents, temperatures, and operational modes. Further, we developed a computational model of the system, which was required to determine the lowest temperatures obtained, since our mechanical oscillator thermometers already became insensitive at the low end of the temperature range, extending down to $\left(90\pm20\right)\,\mathrm{\mu K\approx}\frac{T_{c}}{\left(29\pm5\right)}$ ($T_{c}$ of pure $^3$He). We did not observe any indication of superfluidity of the $^3$He component in the isotope mixture. The performance of the setup was limited by the background heat leak of the order of $30\,\mathrm{pW}$ at low melting rates, and by the heat leak caused by the flow of $^4$He in the superleak line at high melting rates up to $500\,\mathrm{\mu mol/s}$. The optimal mixing rate between $^3$He and $^4$He, with the heat leak taken into account, was found to be about $100..150\,\mathrm{\mu mol/s}$. We suggest improvements to the experimental design to reduce the ultimate achievable temperature further.Comment: 39 pages, 24 figure

Nuclear Ordering in Lithium and an Upper Limit on its Ambient Pressure Superconducting Transition Temperature

We have discovered spontaneous ordering of nuclear spins in lithium metal by NMR measurements at very low temperatures. In low magnetic fields, B < 0:2 mT, the NMR spectra show a pronounced low-frequency anomaly. Also, nonadiabatic response to a slowly varying magnetic field was observed. A rich phase diagram with three different nonparamagnetic regions is proposed. We estimate a critical spin temperature T c 350 nK at B 0. We also report the absence of superconductivity in lithium at normal pressure down to T e 100 K (B < 10 nT). DOI: 10.1103/PhysRevLett.93.157201 PACS numbers: 75.30.Kz, 74.10.+v, 75.30.Cr, 76.60.Jx Lithium is often regarded as the prototype metal due to its apparent simplicity. However, to begin with, its lowtemperature lattice assembly is not that trivial, as competing close-packed structures have been found to coexist The occurrence of superconductivity in lithium at reasonable temperatures has been predicted by many theoretical studies [2 -6]. The estimates for T c vary from over 1 K to a few microkelvins, most predictions suggesting a T c at the millikelvin range. Prior experiments, however, did not indicate any transition down to 4 mK 7 Li, 92.5% abundant with a spin 3=2, is an excellent target for NMR studies due to its reasonably large magnetic moment 7 3:26 N . The remaining 7.5% of 6 Li, with I 6 1 and 6 0:82 N , do not contribute much to the magnetic behavior, but can be used as a probe in analyzing the interactions between the nuclear spins Lithium is dominantly a dipolar-coupled nuclear magnet, more so than any other investigated metal Nuclear-spin order in insulators has been possible due to extremely weak coupling of the spins to the lattice. Even in metals, the nuclear-spin temperature can be reduced by several orders of magnitude below that of the lattice and electrons. While the intermediate microKelvin regime is the practical limit for refrigerating the body of well-prepared specimens, their nuclear spins may be polarized by a high magnetic field and by subsequent adiabatic demagnetization be cooled to the nanokelvin regime and even below By such procedures we were able to prepare a magnetically ordered state of nuclear spins in lithium. On the basis of measurements of the spectral resonance shapes, observation of nonadiabatic effects, and determination of the spin temperature, we propose a nontrivial phase diagram with several distinct regions of different characteristics. We obtained the critical temperature of 350 nK in zero magnetic field. The sample material was purchased from Alfa Aesar [17], whose analysis indicated 99.97% purity. The content of magnetic impurities (iron) was at most 4 ppm, and we measured the residual resistivity ratio 900 100. Lithium reacts eagerly with air, whereby the samples were protected by copper capsules The best conditions for observing the two phenomena under discussion are somewhat contradictory, so that we prepared two different samples to satisfy both. A low transition temperature of superconductivity is associated with a very low critical magnetic field and potential supercooling of the normal state in any finite field. Therefore, the superconductivity (SC) sample was placed inside an efficient magnetic shield with a cylindrical layered high-permeability-superconducting (Pb) -highpermeability structure

Vibrations of a magnetic microsphere levitated above a superconductor: a high-Q oscillator for studies of vorticity in superconductors and superfluids

The oscillations of a small magnetic sphere (radius 100 μm) levitated above a superconductor are investigated. Resonance frequencies between 300 Hz and 600 Hz are observed. At low amplitudes (≤1 gmm) the oscillator has Q values of about 106. At larger amplitudes both the resonance frequency and the damping become amplitude dependent. Nonlinear and hysteretic friction is attributed to vortex motion in the superconducting environment. Application of this oscillator for investigation of vorticity in superfluids is discussed

Microsphere viscometers for low temperature applications

We describe two types of viscometer utilizing metallic microspheres. These spheres are set into stationary translational motion or into translational oscillations. The motion of these charged microparticles is induced and detected via an electric field. The observed damping of the motion yields information on the dissipation mechanisms and the viscosity of the medium investigated. The advantages of our devices for low temperature use are a simple geometry, high resolution, low heat input into the sample and the small sample volume needed. The two viscometers are complementary to each other in the sense that one is applicable at high viscosities while the other is sensitive at low viscosities

Thermodynamics of adiabatic melting of solid He 4 in liquid He 3

In the cooling concept by adiabatic melting, solid He4 is converted to liquid and mixed with He3 to produce cooling power directly in the liquid phase. This method overcomes the thermal boundary resistance that conventionally limits the lowest available temperatures in the helium fluids and hence makes it possible to reach for the temperatures significantly below 100μK. In this paper we focus on the thermodynamics of the melting process, and examine the factors affecting the lowest temperatures achievable. We show that the amount of He3-He4 mixture in the initial state, before the melting, can substantially lift the final temperature, as its normal Fermi fluid entropy will remain relatively large compared to the entropy of superfluid He3. We present the collection of formulas and parameters to work out the thermodynamics of the process at very low temperatures, study the heat capacity and entropy of the system with different liquid He3, mixture, and solid He4 contents, and use them to estimate the lowest temperatures achievable by the melting process, as well as compare our calculations to the experimental saturated He3-He4 mixture crystallization pressure data. Realistic expectations in the execution of the actual experiment are considered. Further, we study the cooling power of the process, and find the coefficient connecting the melting rate of solid He4 to the dilution rate of He3.Peer reviewe

The oscillating magnetic microsphere: a tool for investigating vorticity in superconductors and superfluids

A spherical magnet (radius 0.1 mm) is levitating between the superconducting electrodes of a parallel plate capacitor. Small vertical oscillations of the magnet about its equilibrium position can be excited. From the damping of the oscillations (in vacuum) dissipative processes due to flux motion in the superconductors have been measured. For YBCO thin-film electrodes at 4K Q-values are 106 implying a surface impedance of the order of View the MathML source. At larger amplitudes nonlinear flux dynamics due to current-dependent pinning energies is observed. For Nb electrodes the Q-values exceed 106. When the capacitor is filled with superfluid helium laminar and turbulent drag of the oscillating sphere can be studied. Below 0.5 K we find a range of intermediate driving forces where intermittent switching between potential flow and turbulence occurs. A statistical analysis of the data yields the probability distribution for either direction

Thermal Conductivity of Superfluid 3 He-B in a Tubular Channel Down to 0.1 Tc at the 4 He Crystallization Pressure

We studied the thermal conductivity of superfluid 3He in a 2.5-mm effective diameter and 0.15-m-long channel connecting the two volumes of our experimental assembly. The main volume contained pure solid 4He, pure liquid 3He and saturated liquid 3He–4He mixture at varying proportions, while the separate heat-exchanger volume housed sinter and was filled by liquid 3He. The system was cooled externally by a copper nuclear demagnetization stage, and, as an option, internally by the adiabatic melting of solid 4He in the main volume. The counterflow effect of superfluid just below the transition temperature Tc resulted in the highest observed conductivity about five times larger than that of the normal fluid at the Tc. Once the hydrodynamic contribution had practically vanished below 0.5 Tc, we first observed almost constant conductivity nearly equal to the normal fluid value at the Tc. Finally, below about 0.3 Tc, the conductivity rapidly falls off toward lower temperatures.Peer reviewe

Decoupling of first sound from second sound in dilute 3He-superfluid 4He mixtures

Bulk superfluid helium supports two sound modes: first sound is an ordinary pressure wave, while second sound is a temperature wave, unique to superfluid systems. These sound modes do not usually exist independently, but rather variations in pressure are accompanied by variations in temperature, and vice versa. We studied the coupling between first and second sound in dilute He3-superfluid He4 mixtures, between 1.6 and 2.2 K, at He3 concentrations ranging from 0% to 11%, under saturated vapor pressure, using a quartz tuning fork oscillator. Second sound coupled to first sound can create anomalies in the resonance response of the fork, which disappear only at very specific temperatures and concentrations, where two terms governing the coupling cancel each other, and second sound and first sound become decoupled.Peer reviewe