Continuing Specific Heat Measurements of 3He in 3He - 4He Mixture Films

Additional data from our on-going experiments for the heat capacity of ³ He in ³ He- ⁴ He mixture films on a Nuclepore substrate are reported over the temperature range 90T165 mK, for ³ He coverages between 0.05 and 1.4 bulk-density atomic lagers, on a ⁴ He film of thickness 4.33 bulk-density atomic lagers. This is a two-dimensional Fermi liquid system, in which we can change the ³ He coverage and thus tune the Fermi temperature.     

Third Sound and Quartz Crystal Microbalance Measurements of Helium on Rubidium

We present preliminary results from an experiment in progress which seeks to study third sound propagation on clean glass and rubidiated glass for several ⁴ He coverages. The third sound is driven thermally and detected with thin-film zinc bolometers over the temperature range 0.100T0.670 K. Measurements of the frequency of a quartz crystal microbalance which has rubidium deposited onto one side are made through the temperature range 0.100T1.5 K for each helium coverage studied. Results of measurements for pure ⁴ He films, primarily for third sound, are presented for coverages8.52 atomic layers.     

Heat Capacities of Monolayer 3He Fluids Floated on A Superfluid 4He Thin Film

We have measured heat capacities of monolayer ³ He floated on a superfluid ⁴ He thin film (three atomic layers) adsorbed on graphite at low temperatures. The ³ He films behave as degenerate 2D Fermi fluids with m* 1.3m ₃, where m* is the quasiparticle effective mass and m ₃ is the bare mass of ³ He, in the whole temperature range we studied (1 T 80 mK). No anomalous behavior suggesting puddling nor other phase transitions is observed. In contrast to our previous measurements for pure ³ He films without the underlying ⁴ He film, the temperature independent heat-capacity contribution is not observed. This can be explained by the second-layer localized spins trapped on substrate heterogeneities being replaced by nonmagnetic ⁴ He.     

3He Spin Diffusion Measurements for 3He - 4He Mixture Films on Nuclepore

Preliminary ³ He spin diffusion results for ³ He - ⁴ He mixture films on Nuclepore are presented as a function of ³ He coverage for 0.1 T 0.3 K. We report measurements for a constant ⁴ He coverage of 4.41 bulk density atomic layers with ³ He coverages between 0.3 and 2.1 layers. The diffusion is observed to decrease with increasing amounts of ³ He, and some structure as a function of temperature is present.     

Temperature-, concentration- and pressure-dependence of the viscosity of liquid3He-4He mixtures at low temperatures

We have investigated the viscosity of liquid³He-⁴He mixtures at various³He - concentrations (0.98%x9.5%) in the temperature range1 mK T 100 mK and at pressures 0 bar P 20 bar. At T10 mK the Fermi-liquid behaviour T² = const. as well as x^4/3 could be confirmed. However, there are significant deviations from theoretical predictions for the magnitude of the viscosity as well as for its pressure dependence.     

Shear viscosity of the B phase of superfluid3He

The shear viscosity (T) in the Balian-Werthamer (BW) state of superfluid ³ He is calculated variationally throughout the region 0t 1(t=T/T _c) from the transport equation for Bogoliubov quasiparticles. Coherence factors are treated exactly in the calculation of the collision integral. The numerical result for =_s= _s(T)/_n(T_c) agree very well with experiment in the range 0.8t1.0. Analytic expressions = 0.577 (1–1.0008t) and =1–(23/64) [=(T)/k _B T] are obtained in the low-temperature region and in the vicinity ofT _c, respectively. From the numerical analysis it is shown that the latter equation is valid only in the temperature range 0.9997t1.0.Supported by the Research Institute for Fundamental Physics, Kyoto University.     

Spin diffusion and magnetization studies of3He in3He-4He mixture films

The longitudinal spin diffusion coefficient and magnetization of a submonolayer coverage of ³ He, n ₃ =0.0066 Å^–2, in a thin adsorbed ⁴ He film has been measured as a function of temperature0.024 K T0.5 K and ⁴ He coverage0.21 Å ^–2 n ₄ 0.32 Å ^–2.     

Equation of state of3He near its liquid-vapor critical point

We report high-resolution measurements of the pressure coefficient (P/T) for³He in both the one-phase and two-phase regions close to the critical point. These include data on 40 isochores over the intervals–0.1t+0.1 and–0.2+0.2, wheret=(T–T _c )/T _c and =(– _c )/ _c . We have determined the discontinuity (P/T) of (P/T) between the one-phase and the two-phase regions along the coexistence curve as a function of . The asymptotic behavior of (1/) (P/T) versus near the critical point gives a power law with an exponent (+–1)^–1=1.39±0.02 for0.010.2 or–1×10 ^–2t–10 ^–6 , from which we deduce =1.14±0.01, using =0.361 determined from the shape of the coexistence curve. An analysis of the discontinuity (P/T) with a correction-to-scaling term gives =1.17±0.02. The quoted errors are fromstatistics alone. Furthermore, we combine our data with heat capacity results by Brown and Meyer to calculate (/T) _c as a function oft. In the two-phase region the slope (²/T ²)_c is different from that in the one-phase region. These findings are discussed in the light of the predictions from simple scaling and more refined theories and model calculations. For the isochores 0 we form a scaling plot to test whether the data follow simple scaling, which assumes antisymmetry of – ( _c ,t) as a function of on both sides of the critical isochore. We find that indeed this plot shows that the assumption of simple scaling holds reasonably well for our data over the ranget0.1. A fit of our data to the linear model approximation is obtained for0.10 andt0.02, giving a value of =1.16±0.02. Beyond this range, deviations between the fit and the data are greater than the experimental scatter. Finally we discuss the (P/T) data analysis for ⁴ He by Kierstead. A power law plot of (1/) P/T) versus belowT _c leads to =1.13±0.10. An analysis with a correction-to-scaling term gives =1.06±0.02. In contrast to ³ He, the slopes (²/T ²)_c above and belowT _c are only marginally different.Work supported by a grant from the National Science Foundation.     

Anomalous temperature dependence ofD andT 2 for dilute solutions of3He in solid4He

Results of measurements of the spin diffusion coefficientD and NMR relaxation timesT ₁,T ₂, and T_1p are presented for a range of fractional³He concentrations 1 × 10^–4x ₃2.5 × 10^–3 in solid⁴He at molar volumes 19.85V _m21.0 cm³ and temperatures 0.4<T<2 K in both hcp and bcc phases. We observe a minimumD(T) atx ₃=5×10^–4, which is interpreted in terms of a transition from coherent impuriton motion to thermally activated diffusion. ForT<0.8 K, (lnD)/(lnV _m)=60±8. TheT ₂ measurements show a minimum as a function of temperature forx ₃10^–3. TheT ₂ (T) andT ₁ (T) results yield values for activation energy and tunneling frequency of vacancies in these dilute solutions. Forx ₃=5×10^–4 andT 0.5 K,T ₂ (V _m) is anomalous.T ₁ measurements at the same concentration indicate there is an important contribution to the spectral density of dipole field fluctuations in the kHz region.Financial support provided for apparatus, materials, and a research studentship (ARA) by the Science Research Council.     

Heat capacities of the anomalous fluid phase in two-dimensional 3He

No Heading We measured heat capacities of two dimensional ³He adsorbed on graphite preplated with a ⁴He monolayer (³He/⁴He/gr) in a wide temperature (0.3 T 80 mK) and density range (1.3 7.3 nm^–2). We found that the system behaves as a normal Fermi fluid at low densities between 1.3 and 5.6 nm^–2 where the quasiparticle effective mass seems to diverge at a density for the 4/7 phase (_4/7 = 6.8 nm^–2). At higher densities but below _4/7, we observed anomalous temperature dependencies of heat capacity with two round maxima near 1 and 30 mk. With increasing density in this region, a high temperature weight of heat capacity decreases selectively leaving the 30 mK peak, while the 1 mK peak develops. This unexpected behavior can not be explained by the conventional two-phase co-existence model. Instead, we propose here that the 2D normal Fermi fluid is continuously transformed to the 4/7 Mott localized phase through a new quantum phase where a hopping of the zero-point vacancy plays an important role.PACS numbers: 75.70.Ak, 67.80.Jd, 75.10.Jm, 67.70.+n.     

The spin diffusion coefficient of3He in3He-4He solutions

The transport properties of³He in³He-⁴He solutions with molar concentrations of 5, 9, 14, and 24% have been studied for 0.9 KT2.5 K. The spin diffusion coefficientD _s and the longitudinal relaxation timeT ₁ were measured by the spin-echo method for temperatures both above and below the solution lambda temperatureT . The spin-echo method measures the diffusion coefficient for magnetizationD _s, which differs from the usual diffusion coefficient for particlesD belowT .D _s depends on the³He-³He scattering cross section _FF and the³He-roton/phonon cross section _FB, whileD depends only on _FB. The distinction betweenD _s andD is elaborated in terms of a simple mutual-friction model for diffusion. The two scattering mechanisms are clearly evident in the behavior ofD _s as a function of concentrationx and temperature. The contribution due to the³He-³He scattering is inversely proportional tox, indicating that the³He can be treated in first approximation as a classical gas (the Pomeranchuk model). The predictions of various theoretical models are compared with the results, where possible, but most of the previous theoretical work is not applicable to the concentration range and temperatures of these measurements.Supported in part by the National Science Foundation and the U.S. Office of Naval Research.     

Shear viscosity measurements of liquid 4He and 3He-4He mixtures near the tricritical point

A torsional oscillator cell is described, by means of which simultaneous precision measurements of () and of the molar volume can be made in liquid ⁴He-⁴He mixtures over the temperature range between 0.5 and 3 K. Here is the mass density, the shear viscosity and in the superfluid phase they become the contributions _n and _n of the normal component. The results of for ⁴He near the superfluid transition are compared with the predictions by Schloms, Pankert and Dohm, and by Ferrell. Measurements of () are reported for mixtures with 0.64X0.74, where X is the ³He mole fraction. Those for X = 0.67 and 0.70 are compared with data by Lai and Kitchens. The viscosity experiments show no evidence of a weak singularity at the tricritical point.     

Vibrating-wire measurements in vacuum,liquid3He and liquid3He-4He mixtures

In order to overcome the 200µK - barrier in the refrigeration of liquid ³ He- ⁴ He mixtures we have constructed an experimental cell using only pure materials to minimize possible origins for heat leaks into the liquid. With this arrangement we were able to cool a saturated6.8%- mixture to a temperature of 150µK. A vibrating wire which was immersed in pure ³ He floating on top of the phase-separated mixture was used as a thermometer. This wire was calibrated in a second experiment with pure ³ He only in the cell. In superfluid ³ He-B at T0.15 mK the damping of the wire due to the quasiparticles becomes very small, and we observe typical characteristics of the vacuum damping of the wire which was extensively examined before filling any liquid into the cell.     

Heat capacity of microscopic liquid3He droplets in silver

We report on heat-capacity measurements of liquid³He droplets in a Ag matrix at 15 mKT1 K. The samples have been prepared by implanting about 0.1 at.%³He in 42 µm thick Ag Foils. Annealing of the foils results in high-pressure³He gas bubbles of diameters between 50 Å and 150 Å; the³He in the bubbles liquefies when the metal foils are cooled to low temperatures. After each annealing step we measured the low-temperature thermal relaxation time of the foils and determined in this way the heat capacity of the³He droplets. The results differ from the specific heat of bulk liquid³He. We will discuss possible origins of this deviation.     

Temperature dependence of resistivity for thermally diffused V3Si multilayer films

Results concerning V₃Si films produced by a simple annealed multilayer technique are reported together with X-ray diffraction patterns, Auger spectroscopy, and Rutherford backscattering analysis. Low-temperature electrical resistivity measurements are discussed. It is found that the V₃Si films exhibit aT ² dependence in the temperature rangeT _c T23 K and aT ^2.6 dependence in the rangeT _c T40 K. The normal-state resistivity in the whole temperature range (T _c T600 K) is analyzed in the framework of Cote-Meisel theory. Consistent values of the saturation resistivity _m and of the Debye temperature are obtained by fitting the experimental data with the Cote-Meisel expression for (T).     

The transverse acoustic impedance of dilute solutions of3He in superfluid4He

The transverse acoustic impedanceZ=R–iX of dilute solutions of³He in superfluid⁴He has been measured at a frequency (/2) of 20.5 MHz at temperaturesT from 30 mK to the transition at T. The³He concentrations studied werec=0.014, 0.031, 0.053, 0.060, and 0.092 below 1 K, thoughc decreased slightly near the point. The impedance was found from the temperature dependence of the quality factor and the resonant frequency of anAT-cut quartz crystal resonator immersed in the liquid. Below 1 K,Z is due to the Fermi gas of³He quasiparticles, and in the collisionless limit, 1 ( is a relaxation time),R remains constant whileX goes to zero. Measurements ofR(c, T) andX(c, T) were analyzed to determine the momentum accommodation coefficient (c, T) and (c, T). The relaxation times were in good agreement with previous work, while (c, T) was independent ofc, but increased from 0.29±0.03 below 0.1 K to 1.0±0.1 above 0.8 K. Various mechanisms are suggested to explain this. Between 1.0 and 1.5 K the³He quasiparticles and the thermally excited rotons are in the hydrodynamic region, 1. Values of the total viscosity (c, T) were obtained and analyzed to give the³He gas viscosity and the³He-³He and roton-³He scattering rates, both of which were energy-dependent. The superfluid healing length a was also measured. Near the point we founda=(0.1±0.03)^–2/3 nm, where =1–T/T, proportional to the phase coherence length . Our data are consistent with the hypothesis that _s/T is a universal constant for superfluid dilute solutions, where _s is the superfluid density. Between 1.0 and 1.8 K we found thata(c, T) was comparable to measurements in³He-⁴He films.     

Recombination of Spin Polarized Atomic Hydrogen Adsorbed on a Dilute 3He-4He Mixture

We have been searching for two-dimensional (2-D) superfluidity of spin-polarized atomic hydrogen (H) adsorbed on liquid helium surface. We have investigated H adsorbed on ³ He- ⁴ He mixtures instead of pure ⁴ He because the thermal coupling of H to the mixtures is stronger than ⁴ He. ESR at 129 GHz was carried out to detect H at 4.5 T by using the Fabri-Perot confocal cavity with the cold spot located at the confocal point and thus the 2-D H signal was effectively detected. We investigated the two-body bulk and surface recombination processes of H on a 3% ³ He ³ He- ⁴ He mixture film. From the analysis of the surface recombination process, we found the adsorption energy of H was a 0.6 K for the mixture film in the temperature range between 120 mK and 250 mK, greater than the 0.3–0.4 K found previously for pure ³ He and a 67% ³ He ³ He- ⁴ He mixture.     

Shear viscosity measurements of liquid 3He-4He mixtures above 0.5 K

Simultaneous measurements of () and of the molar volume are reported for liquid mixtures of ³He in ⁴He over the temperature range between 0.5 and 2.5 K. Here is the shear viscosity and is the mass density. In the superfluid phase, the product of the normal components, _n and _n , is measured. The mixtures with ³He molefractions 0.30 < X < 0.80 are studied with emphasis on the region near the superfluid transition T and near the phase-separation curve. Along the latter, they are compared with data by Lai and Kitchens. For X > 0.5, the viscosity singularity near T becomes a faint peak, which however fades into the temperature-dependent background viscosity as X tends to the tricritical concentration X _t. Likewise, no singularity in is apparent when T _t is approached along the phase separation branches _– and ₊. Furthermore, viscosity data are reported for ³He and compared with previous work. Finally, for dilute mixtures with 0.01 X 0.05, the results for are compared with previous data and with predictions.     

Magnetic Ordering in 3He Nano-Clusters

Simultaneous measurements of magnetic susceptibility from 0.5 to 10 mK and pressure from 2.88 to 3.54 MPa have been made in ³ He nano-clusters embedded in a ⁴ He matrix, following phase separation. The susceptibility of the 3.54 MPa, all-solid sample behaves similarly to that of bulk ³ He for v=21.3 cm ³ /mole, with a Weiss constant =–250K. For the 2.88 MPa, liquid-droplet sample, =140K, indicating a ferromagnetic tendency, similar to 2-D films at some coverages. At intermediate pressures, has a peak near 1.05 mK, but without a discontinuity. For all samples, had a solid-like contribution to the lowest temperatures. Magnetic ordering in nano-clusters appears to be different than the U2D2 phase of bulk ³ He.     

Relaxation times and mass diffusion in superfluid dilute3He-4He mixtures

Relaxation times are reported from the transients observed during thermal conductivity _eff and thermal diffusionk _T ^* measurements in superfluid mixtures of³He in⁴He with a layer thickness of 1.81 mm. The experiments extend from 1.7 K toT and over a³He concentration range 10^–6X<5×10^–2. The agreement between the measured and the predicted from the two-fluid thermohydrodynamic equations is satisfactory forX>10^–3 but deteriorates for smaller³He concentrations. This situation is similar to that for _eff andk _T ^* results and indicates that the transport properties in very dilute mixtures with layers of finite thickness are not well understood. ForX>10^–3, the mass diffusion coefficientD _iso for isolated³He in⁴He has been determined from and from _eff measurements. There is an inconsistency by a constant numerical factor between these determinations. This problem might be related to the observations that in the superfluid phase, the relaxation times for different cell heightsh do not scale withh ². FromD _iso derived via the _eff data, the³He impurity-roton scattering cross section is determined. Comparisons with previous work are made.