3He-4He mixtures in aerogel

Superfluid density and heat capacity experiments on³He-⁴He mixtures in 98% porous aerogel show that in this system the coexistence boundary is detached from the superfluid transition line. The tricritical point is removed, and there is a superfluid phase on the³He rich side of the phase diagram. The presence of heat capacity peaks along the transition line down to a⁴He concentration of only 8% indicates the 3-dimensional nature of this transition.This work is supported by NSF under grants DMR-9008461 and DMR-9311918.     

Acoustical Experiments on Superfluid 3He-4He Mixtures in Aerogel

This report discusses our results on the superfluidity of ³ He- ⁴ He mixtures in a 98% porosity silica aerogel. We have used low frequency sound to probe helium mixtures confined to aerogel, and have observed both the slow mode of superfluid ³ He in aerogel, which is manifested only below T_c, and an additional sound mode present only in the mixture. We attribute this novel sound mode to the slow-mode in the ⁴ He rich phase of the dilute ³ He- ⁴ He mixture. This mode exhibits positive frequency shifts below T_c in aerogel, while above T_c the mode is observed at a temperature independent frequency until close to T where it shifts to zero frequency.     

Phase separation of3He-4He mixture in aerogel

Torsional oscillator measurements of ³ He- ⁴ He mixtures confined in aerogel show evidence of a well defined phase separation region. This region is detached from the superfluid transition line, opening up a region of miscible superfluid mixture at high ³ He concentration.     

Capillary Condensation of Phase Separated Liquid 3He-4He Mixtures in Aerogel

We have studied details of the phase separation of ³ He- ⁴ He mixtures in aerogel for ⁴ He concentrations between 13 - 36% and at pressures of 0 and 22 bar. Simultaneous measurements of the ⁴ He concentration (measured with a parallel-plate capacitor) and of the tortuosity of the ⁴ He-rich phase (using the period of the torsional oscillator) provide evidence for the diversity of configurations of the ³ He- ⁴ He interface as a consequence of capillary condensation. Thus, for the same ⁴ He content within the aerogel, the ⁴ He-rich phase can have different interconnectivities determined by preparation history.     

The Tricritical Region for Helium Mixtures in 0.87 Porosity Aerogel

We have used ultrasonic velocity measurements to study ³ He- ⁴ He mixtures in aerogel with a porosity 0.87. The phase diagram resembles that of bulk mixtures, with a single transition for ³ He-rich mixtures, in contrast to the detached phase separation curve seen in 0.98 porosity aerogel. A kink in the lambda line at a 3He concentration of X _C =0.51 suggests that the phase separation line meets it at a tricritical point. We have measured the amount of superfluid which decouples both at low temperature and close to the superfluid transition, as functions of ³ He concentration. Each showed a sudden change at the concentration where the kink appeared in the lambda line, suggesting an abrupt change in the morphology of the superfluid phase in the mixtures. Similar measurements were made for pure 4He films on the same aerogel. We discuss the nature of ³ He-rich mixtures in aerogels based on these experiments.     

3He in Aerogel – an Inhomogeneously Disordered Unconventional Superfluid

We have examined the superfluidity of ³ He in 98.2% porous silica aerogel with up to 34% ⁴ He at 21.6 bar. The mixture is phase-separated for ⁴ He fractions between 11% and 34%. The ⁴ He-rich, phase preferentially occupies the regions of highest silica density in the aerogel, thus modifying the distribution of the correlated disorder seen by superftuid ³ He. The ³ He T _c increases slightly with ⁴ He content while the superfluid fraction decreases rapidly. This behavior is inconsistent with that of ³ He in a homogeneously scattering medium and is analogous to that of a granular superconductor.     

Percolative diffusion of dissolved3He atoms in He II through porous media

The diffusion of³He quasiparticles in a dilute³He-⁴He solution confined in the porous medium is discussed on the basis of the percolation theory. It is pointed out that when³He quasiparticles diffuse through the porous medium,³He quasiparticles feel the random potentials originating from the random distribution of channel radii connecting pores. Noticing that the³He concentration can be varied over a wide range in³He-⁴He solutions, we find that the chemical potential of³He quasiparticles is related to the bond percolation densityp of the porous medium. It is emphasized that the mobility edge for³He quasiparticles is different between up and down spins under high magnetic fields. A novel mechanism utilizing this characteristics is proposed to produce the degenerate Fermi system with a very high polarization ratio. A discussion is given of the spatial localization of dissolved³He atoms due to the quantum interference. It is suggested that the localization effect is realized by the NMR experiments at very low temperatures.     

Quenched bond randomness: Superfluidity in porous media and the strong violation of universality

The effects of quenched bond randomness are most readily studied with superfluidity immersed in a porous medium. A lattice model for³He-⁴He mixtures and incomplete⁴He fillings in aerogel yields the signature effect of bond randomness, namely the conversion of symmetry-breaking first-order phase transitions into second-order phase transitions, the λ-line reaching zero temperature, and the elimination of non-symmetry-breaking first-order phase transitions. The model recognizes the importance of the connected nature of aerogel randomness and thereby yields superfluidity at very low⁴He concentrations, a phase separation entirely within the superfluid phase, and the order-parameter contrast between mixtures and incomplete fillings, all in agreement with experiments. The special properties of the helium mixture/aerogel system are distinctly linked to the aerogel properties of connectivity, randomness, and tenuousness, via the additional study of a regularized “jungle-gym” aerogel. Renormalization-group calculations indicate that a strong violation of the empirical universality principle of critical phenomena occurs under quenched bond randomness. It is argued that helium/aerogel critical properties reflect this violation and further experiments are suggested. Renormalization-group analysis also shows that, adjoiningly to the strong universality violation (which hinges on the occurrence or non-occurrence of asymptotic strong coupling—strong randomness under rescaling), there is a new “hyperuniversality” at phase transitions with asymptotic strong coupling—strong randomness behavior, for example assigning the same critical exponents to random-bond tricriticality and random-field criticality.     

NMR experiments on pure3He and3He-4He mixtures in silica aerogel

We have carried out a series of NMR experiments on³He systems filling the pores of silica aerogel with 95% porosity. The systems studied included³He-⁴He mixtures with a wide range of³He concentrations x₃ as well as pure³He. All experiments were conducted in an 8 T field and for temperatures T 6 mK. This resulted in strong spin polarization at the lowest temperatures (up to approximately 80%) for the localized layer observed for a pure³He sample. For pure³He, the magnetic behavior is dominated by the localized spins, which are found to constitute 6% of the sample. The coupled system of localized plus liquid spins displays rapid transverse magnetization relaxation with an anomalous temperature dependence. For intermediate x₃ magnetization measurements provide a preliminary indication of the phase diagram of mixtures filling this porous material. The magnetization is hysteretic over some ranges of x₃.     

Phase separation in solid mixtures of helium-3 and helium-4

Phase separation temperatures have been determined in bcc³He-⁴He mixtures as a function of³He concentration and melting pressure from measurements of changes in the X-ray lattice parameter and Bragg peak shape. A new rigid tail dilution refrigerator cryostat was used to study³He-⁴He crystals with³He concentrations of 0.10, 0.20, 0.30, 0.45, 0.60, and 0.70 and melting pressures between 3.0 and 4.3 MPa. The phase separation temperatures determined are in good agreement with regular solution theory and give little support for an asymmetry in the coexistence curve expected from a Nosanow-type model and reported from previous experiments using other signatures of phase separation. At a given concentration, differences in phase separation temperatures determined from slow cooling and warming data, respectively, are as much as 25 mdeg, but this is less than half the differences reported from previous experiments. A bcc-hcp transformation was seen in a crystal with 10%³He at aboutT=0.3 K for a melting pressure of3.7 MPa.     

Experiments on 3He–4He Mixtures in Aerogel

We describe experiments on ³ He- ⁴ He mixtures in 98% open aerogel grown by cold-deposition (T80mK) of ⁴ He followed by the deposition of ³ He or alternatively by cooling down a homogenous mixture. The two approaches led to different ⁴ He film morphologies. We will also describe the observation of migration of ⁴ He from or toward the cell below 100 mK. This migration can lead to the exclusion of ⁴ He (other than the localized surface layers) for ⁴ He concentrations between 4% and 11% in the cell.     

X-ray Scattering Measurements of Helium Adsorption into Silica Aerogel

We have performed simultaneous adsorption isotherm and small angle x-ray scattering (SAXS) measurements of ⁴ He adsorption into 98% porous aerogel at 3.5K. Measurements indicate a two phase coexistence at vapor pressures slightly below the bulk liquid-vapor equilibrium point. SAXS data are interpreted according to a model which consists of the coexistence of a film phase where the aerogel strands are coated with a liquid film and a filled-pore phase were the pores defined by neighboring strands are filled with liquid.     

Nuclear Magnetism of Normal 3He and 3He-4He Mixtures in Aerogel

We report NMR experiments at 8 T on ³ He and ³ He- ⁴ He mixtures filling the pores of 95% porous aerogel, for temperatures T 6 mK. Magnetization measurements of pure ³ He reveal a localized layer approximately one monolayer thick. The longitudinal relaxation includes a component logarithmic in time, which is apparently associated with a fraction of the localized ³ He atoms. When the localized ³ He is displaced by adding ⁴ He the logarithmic relaxation disappears and T ₁ for the dominant exponential relaxation increases. Measurements of the spin diffusion coefficient with the aerogel filled with dilute solution in equilibrium with bulk phase-separated mixture provide an unambiguous determination of the spin mean free path,_s = 58 nm     

3He-3He quasiparticle interaction in3He-4He mixtures under pressure

Based on our recent phase separation curve of³He-⁴He solution at elevated pressures, we propose new³He-³He quasiparticle interaction potentials, which reproduce the existing experimental results pretty well except for³He effective mass under pressure.     

Scaling Properties of Superfluid 3He in Aerogel

We have investigated the superfluid transition of ³ He in different samples of silica aerogel. Several of these samples have been characterized using x-ray imaging, yielding information about the microstructure of the aerogel. In comparing new measurements on a 99.5% sample with previous observations on the behavior of ³ He in 98% porous aerogel we have found evidence for a scaling of the superfluid transition temperature to the correlation length of the aerogel. Furthermore, the superfluid density exhibits a similar universal behaviour over a range of values of reduced temperature. We discuss these new results in the context of superfluid pairing in the presence of a correlated disorder, specifically focussing on the fractal nature of the aerogel.     

Universal behavior of3He-4He mixture films near the Kosterlitz-Thouless transition

We report measurements of the convective thermal conductance of³He-⁴He mixture films near the Kosterlitz-Thouless transition. The thickness of our⁴He films is 14.7 and 19.1 Å above the inert layer and the³He concentration ranged from 0.033 to almost 2%. The thermal response is tested for the critical behavior as observed in pure films, and it is found to be preserved in the mixture films case. However, the parametersb, D/a ² andT _c exhibit a strong dependence on the concentration. The mixture film conductance at fixedT-T _c is found to decrease upon addition of³He implying a decrease in the 2D correlation length. Mixture films thus exhibit 2D behavior over a narrower temperature range than pure films. Further, for temperaturesT _c , the largest measurable conductance decreases sharply with the addition of³He. We attribute this behavior to a³He-⁴He scattering mechanism and a³He induced free-vortex density.     

The proximity effect between superfluid3He and a3He-4He mixture

The quasiclassical theory is used to study the proximity effect between superfluid ³ He and a mixture of ³ He- ⁴ He. The order parameter and the surface tension are calculated, and their dependence on temperature and on the hypothetical transition temperature of the ³ He- ⁴ He mixture is discussed.     

Thermal convection and nonlinear effects of a superfluid3He-4He mixture in a porous medium

The convective instability of superfluid³He-⁴He mixtures in porous media is investigated. The general hydrodynamic equations are derived and reduced to a single nonlinear equation for a scalar field. The superfluid mixtures in a porous medium have a constant⁴He chemical potential and behave essentially like a classical fluid in a porous medium. Two-fluid effects are calculated both at the onset of steady convection and the subsequent boundary of instability. The shift of critical Rayleigh number is about 1% or less at the onset of convection, but can be as large as 20% or more at the instability boundary for some regions aroundT 1 K. This two-fluid shift is quite large compared to the corresponding 0.001% shift at the onset of convection for bulk superfluid³He-⁴He mixtures.     

3He impurity excitations in solid4He

The problem of³He mobility in dilute³He-⁴He solid mixtures has been treated both theoretically and experimentally. The Hamiltonian of the system can be reduced to the Hamiltonian of strongly interacting impurity quasiparticles corresponding to some time-averaged states. The experiments carried out on solid mixtures with³He concentration 2.17%, 0.75%, 0.25%, or 0.092% by the NMR method show that at sufficiently low (T<1.2 K) temperatures the diffusion coefficient becomes temperature independent and inversely proportional to³He concentration. These results substantiate qualitative conclusions of the theory. Analysis of the experimental data makes it possible to take into account the phonon part of the³He diffusion coefficient and to obtain, up to a constant, the³He-⁴He exchange energyJ10^–7 K. All the facts mentioned above testify to the substantially quantum nature of the³He diffusion process in dilute³He-⁴He mixtures.     

Capacitative Detection of Phase Separation in 3He-4He Mixtures near the Tricritical Point

We have used two different types of capacitative sensors for detecting the phase separation boundary in ³ He- ⁴ He mixtures. We have used a parallel plate geometry to make bulk concentration measurements, and we have developed inter-digital capacitors (IDC's) to make local concentration measurements. The IDC's were developed as part of our on going effort to study the tricritical point in the absence of acceleration. The IDC's should be well suited for making measurements of the phase separation on the ³ He rich side of the phase diagram where the minority ⁴ He rich phase will grow out from the walls. The resolution and advantages of these two types of sensors are presented below along with preliminary ground based measurements of the phase separation boundary taken with the IDC's.