NMR Studies of 3He Droplets in Dilute 3He-4He Solid Solutions

We have performed measurements of the temperature dependence of the nuclear spin-lattice relaxation times (T ₁) for a wide range of ³He concentrations for dilute mixtures of ³He in solid ⁴He. The temperatures for phase separation are determined for ³He concentrations 500<x ₃<2000 ppm for a molar volume V _M =20.7 cm³. We report the temperature dependence of the nuclear spin-lattice relaxation times for ³He in the droplets formed after phase separation at low temperatures. The temperature dependence suggests that the interface ³He atoms responsible for the relaxation are degenerate, not solid-like.     

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.     

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.     

Influence of Supercooling Level on Kinetics of Phase Separation in Solid Mixtures of 4He in 3He

We studied the kinetics of phase separation in the solid mixture of ⁴ He in ³ He at various supercooling in the temperature range of 100–200 mK through precise pressure measurements. The time dependences of the pressure change during phase separation were exponential. At small supercooling the characteristic time constant is almost independent of the final temperature T_f and is about 10 hours, which is considered to result from heterogeneous nucleation. In a narrow range of T_f decreases more than an order of magnitude. At larger supercooling is independent of T_f again. This behaviour agrees qualitatively with the theoretical consideration of the phase separation kinetics at homogeneous nucleation taking into account the finiteness of a cooling rate. The value of interphase surface tension has been obtained from comparison of the theory with the experimental results.     

The Fermi Liquid theory of4He in3He

The Zharkov-Silin Fermi Liquid theory of solutions of⁴He in normal (non-superfluid) liquid³He is reviewed and slightly extended. The theory is expected to be valid only below 0.1 K, and it predicts that there should be a hundred-fold increase in the diffusion coefficient as the temperature is lowered into this region. The limited range of validity explains the apparent disagreement between the recent very low temperature measurements of the phase separation line by Nakamura et al. and extrapolations from higher temperatures. In the low temperature experiments the⁴He concentration X₄ is so small that there is no macroscopic phase separation, only a gradual thickening of the⁴He-rich film on the walls. We confirm that the phase separation temperature T_ps(X₄) estimated from the thickening is close to the values which would be observed in an ideal experiment with a macroscopic phase. Fits to T_ps(X₄) including the new data show that the⁴He effective mass m ₄ ^* is close to, and may be equal to, the bare mass m₄. The difference in binding at zero pressure between⁴He in liquid⁴He and in liquid³He is (E₄₄–EE₄₃)/k_B=(0.21+0.03/–0.01)) K. Using the volume measurements of Laheurte to calculate the pressure dependence of E₄₃ indicates that the difference in binding has a minimum of (0.0±0.2) K near 11 atm. This implies that the solubility of⁴He in³He is enhanced in this region of pressure. The behavior of the spinodal line at low temperature, and the possibility of observing Bose condensation in a metastable solution of⁴He in liquid³He are also discussed.     

Pinning of Quantized Vortices in Mixed 3He-4He Droplets

We use density functional theory to investigate the structure of mixed ³ He _{N 3} – ⁴ He _{N 4} droplets with an embedded Xe atom that pins a quantized vortex line. While ³ He atoms are distributed along the vortex line and on the surface of the ⁴ He drop, the impurity is mostly coated by ⁴ He atoms. Results for N ₄ =500 and a number of ³ He atoms up to N ₃ =100 are presented, and the binding energy of the dopant to the vortex line is determined.     

Vortex-Loops and Solid Nucleation in Superfluid 4He and 3He

We propose a new model for the nature of the nucleation of solid from the superfluid phases of ⁴He and ³He. Unique to the superfluid phases the solid nucleation involves an extremely fast solidification front. We depart from the usual quasi-static treatment of solid nucleation by proposing that the nucleation of a solid seed is helped by the simultaneous nucleation of vortex-loops in the superfluid around it. It is the composite entity which is nucleated out of the over-pressurized liquid. This occurs when the local release of pressure creates a velocity field in the superfluid which in turn facilitates the nucleation of vortex-loops. The kinetic energy gain of this process balances the surface tension, as the solid surface is quickly covered by many vortex-loops (hairy snow-ball). We show that this scenario gives good agreement with many experiments on heterogeneous nucleation, where the energy barrier is found to differ with the classical theory of homogeneous nucleation by 8 orders of magnitude. We propose several experiments that could show the involvement of vortices with solid nucleation.     

Phase Separation Line for Solid Mixtures of 3He in 4He

The excess pressure due to the phase separation of solid mixtures of ³He in ⁴He held at a constant volume was measured and used for constructing the phase separation diagram of this system. We obtained high-quality homogeneous samples of the solid mixtures after several cycles of cooling down and heating up the two-phase crystal. This gave reliable and reproducible experimental data without hysteresis efects. We compared the phase diagram line obtained with various theoretical approaches, which describe the phase separation of the helium isotope mixtures. The regular solution model can not describe the experimental data well and neither can the asymmetrical Mullin's model. Good agreement is observed only with the theory of Edwards and Balibar which takes into account the difference between the crystal symmetry (hcp and bcc) of the coexisting phases.     

Threshold Effect During Dissolution of 3He Inclusions in Solid 4He

A pressure jump has been found at the onset of the dissolution of bcc inclusions in separated solid ³ He - ⁴ He mixture if the crystal is overheated above a certain critical value. This effect can be explained in the framework of a multistage dissolution process model.     

Observation of Anomalously Low Momentum Transfer in the Low Energy Scattering of Large 4He Droplets From 4He and 3He Atoms

The momentum transferred to large superfluid ⁴ He droplets in low energy ( 4–10 K) scattering from ⁴ He and ³ He atoms was determined from time of flight measurements after the droplets have passed through a low temperature (T = 1.7–4.2 K) scattering box filled with the gas of either He isotope. The results are compared with ³ He droplets scattered from either ⁴ He or ³ He gas for which all of the incident momentum is transferred, as expected for classical capture of the scattering gas atoms. In the case of the ⁴ He droplets a smaller momentum transfer is found amounting to 65% for ⁴ He atoms and 45% for ³ He atoms but only at the lowest collision energies. These results are consistent with transmission of some of the atoms through the droplets.     

Surface Magnetism of Liquid 3He on 4He Pre-plated Graphite

No Heading The nuclear susceptibility of liquid ³He in Grafoil pre-plated by 2.5 and 3.5 layers of ⁴He has been studied with a cw NMR method at temperatures between 0.7 and 100 mK under various liquid pressures. The 3.5 layers of ⁴He pre-plating suppresses a formation of the first and second solid ³He layer, eliminating most of surface magnetization at saturated vapor pressure. However, with increasing liquid pressure, a magnetization obeying a Curie Weiss law gradually grows in the same way as in the previous experiment for pure liquid ³He. This magnetization, induced by pressurization, is attributable to the formation of solid ³He layer above the pre-plated ⁴He.PACS numbers: 67.80.Jd, 75.70 Cn, 67.70.+n.     

Elementary Excitations in Solid and Liquid 4He at the Melting Pressure

Recent discovery of a nonclassical rotational inertia (NCRI) in solid ⁴He below 0.2 K by Kim and Chan has revived great interest in the problem of supersolidity and initiated intensive study on the properties of solid ⁴He. A direct proof that the onset of NCRI corresponds to the supersolid transition would be the observation of a corresponding drop of the entropy of solid ⁴He below the transition temperature. We have measured the melting pressure of ultrapure ⁴He in the temperature range from 0.01 to 0.45 K with several single crystals grown at different pressures and with the accuracy of 0.5 μbar. In addition, supplementary measurements of the pressure in liquid ⁴He at constant volume have been performed, which allowed us to eliminate the contribution of the temperature-dependent properties of the pressure gauge from the measured melting pressure data. With the correction to the temperature-dependent sensitivity of the pressure gauge, the variation of the melting pressure of ⁴He below 320 mK obeys the pure T ⁴ law due to phonons with the accuracy of 0.5 μbar, and no sign of the transition is seen (Todoshchenko et al. in JETP Lett. 85:454, 2007). This sets the upper limit of ∼5⋅10⁻⁸ R for a possible excess entropy in high-quality ⁴He crystals below 320 mK. At higher temperatures the contribution from rotons in the superfluid ⁴He has been observed. The thermal expansion coefficient of the superfluid ⁴He has been measured in the range from 0.01 to 0.7 K with the accuracy of ∼10⁻⁷ 1/K, or by two orders of magnitude better than in previous measurements. The roton contributions to the melting pressure and to the pressure in liquid at a constant volume are consistent and yield the value of 6.8 K for the roton gap, which is very close to the values obtained with other methods. As no contribution due to weakly interacting vacancies to the melting pressure of ⁴He has been observed, the lower limit of about 5.5 K for their activation energy can be set.      

Experimental and Theoretical Problems of the Quantum Phase-Separation Kinetics of Liquid 3He-4He Mixtures

The nucleation of the ³ He-concentrated phase is analyzed at the phase-separation of a supersaturated liquid ³ He– ⁴ He mixture in a wide range of temperatures. The crossover from the classical kinetics to the quantum kinetics is considered. Besides the homogeneous bulk nucleation the nucleation under heterogeneous conditions due to the possible presence of quantized vortices is examined.     

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.     

Formation of Vacancion-Impurity Complexes in Phase-Separated Solid Mixtures of 4He in 3He

New features are observed for the pressure in a phase-separated dilute solid mixtures of ⁴ He in ³ He subjected to multiple temperature cycling within the phase-separation region. The results are explained within the framework of the hypothesis of A.F. Andreev and D.I. Pushkarov that the vacancies in a crystal without ideal periodicity are surrounded by clusters with a periodic structure.     

3He Impurity Effects on the Growth Kinetics of 4He Crystals

We report the growth kinetics of the⁴He crystals with a small amount of³He impurities around 0.8 K. The growth resistance was measured using the response of the charged interface with respect to an externally applied voltage. In 5 ppm and 10 ppm³He mixtures, it is found that (1) the relaxation process can be expressed as an exponential behavior, (2) the growth resistance becomes larger compared to pure⁴He and does not have a strong³He concentration dependence, and (3) the temperature dependence of the growth resistance is much the same as pure⁴He. We discuss several possible explanations of the present experiment.     

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.     

Dynamical Response of Liquid 3He Films Adsorbed on Solid Substrates

Within the general framework of linear response theory, we investigate the excitation spectrum of ³He films adsorbed on substrates. Starting from the quasiparticle spectrum and the effective interaction derived in a finite range density functional scheme, we analyze the properties of the particle-hole (ph) excitations as well as the collective modes in the Random Phase Approximation. On the one hand, the most important features of the ph spectrum, originated in the band structure of the single particle spectrum together with the fermionic character of the quasiparticles, are clearly exhibited when the free response to a probe parallel or transverse to the film is considered. On the other hand, for any film, the collective spectrum presents various branches which, in many situations, can be associated with predominantly intraband longitudinal transitions or with almost pure interband transitions. Analyzing the RPA response of a monolayer on substrates of very different adsorbing power (cesium and graphite) we can interpret the nature of the existing collective excitations and determine the influence of the geometrical features of the film on the effective quasiparticle interaction responsible of these oscillations.     

Features of Phase Separation Kinetics of Solid 3He-4He Mixtures. Role of Boundary Resistance

No Heading Precise pressure measurements were carried out at phase separating the solid ³He - ⁴He mixtures in the temperature range of 100200 mK for pressures between 3036 bar. The relaxation time was found to be temperature independent at large supersaturations and/or low temperatures. This fact was explained with existence of large resistance under impurity atom transfer through the inclusion-matrix boundary. The results were compared with the calculate in the framework of diffusion problem which takes into account the finiteness of atom stay time on the boundary. The comparison of the calculated and experimental data allowed us to find the value of the new phase inclusion concentration. The measured temperature dependence of is in agreement with theoretical predictions that the diffusion coefficient must be proportional to x^–4/3 (x is a impurity concentration) when there is strong impurity interaction.PACS numbers: 67.80.–s.     

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.