Spin Diffusion Measurements in Spin-Polarised Liquid 3He-4He Mixtures

We report on investigations of spin diffusion in isotopic helium liquid mixtures using a multi-echo technique in applied magnetic field gradients. Samples (up to 1 cm ³ in volume) are obtained by liquefaction of optically polarised gas. NMR measurements are performed at saturated vapour pressure in a low magnetic field (2.2 mT). Signal-to-noise ratios stay high down to ³ He concentrations of order a few parts per thousand at 1K for instance. We demonstrate that the experimental accuracy of spin diffusion measurements is substantially improved using optically polarised mixtures. We have observed that the dynamics of the precession of the transverse magnetisation can be altered due to large dipolar fields at high magnetisation densities. Effects on spin-echo signals and implications for the extension of spin diffusion measurements with our technique are discussed.     

NMR Study of Solid 3He Droplets In Phase-Separated 3He-4He Mixtures

We report measurements on solid ³ He droplets embedded in a solid ⁴ He matrix. A feature of our experiments is that the mixture crystals, of 1% ³ He concentration, are grown under constant pressure conditions to minimise the formation of defects. Upon cooling the mixture isotopic phase separation is clearly observed in both pressure and NMR data. At a pressure of 36 bar the ³ He separates as solid droplets. NMR measurements on these droplets indicate values of T ₁ and T ₂ similar to those in bulk solid ³ He at the same pressure in the temperature-independent régime. Measurements of the bounded diffusion in the droplets indicate a spin diffusion coefficient similar to that in bulk solid ³ He at the same pressure. These measurements also show the size of the droplets to be a few microns.     

NMR Studies on 3He-3He and 3He-4He tunneling motions in solid 3He-4He mixtures

Helium-3 nuclear spin relaxation times T ₁, T ₂, and T ₁have been measured for ³He-⁴He solid mixtures at the exchange plateau region (~0.5K). The ³He concentrations X ₃of the samples were 7.2, 2.9, 1.8, 1.4, 0.67, 0.65, and 0.22%, and their molar volumes varied between 19.9 and 20.9cm³/mole in hcp phase. The spectral density function J() for dipolar field fluctuations was determined in the low-frequency branch from T ₁measurements and in the high-frequency branch from conventional T ₁measurements. It was found that J() is given by J() = cJ()|_3–4 + (1–c)J()|_3–3, where J()|_3–4 is the spectral density function due to the ³He-⁴He tunneling motions, and J()|_3–3 is that due to the ³He-³He tunneling motions. Using the Torrey theory, the correlation frequency of the ³He-⁴He tunneling motions was evaluated from T ₁data, and was found to be in good agreement with Landesman 's theory.Supported in part by the Japan Society for the Promotion of Science through a grant to Y.H.     

NMR Time Reversal Experiments in Highly Polarised Liquid 3He-4He Mixtures

Long-range magnetic interactions in highly magnetised liquids (laser-polarised ³He-⁴He dilute mixtures at 1 K in our experiment) introduce a significant non-linear and non-local contribution to the evolution of nuclear magnetisation that leads to instabilities during free precession. We recently demonstrated that a multi-echo NMR sequence, based on the magic sandwich pulse scheme developed for solid-state NMR, can be used to stabilise the magnetisation against the effect of distant dipolar fields. Here, we report investigations of echo attenuation in an applied field gradient that show the potential of this NMR sequence for spin diffusion measurements at high magnetisation densities.      

Structure Factors of 3He-4He Mixtures

We briefly summarize the present understanding of the dynamic structure factors of liquid ³He-⁴He mixtures in the phonon-maxon-roton region and then present a new calculation using the memory function formalism. Results agree well with experimental data.     

Adiabatic Fountain Resonance for 4He and 3He-4He Mixtures

We report an analysis of a superfluid Helmholtz resonance in the case of helium confined in a superleak. The resonance of the superfluid is achieved under nearly adiabatic conditions. Equations are derived for the resonance frequency, the temperature oscillations of the superleak and the phase relation of this signal relative to an ac heat input. The resonance frequency yields the superfluid fraction of the confined helium. Data are analyzed as function of frequency and temperature and yield parameters such as the dissipation and thermal conductivity which determine the resonance line shape. Estimates are made of the thermodynamic parameters in the resonance equation by using derivatives along the pressure-temperature-concentration lambda surface. These parameters are compared with results from the analysis of the resonance.     

Pulsed Nonlinear Sound in Superfluid 4He and 4He-3He Mixtures

Sound modes in ⁴ He and ⁴ He- ³ He mixtures which arise out of the two-fluid equations are made up up a vector convective flow and scalar temperature changes. A method for modeling nonlinear pulses of sound with geometric approximations to the vector and scalar components has recently been applied towards understanding nonlinear second sound near the lambda point. ⁶ The same method may be used, in general, for modeling linear and nonlinear sounds in Helium II. We demonstrate with a model for nonlinear second sound pulses in ³ He- ⁴ He mixtures and compare the results to experimental observations.     

Liquid-Vapor Coexistence in Two-Dimensional 3He-4He Mixtures

We present results from an ongoing study of the Liquid (L)-Vapor (V) coexistence boundary for single layer mixtures of ³ He and 4He adsorbed on two layers of H ₂ plating graphite. We are studying mixtures with ³ He molar fractions, x, of approximately 0.05, 0.1, 0.35, and 0.5, which we compare with previously published data for the pure isotopes. For the concentrations under study, we have approximate determinations of the L- V critical temperatures and of the low temperature density of the condensed phase.     

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     

Fermi Liquid Properties of 3He-4He Mixtures

We calculate microscopically the spectrum of a ³ He impurity atom moving in ⁴ He, determine the Fermi-Liquid interaction between ³ He atoms and then calculate the pressure and concentration dependence of the effective mass and the magnetic susceptibility. The long wavelength limit of the spectrum defines the hydrodynamic effective mass. When k 1.7Å^–1 the motion of the impurity is damped due to the decay into a roton and a low energy impurity mode. The calculations of the Fermi-Liquid interaction are based on correlated basis functions (CBF); the relevant matrix elements are determined by the Fermi hypernetted-chain theory. Our theoretical effective masses agree well with recent measurements, ^1,2 but our analysis suggests a new extrapolation to the zero-concentration limit. With that effective mass we also find a good agreement with the measured ³ Landau parameter F ₀ ^a .     

Critical Supersaturation of Superfluid 3He-4He Mixtures

We report the results of our systematic study of the phase separation in supersaturated ³He-⁴He liquid mixtures of the ³He-dilute phase. The amount of the critical supersaturation is determined within the wide ranges of the temperature (0.4–645mK) and the pressure (1–8.5kgf/cm²). Using the data we construct the surface of critical supersaturation, x _3,cr (T,P), which enables us to recognize almost the overall behavior of the critical supersaturation in superfluid ³He-⁴He mixtures. The main specific features observed are (i) below 10mKx _{3, cr} is almost temperature-independent, (ii) above 10mK up to 500mKx _{3, cr} increases with the temperature, and (iii) above 500mKx _{3, cr} decreases smoothly with the increase of temperature down to zero at the tricritical point. We give various discussions from the viewpoint of the quantum nucleation, the classical thermal nucleation and the crossover between them.     

3He-4He Mixtures in 95% Porous Aerogel

Torsional oscillator measurements of ³ He- ⁴ He mixtures in 95% porous aerogel found a phase diagram similar to that in 98% porous aerogel. The coexistence boundary on the ³ He rich side resides very close to, but nevertheless is detached from the superfluid transition line. Together with the findings in 98%, 87%, and 99.5% porous aerogel, this result supports the interpretation that the phase separation of ³ He- ⁴ He mixture in aerogel is induced by the capillary condensation of ⁴ He films from neighboring silica strands into ⁴ He rich domains.     

Spin-Spin Relaxation in Phase-Separated 3He-4He Solid Mixtures

The spin-spin relaxation time T ₂ in a ³ He- ⁴ He solid mixture with an initial concentration of 3.18% ³ He is measured during its phase separation in a temperature range of 1-250 mK. Cooling down to the region of separation was carried out by small steps (10 mK) followed by temperature stabilization for many hours. The time T ₂ was measured by using the pulsed NMR technique at a frequency of 250 kHz. The spin echo method makes it possible to distinguish the contributions to magnetic relaxation from both the concentrated and the dilute separated phases. The relaxation time T ₂ in the concentrated phase is found to be practically independent of temperature down to 50 mK and is determined by the same ³ He- ³ He exchange interaction as in pure bulk solid ³ He. It is found that the behavior of the spin echo signal at ultralow temperatures exhibits an anomaly, which may be connected with quasi-one-dimensional spin diffusion. In the dilute daughter phase the spin-spin relaxation time is inversely proportional to concentration and is described correctly by the Torrey model taping into account ³ He- ⁴ He tunnel exchange. The values of T ₂ in this phase coincide with those for a homogeneous (non-separated) mixture of the same concentration.     

Melting and Crystallization of 3He Inclusions in Two-phase Solid 3He-4He Mixtures

The peculiar features of the phase diagram for the ³ He- ⁴ He system make it possible to melt the ³ He inclusions formed during phase separation of the mixture by further cooling and to crystallize them in subsequent heating. The kinetics of these processes is studied on a sample with a molar volume of 20.54 cm ³ /mole (P=31.7 bar) using pressure measurements. The time dependence of the crystal pressure P(t) is measured on cooling at a rate of 10 mK/h followed by heating. The dependence P(t) has two distinct rises in pressure, the first rise being associated with the phase separation of the mixture and the second one with the melting of the ³ He inclusions formed. It is shown that the melting of the ³ He inclusions is almost complete after the fast cooling and the observed pressure jump is in good agreement with the corresponding change in the molar volume. The repeated crystallization of the inclusions is found to give rise to a large pressure gradient near the boundary of the inclusions, suppressing quantum diffusion considerably. This may result in an incomplete crystallization of the inclusions. The experimentally observed difference between the initial and final pressure in the sample corresponds to the fact that approximately 20% of the ³ He remains in the liquid state.     

Phase Separation Kinetics of Solid 3He-4He Mixtures

The kinetics of isotopic phase separation in solid mixture of ³ He in ⁴ He with the initial concentration 2.05 % at various molar volumes has been investigated by precise pressure measurements. It has been shown that during both stepped and fast cooldown into the metastable region the equilibrium of coexisting phases is described by the exponential law with a characteristic time constant , The value of is found to decrease as the molar volume increases and the temperature lowers. It confirms that the growth of the ³ He-rich phase is connected with nonthermally activated (quantum) diffusion in the gas of delocalized ³ He quasiparticles. The obtained experimental results can be described only qualitatively by current kinetic theory of binary quantum solid mixtures. The conditions permitting the realization of the isotopic phase separation during the time observed in the experiment are analyzed. The effective quantum diffusion coefficient providing required ³ He atoms transport is about an order of magnitude higher than the corresponding value measured in NMR experiments. These conditions are probably fulfilled at the big concentration gradient which takes place at isotopic phase separation. The corresponding kinetic theory should be developed.     

Critical Behavior and Scaling of Confined 3He-4He Mixtures

When helium is confined to a uniform small dimension L, its behavior is modified due to the limitation of the growth of the correlation length. This has been explored for planar confinement over a wide range of L. Less is known about confined mixtures, especially in the case of the specific heat. Here two principal effects come into play: the magnitude of the correlation length increases, and the measured heat capacity C_px must be converted to C_p, where = ₃ – ₄ , before finite-size scaling predictions can be verified. The increase in makes a given confinement L look smaller as the concentration x is increased. This, as well as changes of L itself, can be used to test predictions of correlation-length scaling. We report measurements of the specific heat of confined mixtures and compare with the well established scaling for the pure system.     

Slip in Vibrating Wire Experiments on 3He-4He Mixtures

No Heading We present vibrating wire viscometer experiments in concentrated and dilute ³He-⁴He mixtures showing that the slip length may become orders of magnitude larger than the mean free path due to increased specular scattering of the ³He quasiparticles with the superfluid ⁴He film on the wire. The experimental results are in good agreement with a recent theory for slip which accounts for the cylindrical geometry of the wire and for velocity slip in directions normal as well as tangential to the surface of the wire.PACS numbers: 67.60.Fp, 51.20.+d     

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.     

Measurement of the 4He Chemical Potential in Phase-Separated 3He-4He Liquid Mixtures

As a first step towards thermodynamic measurements in highly polarised dense ³ He fluids, an accurate determination of the ⁴ He chemical potential ₄ was performed in unpolarised phase-separated ³ He- ⁴ He liquid mixtures at low pressures (0-1 bar) over a temperature range 0.12 - 0.65 K. A method introduced by H. London and relying on heat flush effects was used. Two volumes containing : a) a cold, phase-separated helium mixture and b) a warmed, pure ⁴ He liquid are connected by a narrow tube, and their temperatures are recorded under various conditions. The results agree with existing data obtained by the same technique for T >0.2K, but cannot be analysed with the simple regular solution model fitting vapour pressure data at T >0.6K. The sensitivity of the technique is shown to be sufficient to observe expected effects of nuclear polarisation on ₄.     

The Formation and Melting of 3He Clusters in Phase-Separated Solid 3He-4He Mixtures

Melting pressure measurements have been made on the ³ He-rich phase formed by cooling a solid mixture of 0.6% ³ He in ⁴ He through phase separation, at pressures between 2.78 and 3.56 MPa. For comparison, simultaneous observations were made with the mixture confined in the pores of a silver sinter and in an open volume connected to the same fill-line. Samples in the sinter cell solidify at higher pressures than the open cell and equilibrate more quickly. Both cells exhibit hysteresis between melting and freezing temperatures, and the transitions are broader in the open-volume cell. Relative to pure ³ He, the melting pressure is elevated by as much as 60 kPa in the sinter cell and 20 kPa in the open cell. The size of the pressure change on melting indicates that a large fraction of the ³ He remains solid at pressures below the melting curve, and this effect is more pronounced in the sinter cell. Measurements are in progress to measure the magnetisation through the magnetic ordering transition.