A-B Phase Conversion and Coexistence of Superfluid 3He in Aerogel

We have studied phase transition of superfluid ³He at 2.4 MPa in cylindrical aerogel by NMR method. When the liquid is cooled down from the normal state, the A-like phase appears below superfluid transition temperature T _c ^a which is suppressed in comparison with the transition temperature of the bulk liquid. With further cooling below the certain temperature T _ab,c ^a , the A-like phase is converted into the B-like phase gradually. Both phases stably coexist within about 90 μK. When you keep the temperature constant in which both phases coexist, the A-B phase conversion stops. With furthermore cooling, the whole liquid becomes the B-like phase. The cwNMR spectra at the coexistence state suggest that the B-like phase is not uniformly distributed in the A-like phase like a large number of small bubbles in a liquid, but separated as a whole from the A-like phase. By applying a field gradient which changes as a function of square of radius, we found that the A-like phase is in the edge part with a cylindrical shape and the B-like phase is in the central part with a columnar shape.      

Textures of Superfluid 3He A-like and B-like Phases in Aerogel under Rotation

Superfluid ³He A-like and B-like phases in 98% aerogel under rotation up to 2π rad/sec have been studied by cw-NMR and Homogeneous Precessing Domain (HPD) NMR at 29 mT and 3.0 MPa. In the A-like phase, a large negative frequency shift was observed in the cw-NMR spectrum and no effect of rotation on the spectrum was found. In the B-like phase, the spin wave spectrum was observed when the sample was cooled through T _c under rotation and was affected by the counter flow due to the trapped vortices. The HPD was excited in a part of the aerogel sample but introduction of vortices into the sample by rotation or trapped vortices destroyed the HPD.     

QCM Measurements of Superfluid Response in 4He Films up to 180 MHz

At finite frequencies, a dynamic Kosterlitz–Thouless (KT) theory predicts a frequency dependence of the superfluid transition in ⁴He films on planar surfaces. We report results of QCM measurements to study the superfluid response on planar gold surfaces for very high frequencies up to 180 MHz in the temperature range of 0.6–1.0 K. As the frequency is increased, we observed the expected KT behavior that the superfluid transition shifts to a higher temperature from the static transition temperature T _KT and the transition temperature region broadens. The frequency dependence of the dissipation peak temperature at the transition agrees with a simple equation of the frequency dependence based on the dynamic KT theory. The microscopic parameter for the dynamic transition, the ratio of the diffusion constant to the square of the vortex core radius D/r ₀ ², is estimated to be on the order of 10¹⁰ s⁻¹.     

Adiabatic Melting of 4He Crystal in Superfluid 3He at Sub-millikelvin Temperatures

Adiabatic melting of ⁴He crystal to phase separated ³He–⁴He solution (at T< 2 mK) is probably the most promising method to cool the dilute phase down to temperatures substantially below 0.1 mK. When started well below the superfluid transition temperature T _c of pure ³He, this process allows, in principle, to get the final temperature (T _f ) several orders of magnitude less than the initial one (T _i ). This work is the first practical implementation of the method below the T _c of ³He. The observed cooling factor was T _i /T _f =1.4 at 0.9 mK, being mainly limited by the bad performance of the superleak filling line, by incomplete solidification of ⁴He in the cell, and by the improper thermal contact between the cell wall and the liquid.     

The AB Interface in Superfluid 3He as a Simulated Cosmological Brane

We present measurements of the transport of superfluid ³He quasiparticle excitations in the ballistic limit at temperatures well below T _c , and an interpretation of unexpected results as an experimental simulation of cosmological processes. Using a variable magnetic field profile we stabilize a layer of A phase across a cylinder of B phase, creating both an AB and a BA interface. These highly ordered interfaces may provide an ideal laboratory analogy for the branes and anti-branes of current cosmology. It has been suggested that brane interaction and annihilation are involved in inflation in the early Universe and leave behind topological defects such as cosmic strings. In our experiments we have annihilated our AB/BA branes by ramping down the magnetic field to remove the A phase layer. We then find that the quasiparticles face an extra impedance owing to defects left behind in the B phase texture. This is the first definitive observation of such a phenomenon.     

Specific heat of normal and superfluid3He

Extensive measurements of the heat capacity of liquid ³ He in the normal and superfluid phases are reported. The experiments range from 0.8 to 10 mK and cover pressures from 0 to 32.5 bar in zero magnetic field. The phase diagram of ³ He, based on the platinum NMR temperature scale, is presented. In the normal liquid at low pressures and near the superfluid transitionT _c an excess specific heat is found. The effective massm* of³He is at all pressures about 30% smaller than the values reported earlier. The calculated Fermi liquid parameters F₀ and F₁ are reduced asm*/m, while the spin alignment factor (1 + Z₀/4)^–1 is enhanced from 3.1–3.8 to 4.3–5.3, depending on pressure. The specific heat discontinuity C/C atT _c is forP = 0 close to the BCS value 1.43, whereas at 32.5 bar C/C is 1.90±0.03 in the B phase and 2.04±0.03 in the A phase, revealing distinctly the pressure dependence of strong coupling effects. The temperature dependence of the specific heat in the B phase agrees with a model calculation of Serene and Rainer. The latent heatL at the AB transition is 1.14±0.02 µJ/mole forP = 32.5 bar and decreases quickly as the polycritical point is approached; at 23.0 bar,L = 0.03 ± 0.02 µJ/mole.Work supported by the Academy of Finland.     

NMR Study of Superfluid Phases of 3He Confined in 97.5% Porous Silica Aerogel

We have studied the scattering effect from aerogel strands on superfluid phases of ³He by a cw NMR method at 920 kHz. Liquid ³He at a pressure of 13 bar was confined in 97.5% porous aerogel from the same batch as that of a recent 4th sound study. The NMR experiment was performed in a magnetic field of 28.4 mT down to 0.3 mK. As temperature decreased, the NMR resonant frequency increased below 0.76 mK. The temperature of 0.76 mK agrees with the superfluid transition temperature T ^aerogel _c observed in the 4th sound study at the same pressure. Below T ^aerogel _c the behavior of thefrequency shift as a function of temperature indicates that there is no phasetransition to the other superfluid phase down to about 0.4 T ^aerogel _c . Owing to a very large surface solid ³He magnetization, we could not determine the superfluid phase of ³He in the aerogel in the magnetization measurement.     

Anisotropic Aerogels for Studying Superfluid 3He

It may be possible to stabilize new superfluid phases of ³He with anisotropic silica aerogels. We discuss two methods that introduce anisotropy in the aerogel on length scales relevant to superfluid ³He. First, anisotropy can be induced with uniaxial strain. A second method generates anisotropy during the growth and drying stages. We have grown cylindrical ∼98% aerogels with anisotropy indicated by preferential radial shrinkage after supercritical drying and find that this shrinkage correlates with small angle x-ray scattering (SAXS). The growth-induced anisotropy was found to be ∼90° out of phase relative to that induced by strain. This has implications for the possible stabilization of superfluid phases with specific symmetry.     

Dynamic Remanent Vortices in Superfluid 3He-B

We investigate the decay of vortices in a rotating cylindrical sample of ³He-B, after rotation has been stopped. With decreasing temperature vortex annihilation slows down as the damping in vortex motion, the mutual friction dissipation α(T), decreases almost exponentially. Remanent vortices then survive for increasingly long periods, while they move towards annihilation in zero applied flow. After a waiting period Δt at zero flow, rotation is reapplied and the remnants evolve to rectilinear vortices. By counting these lines, we measure at temperatures above the transition to turbulence ∼0.6 T _c the number of remnants as a function of α(T) and Δt. At temperatures below the transition to turbulence T≲0.55 T _c, remnants expanding in applied flow become unstable and generate in a turbulent burst the equilibrium number of vortices. Here we measure the onset temperature T _on of turbulence as a function of Δt, applied flow velocity v=v _n−v _s, and length of sample L.     

4He in Nano-porous Media: Superfluidity and Quantum Phase Transition

This paper reviews recent findings of novel phenomena in ⁴He confined to a nano-porous glass. We examined pressure–temperature (P-T) phase diagram of ⁴He confined in a porous Gelsil glass that had nanopores 2.5 nm in diameter, by torsional oscillator and pressure studies. The obtained phase diagram is fairly unprecedented the superfluid transition temperature approaches zero at 3.4 MPa, and a novel nonsuperfluid phase exists between the superfluid and solid phase. These observations indicate that the confined ⁴He undergoes a superfluid-nonsuperfluid-solid quantum phase transition at zero temperature. We propose that the nonsuperfluid phase may be a localized Bose-condensed state in which global phase coherence is destroyed by a strong correlation between the ⁴He atoms or by a random potential. ⁴He in nanospace is an excellent model system for studying a strongly correlated Bose liquid and solid in a confinement potential.     

Quantum Fluid Dynamics of Rotating Superfluid 3He in Aerogel

Superfluid ³He A-like and B-like phases in 98% aerogel have been studied under rotation up to 2π rad/s by using cw-NMR and Homogeneous Pressing Domain (HPD) NMR at 29 mT and 3.0 MPa. Triplet superfluid ³He has continuous symmetries whose degeneracies are lifted by small perturbations of magnetic field, boundary condition of the sample cell, counterflow and global anisotropies of aerogel. We report NMR results of the two typical samples in aerogel under rotation, which are almost identical in the phase diagram, T _c and the critical velocity of the multiplication of vortex but are very different in textures and responses to the flow with each other. One samples (S-D) is slightly compressed by squeezing and thermal stress and thus has global anisotropic deformation along the sample axis. The other cell (S-H) has randomly(not uniaxially)-oriented global anisotropy. In the S-D, we observed a large negative shift in cw-NMR and spin wave and HPD in the B-like phase. Comparing textures determined by NMR and its response to the counterflows between two samples, we discuss how the long-range order of the continuous symmetry and textures are controlled by orientation effects due to global anisotropy in aerogel.      

Sound Velocity Measurements in the Low and the High Field Phases of the Nuclear-Ordered bcc Solid 3He in Magnetic Fields

We have measured the temperature and magnetic-field dependences of the sound velocity for one longitudinal and two transverse waves in the low field phase (LFP) and the high field phase (HFP) of nuclear spin ordered bcc solid ³He crystals with a single magnetic domain along the melting curve. From sound velocity measurements for various crystal orientations as a function of the sound propagation direction, we determined the elastic stiffness constants, c _ij (T,B). In the LFP with tetragonal symmetry for the nuclear spin structure, we extracted six nuclear spin elastic stiffness constants Δc _ij ^ℓ (T,0.06 T) from the temperature dependence of the sound velocity at 0.06 T and Δc _ij ^ℓ (0.5 mK,B) from the magnetic-field dependence of sound velocity at 0.5 mK. In the HFP with cubic symmetry for the nuclear spin structure, we extracted three Δc _ij ^h (T,0.50 T) at 0.50 T and Δc _ij ^h (0.5 mK,B) at 0.5 mK. At the first-order magnetic phase transition from the LFP to the HFP at the lower critical field B _c1, large jumps in sound velocities were observed for various crystal directions and we extracted three . Using the thermodynamic relation between Δc _ij and the change in the internal energy for the exchange interaction in this system, ΔU _ex(T,B), Δc _ij are related to the generalized second-order Grüneisen constants Γ _ij ^X ≡∂ ²ln X/∂ ε _i ∂ ε _j as Δc _ij (T,B)=Γ _ij ^X ΔU _ex(T,B), where X represents some physical quantity which depends on the molar volume and ε _j is the j-th component of a strain tensor. In the LFP, the Δc _ij ^ℓ (T,0.06 T) were proportional to T ⁴, and Δc _ij ^ℓ (0.5 mK,B) were proportional to B ². We extracted for the spin wave velocity in the LFP, s ^ℓ , from Δc _ij ^ℓ (T,0.06 T) and for the inverse susceptibility, 1/χ ^ℓ from Δc _ij ^ℓ (0.5 mK,B). In the HFP, Δc _ij ^h (T,0.50 T) were proportional to T ⁴ and Δc _ij ^h (0.5 mK,ΔB) were proportional to ΔB(≡B−B _c1). We obtained for the spin wave velocity in the HFP, s ^h , from Δc _ij ^h (T,0.50 T) and for B _c1 from Δc _ij ^h (0.5 mK,ΔB). The values obtained for and were compared with the Multiple Spin Exchange model (MSE) with three parameters by using analytic expressions for s ^ℓ and χ ^ℓ . The three-parameter MSE does not agree with the observed Δc _ij in the LFP.      

Positive ion mobility in normal and superfluid 3He

The mobility of positive ions has been measured in the normal and superfluid phases of ³He at several pressures. Below 100 mK the normal phase mobility increases logarithmically with decreasing temperature down to the superfluid transition temperature T _c; it shows an anomalous jump near 100 mK. At low temperatures the drift velocity is nonlinear for electric fields exceeding 30 V/cm. In the superfluid the mobility, normalized to its value at T _c, is much less than for negative ions. We have also observed the anisotropic mobility in the A phase and the Landau critical velocity for pair-breaking in both superfluid phases.Work supported by the Academy of Finland.On leave of absence from Regensburg University, Regensburg, West Germany, supported by Deutsche Forschungsgemeinschaft.     

Perturbative Study of Strong Coupling Correction in Superfluid 3He in Aerogel

The AB transition curve of superfluid ³He in aerogel often shows a positive slope dT _AB(P)/dP>0 over the measured pressures P, contrary to that of the bulk liquid. Bearing this behavior in mind suggestive of a unexpectedly strong reduction of the strong coupling (SC) correction due to the aerogel, we examine impurity effects on the SC contributions to the quartic term of the Ginzburg-Landau (GL) functional. Our analysis perturbative both in the repulsive interaction and the impurity scattering suggests that, in agreement with experimental data, the impurity scattering weakens the relative stability of the ABM state to the BW state and notably reduces the SC correction for the ABM phase.     

Phase diagram of turbulence in superfluid 3He-B

No Heading In superfluid ³He-B mutual-friction damping of vortex-line motion decreases roughly exponentially with temperature. We record as a function of temperature and pressure the transition from regular vortex motion at high temperatures to turbulence at low temperatures. The measurements are performed with non-invasive NMR techniques, by injecting vortex loops into a long column in vortex-free rotation. The results display the phase diagram of turbulence at high flow velocities where the transition from regular to turbulent dynamics is velocity independent. At the three measured pressures 10.2, 29.0, and 34 bar, the transition is centered at 0.52–0.59 T_c and has a narrow width of 0.06 T_c while at zero pressure turbulence is not observed above 0.45 T_c.PACS numbers: 47.37, 67.40, 67.57     

Correlation between changes in Curie temperature and electrical resistivity during structural relaxation in Fe27Ni53P14B6 metallic glass

Changes in Curie temperature (ΔT _c, electrical resistivity (Δϱ/ϱ) and volume (ΔV/V) caused by isochronal annealing in as-quenched and pre-annealed Fe₂₇Ni₅₃P₁₄B₆ metallic glasses were compared. It was found that the ΔT _c against annealing temperature (T _a) curves in as-quenched and pre-annealed samples are very similar to the Δϱ/ϱ against T _a curves. Particularly, almost a linear relationship was observed between ΔT _c and Δϱ/ϱ in the pre-annealed sample. The results strongly suggest that the origins of both ΔT _c and Δϱ/ϱ during structural relaxation in the pre-annealed sample are attributed to identical, reversible, short-range ordering.     

Thermodynamic properties of liquid3He-4He mixtures near the tricritical point. II. Data analysis by the scaling-field method

The scaling theory for tricritical phenomena by Riedel is applied to the analysis of thermodynamic properties of liquid³He-⁴He mixtures near the tricritical point. Within this theory experimental data for the phase diagram, the³He molar concentrationX, and the concentration susceptibility (X/) _T are discussed in terms of two scaling fields that are functions of the temperatureT and the difference = ₃ – ₄ of the chemical potentials of the two helium isotopes. The quantitiesX and (X/) _T in terms of thefields T and as independent variables are obtained for the intervals –0.1<T – T _t<0.53 K and –9< – _t <0.8 J/mole, from vapor pressure and calorimetric data described in a previous paper by Goellner, Behringer, and Meyer. The transformed data are analyzed to yield the tricritical exponents, amplitudes, scaling fields, and scaling functions. The values of the tricritical exponents are found to agree with those predicted by the renormalization-group theory of Riedel and Wegner. (Logarithmic corrections are beyond the precision of the present experiment.) Relations between amplitudes are derived and tested experimentally. The (linear) scaling fields are determined by using their relationship to geometrical features of the phase diagram. The data forX and (X/) _T are found to scale in terms of these generalized scaling variables. The sizes of the tricritical scaling regions in the normal and superfluid phases are estimated; the range of apparent tricritical scaling is found to be appreciably larger in the normal-fluid phase than in the superfluid phase. The tricritical scaling function for the concentration susceptibility is compared with the analogous scaling function for the compressibility of pure³He near thecritical gas—liquid phase transition. Finally, when the critical line near the tricritical point is approached along a path of constant < _t , the experimental data are found to exhibit the onset of the crossover from tricritical to critical behavior in qualitative agreement with crossover scaling.Work supported in part by the National Science Foundation through Grant No. GH-36882 and Grant No. GH-32007, and by a grant of the Army Research Office (Durham).     

NMR experiments on the superfluid phases of3He in restricted geometries

We report transverse cw NMR measurements on the superfluid phases of³He at temperatures between 3 and 0.7 mK. Nuclear demagnetization of copper was used for refrigeration. For thermometry we employed pulsed NMR on platinum powder immersed in the liquid. The measurements on³He were carried out in two NMR coil assemblies in which the liquid was confined between parallel Mylar foils with separations of 0.37 mm and 4 µm. The transition temperatureT _c was measured at pressures between 32 bars and the saturated vapor pressure; a pressure-independent increase of 11% was observed inT _c with respect to earlier data obtained with the same apparatus. We found that our temperature scale is not proportional to that used in La Jolla. In the 4-µm stack we observe a reduction in the B A transition temperature. In our measurements on the orientational anisotropy of the B phase we found qualitative agreement with the theory of Brinkman et al. We also measured the longitudinal resonance frequencies of the A and B phases between 32 bars and the polycritical point. In the 4-µm stack we found a negative NMR shift in the A phase when the field was oriented perpendicular to the Mylar plates, in agreement with the prediction of Takagi. The static susceptibility X_B of the B phase was measured as a function of temperature at 18.7 and 29 bars; its low-temperature limiting value was observed to be (0.33±0.02)_XN , independent of pressure. We use our data to estimate the strong coupling corrections to the size of the energy gap. The initial slope of the reduced gap in the A phase, _A/T _c , was found to increase by 25% when the pressure increased from 21.1 bars to the melting curve, whereas in the low-temperature limit _B(0)/T _c was found to be independent of pressure and close to its weak coupling value.     

Point-Contact Spectroscopy of the Borocarbide Superconductor YNi2B2C in the Normal and Superconducting State

Point-contact (PC) spectroscopy measurements of YNi₂B₂C single crystals in the normal and superconducting (SC) state (T _c ≃ 15.4 K) for the main crystallographic directions are reported. The PC study reveals the electron–phonon interaction (EPI) spectral function with dominant phonon maximum around 12 meV and further weak structures (hump or kink) at higher energy at about 50 meV. No “soft” modes below 12 meV are resolved in the normal state. The PC EPI spectra are qualitatively similar for the different directions. Contrary, directional study of the SC gap results in Δ_{[100] ≈ 1.5 meV for the a direction and Δ_{[001] ≈ 2.3 meV along the c axis; however the critical temperature T _c in PC in all cases is near to that in the bulk sample. The value 2Δ_[001]/k _B T _c ≈ 3.6 is close to the BCS value of 3.52, and the temperature dependence Δ_[001](T) is BCS-like, while the for small gap Δ_[100](T) is below BCS behavior at T > T _c /2 similarly as in the two-gap superconductor MgB₂. It is supposed that the directional variation Δ can be attributed to a multiband nature of the SC state in YNi₂B₂C.     

Nonlinear Transport of Wigner Solid on Superfluid 3He–A

Electrons trapped on the surface of liquid helium form the Wigner solid accompanied with the periodic surface deformation (dimple lattice). Because of the soft surface, the Wigner solid shows unique nonlinear transport properties. Here we present the results of the nonlinear transport measurements of the Wigner solid on the superfluid ³He A phase at temperatures down to 200 μK in a magnetic field of 0.363 Tesla. The transition from linear to nonlinear behavior is observed as increasing the driving voltage. This behavior is very similar to those previously observed in the B phase and normal phase, and attributable to the deformation of the dimple shape caused by the strong damping of liquid ³He.