NMR study of 3He bubbles in phase-separated solid 3He –4He mixtures

³ He droplets embedded in a solid ⁴ He matrix have been studied by NMR and pressure measurements. One feature of the experiment is that the mixture crystals, of ³ He concentration 1%, are grown under constant pressure conditions to minimise the formation of defects. A number of sample pressures below 34 bar have been studied. Isotopic phase separation and the melting of the bubbles are clearly observed. Measurements of T₁ , T₂ and magnetisation give detailed information on the structure of the droplets. At an initial sample pressure of 28.3 bar preliminary measurements of the T₁ of the liquid bubbles show a temperature dependence of the form (A+ B/T²)^–1. This indicates that the expected relaxation in the liquid is augmented by a constant contribution, probably from the surface of the droplets.     

Bulk nuclear polarization of solid3He

Measurements are given on the bulk nuclear spin polarization in a liquid-solid³He mixture cooled by compressional cooling to below 5 mK in a magnetic field of 54.5 kG. Owing to the low Pauli spin susceptibility of liquid³He, the observed polarization is primarily due to solid³He. A maximum average nuclear polarization of 47% was observed, although the corresponding solid³He polarization is believed to be higher. Our novel detection system, using a dual directional coupler for cw NMR, is a simple and versatile means of working in the awkward frequency range around 180 MHz. We also report transient heating measurements in the³He system which indicate that the internal thermal equilibrium time in bulk solid³He on the³He melting curve appears to be quite short (less than 5 min) at these temperatures. One type of transient measurement is complicated by the dramatic effect of the contribution of the³He nuclear magnetization to the total local magnetic field. This contribution is considered via a simple model.This work has been supported by the U.S. Atomic Energy Commission under Contract No. AT(04-3)-34, P.A. 143.     

NMR study of the solidification and melting of3He in porous glasses

TheP-T phase diagrams of the liquid-solid phase transition of³He in three porous glasses with different pore sizes have been determined from spin-lattice relaxation measurements in the temperature range 0.5–4.2 K. The onset of solidification of³He in the pores occurs at excess pressure over the bulk phase transition. The excess pressure depends on the pore size. A model of the phase transition in small pores which takes into account the contribution of the surface energy to the free energy is described and compared with experimental results. TheT ₁ relaxation mechanism of³He in the pores is found to be due to the surface relaxation when³He is in the liquid phase and due to the relaxation of bulk solid³He when it is in the solid 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     

Magnetic Relaxation of Solid and Liquid 3He Confined Inside a Silver Sinter

We present T ₁ measurements performed in liquid and solid ³ He confined in sintered silver. In the liquid case, we find a close to linear relationship between T ₁ and the applied magnetic field, similar to other (non metallic) systems, and up to higher frequencies (corresponding to 11 T) than previously reported. In the solid, the relaxation rate is found to increase spectacularly at large polarizations, which may indicate a polarization dependence of the exchange motion. Now atNow at     

Concentration dependence ofD,T 1, andT 2 for dilute solutions of3He in solid4He

Measurements of the spin diffusion coefficientD and NMR relaxation timesT ₁ andT ₂ are reported for dilute solutions of³He in solid⁴He at two molar volumes, 20.95 and 20.7 cm³. The weakly interacting impuriton model, for whichD ^–1 is proportional to impurity concentration, is observed only at fractional impurity concentrationx ₃ below 3 × 10^–4. Forx ₃ around 10^–3,T ₁ andT ₂ are controlled by the formation and breakup of³He₂ molecules.     

Molar-Volume Dependence of the Pressure in hcp Solid 3He in Magnetic Fields

Pressure measurements have been made in a hcp solid ³ He at molar volumes from 18.90 to 19.45 cm ³ /mol, at temperatures down to 1 mK and in magnetic fields up to 0.16 Tesla. The results are analyzed by a high-temperature series expansion with multiple-exchange processes. The molar volume dependence of the multiple-exchange interactions has been determined by pressure measurements in magnetic fields. The results indicate that the exchange frequencies determined by the pressure measurements in a hcp solid ³ He are consistent with those obtained by magnetization measurements.     

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.     

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.     

Nuclear magnetic relaxation of3He gas. II.3He-4He mixtures

Longitudinal relaxation timesT ₁ have been measured in³He-⁴He gas mixtures, using pulsed NMR, in the temperature range 0.6–15 K. Helium-3 number densities of the order of 10²⁴ atoms m^–3 were used. Relaxation takes place on or near the walls of the Pyrex sample cells and measurements ofT ₁ give information about the surface phases. A cryogenic precoating of solid molecular hydrogen was used to reduce the helium-substrate binding energy from 100 K on Pyrex to 13 K for³He and 15 K for⁴He. TheT ₁ data at high temperatures were similar to those observed previously in the pure³He-H₂ system. The presence of⁴He generally causedT ₁ to rise on cooling below 2 K due to the preferential adsorption of⁴He over³He at the surface. However,³He atoms that go into quasiparticle states in the superfluid helium film can be an extra source of relaxation. In uncleaned cells, relaxation probably takes place in quasiparticle states at the free surface of the superfluid film, which are bound with an energy of 5.1±0.3 K. Baking the Pyrex cells under vacuum and rf discharge cleaning the walls before sealing in the sample gas were found to increase the bulk gasT ₁ by two or three orders of magnitude. In a cleaned, sealed cell aT ₁ of 8 h was measured at 7.7 MHz and 0.8 K. In this case relaxation is probably occurring two or three helium layers away from the helium-hydrogen interface. It may be possible to observe a predicted minimum in the intrinsic dipolarT ₁ of the bulk gas by using a⁴He wall coating to suppress wall relaxation effects (which usually dominate the nuclear relaxation of the bulk gas).     

Kinetics of Liquid 3He Droplets in Solid 4He Matrix

Precise measurements of pressure in the crystal at constant volume were used to obtain the data on growth and dissolution kinetics of liquid ³ He droplets formed as a result of isotopic phase separation of solid ³ He- ⁴ He Mixtures. We studied several crystals with an initial ³ He concentration of 2.05% in the pressure range of 26–27 bar. It is shown that the growth of the liquid droplets during the stepwise cooling of the two-phase crystal is correctly described by the superposition of two exponential processes: diffusion decomposition with a small time constant and strain relaxation with a big time constant. The strain layer near the droplet boundaries is due to a great difference in molar volume between the droplets and the matrix, and leads to a plastic deformation of the matrix and to a non-equilibrium ³ He concentration in the matrix. Under such conditions quantum diffusion is significantly suppressed and ³ He atom transport occurs only as the strain is relaxed.     

Thermodynamics of the liquid-solid interface in dilute solutions of3He in4He

We show that the (p, T, x) phase diagram of⁴He close to melting pressure (25.3 bars) with small concentrations of³He and at very low temperatures has several unanticipated and novel features. For pressures between 25.3 bars and a triple point pressurep*, estimated to be 25.8 bars, we find a dilute liquid solution of³He in equilibrium with solid⁴He. The concentration of the liquidx _c increases from zero to the dilute liquid solubility limitx ₀ as the pressure increases from the pure⁴He melting pressure atT=0 top*. We explore the possibility of self-cooling by lowering the pressure throughp*. We also consider the effects of a strong magnetic field, and show that it lowersx _c. An estimate of the kinetic growth coefficient is given. Finally, we discuss the possible adsorption of³He on the melting front and the consequent faceting enhancement of the solid⁴He.     

Phase Transition of Superfluid 3He in Aerogel

We have studied phase transition of superfluid ³He in 97.5% porosity aerogel by NMR method. Above 1.0 MPa, superfluid phase transition has been observed. The transition temperature T _c ^a is strongly suppressed from its bulk value. The Pressure-Temperature diagram suggests that superfluid phase will not appear below near 0.8 MPa. The A-B phase transition has been observed above 1.3 MPa, below which a state of superfluid phases remains to be identified. The temperature dependence of NMR frequency shifts Δf in the A-like and the B-like phases are almost linear at pressures below 2.4 MPa. We obtained the differential coefficient of NMR frequency shifts ∂(Δf)/∂(T/T _c ^a ) at 0.9T _c ^a as a function of pressure, and it suggests that superfluid phase will not appear below near 0.8 MPa which is the same pressure estimated by P-T diagram.     

Order of the PP-HFP transition in solid3He

New measurements of the melting pressure of solid³He P_m(T,B) have been made through the paramagnetic phase-to-high field phase transition. Temperatures were determined with Pt NMR and the³He melting pressure in zero field measured in a second cell. In a field of 0.405 T, we find a change in entropy through the HFP-PP transition of S/Rln2=0.13 over a temperature interval of only about 4 µK. Thus, we conclude that the transition is first-order at low fields. The entropy discontinuity decreases with field and the transition region broadens, with the transition possibly becoming second-order above a tricritical point near 0.6 T.     

NMR in pure3He films on a Nuclepore substrate

The properties of³He films on a Nuclepore substrate have been measured by pulsed NMR at a Larmor frequency of 10 MHz between 1.3 and 4.2 K. The³He film thickness was varied from 0.14 to 2 layers. The spin-spin relaxation timeT ₂ agrees well with previous measurements of³He films on Mylar and Vycor glass at low temperatures. The spin-lattice relaxation timeT ₁ for submonolayer films shows a strong temperature dependence consistent with a thermally activated process. This behavior has not previously been observed on amorphous substrates. The spin diffusion coefficient was measured for the thickest films at 4.2 and 2.6 K and found to be consistent with free atom motion of the³He in the vapor. In thin films or at low temperatures, the diffusion was too small to be observed. The magnetic coupling between the³He nuclei in a film and the protons in the Nuclepore substrate was determined from the effect of the³He on the proton-lattice relaxation time. It is about 100 times weaker than the interaction between³He and the fluorine nuclei in a Teflon substrate.     

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.     

Properties of 3He in thin 4He films

Substantial progress has been made in our understanding of the properties of ³He atoms in thin films of ⁴He. For such films the ³He occupies discrete quantum states in the film and the system is both rich and complex. Here we discuss progress in this field from several points of view; we briefly discuss early heat capacity and third sound results and concentrate on more recent NMR measurements of the magnetization and relaxation times T ₁ and T ₂. Further experimental work and theory for systems of finite ³He coverage is needed to fully understand this fascinating system.Presenter at the Elba Summer School; authors are listed alphabetically.     

The influence of3He on the wetting of4He to a cesiated substrate

We report preliminary measurements of the influence of ³ He in the adsorption of ⁴ He to a cesiated substrate by the use of quartz crystal resonance techniques. When compared with the case of pure ⁴ He, the presence of ³ He in the apparatus induces the wetting of the mixture film to Cesium at low temperatures. The wetting is hysteretic, beginning at a concentration-dependent T_c on cooling with continued wetting for T>T_c on warming. The temperatures T_c are given as a function of the total concentration of ³ He in the apparatus.     

3He Anomalously High Spin Diffusion in Solid Para-Hydrogen

NMR measurements of ³He spin diffusion coefficient in solid para-H₂ are carried out at the temperatures 0.45–1.5 K. The crystals have been grown under constant pressure 20–130 bar. The ³He concentrations in the initial para-H₂–³He gas mixtures were 0.1% and 0.3%. It is found out that the decay of echo amplitude vs both magnetic field gradient G and time interval τ between RF pulses is of non-exponential character, typical of one-dimensional diffusion in restricted geometry. The values of true spin-diffusion coefficient D _S measured are found to be ∼10⁻⁴ cm²/s at 20 bar. At 108 bar D _S value is one order of magnitude less. D _S does not depend on temperature. Such spin diffusion coefficient values seem to be anomalously high in comparison with well-known values of D _S =10⁻⁵ cm²/s for bulk liquid ³He at 27 bar and D _S =10⁻⁸ cm²/s for bulk solid ³He at 108 bar. The special experiments with the crystal annealing make it clear that the high spin diffusion here is connected with fast diffusion along dislocation lines.     

3He Melting Pressure Measurements in High Magnetic Fields

Experimental methods and preliminary results of high-precision measurements of the ³ He melting curve in high magnetic fields have been described. The purpose of this work is twofold. One is to establish a reliable millikelvin temperature scale in high fields (T 10 mK, B 15 T), The other is to investigate a high field region of the magnetic phase diagram of solid ³ He by measuring the melting pressure down to temperatures below 1 mK. Besides the two superfluid transitions, the phase transition temperatures between the spin ordered solid and the paramagnetic solid, T _HFP , were determined at B = 12 and 10 T with good accuracy, which is an extension of previous measurements up to 8 T. The present T _HFP (B) line can not be scaled to that at a higher density with a single Grüneisen parameter, indicating a variation of density dependencies of the multiple-spin exchange interactions.