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.     

Pulsed NMR studies of superfluid3He

We present a review of our pulsed NMR experiments in the A and B phases of superfluid³He, at pressures of 23 and 27 bar. We have measured the dipole frequency in³He-A, spin susceptibility in³He-B, and tip-angle-dependent frequency shifts in both phases. In general, we find excellent agreement with results by other workers. In³He-B, complex spin motions were observed involving long-lived free induction decays with a time-dependent precession frequency. Spin relaxation measurements for both³He-A and³He-B are discussed and compared with those of other workers. After driving the magnetization far from equilibrium, anomalous frequency shifts were found to persist in the A phase. We discuss a soliton-texture model by Bruinsma and Maki which accounts for these resonances.Work supported by the National Science Foundation Grant DMR-78-10901 and through the Cornell Materials Science Center through NSF Grant DMR-79-24008 A02. (MSC Report #4459).     

Thermodynamic measurements in magnetically ordered solid3He

Measurements of the melting pressure and constant-volume pressure of solid³He have been made in the vicinity of the various magnetic-ordering transitions. Data have been obtained at several magnetic fields for both the low-field phase and the high-field phase, with particular attention given to the region of the polycritical point. The absence of a latent heat indicates that the transition from the paramagnetic to the high-field phase is second order or type. A spin-wave velocity of 6.95 cm/sec was obtained from theT ⁴ temperature dependence of the melting pressure in the high-field phase forB=0.495 T. These data provide the entropy and volume discontinuities as functions of field along the first-order low-field phase boundary. The volume dependence of the transition temperatures has been extracted from these and other data.     

The dielectric tensor of magnetically ordered solid 3He

Solid (bcc) ³He undergoes a magnetic ordering transition at a temperature of about 1 mK. In the low-temperature ordered phase, two adjacent atomic planes of up nuclear spins are followed by two planes of down spins. A recent explanation by Guyer and Kumar depends on the spin-lattice coupling. Their theory predicts that in the magnetically ordered phase the lattice will be deformed. The deformed (tetragonal) lattice will exhibit dielectric anisotropy. The dielectric tensor is calculated, using a simple generalization of the Clausius-Mosotti theory.On sabbatical leave from Department of Physics, Technion—Israel Institute of Technology, Haifa, Israel.     

Pulsed NMR study of submonolayer and multilayer 3He films adsorbed on Grafoil

The nuclear spin relaxation times T ₁ and T ₂ of submonolayer and multilayer ³He films adsorbed on Grafoil have been measured at temperatures between 1.2 and 4.2 K by a pulsed NMR technique. The T ₁ data for high-coverage films (solid and dense fluid phases) and the substrate registered phase are interpreted in terms of thermally activated vacancies. In solids the quantum exchange inherent in ³He is shown to be important at low temperatures. The data for multilayer films are discussed in the light of the particle exchange between layers and the relaxation time of each layer. The dynamical behavior of adatoms in the solid, fluid, and substrate registered phases as well as the nature of phase transitions between them are discussed on the basis of information obtained from the analysis of T ₁ and T ₂ data. The present results as a whole seem to support the phase diagram determined by specific heat measurements. In addition, the nuclear susceptibility in submonolayer films has been measured by the same technique. The effect of Fermi degeneracy was not seen in the temperature range between 1.2 and 4.2 K.     

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 measurements on dilute solutions of3He in solid4He

Measurements of the spin diffusion coefficientD and relaxation timesT ₁ andT ₂ are reported for³ He impurity in solid⁴ He of fractional concentrationx ₃ down to 10^–4. Forx ₃10^–3,T0.5 K, and molar volume 21.0 cm³,Dx ₃=1.2±0.4×10^–11 cm² sec^–2,T ₂ x ₃=1.7×10^–4 sec, andT ₁ x ₃=6.6×10^–2 sec at 2 MHz. The spectral densityJ() for dipole field fluctuations has been studied as a function of frequency from 10⁴ to about 10⁷ Hz. Two branches of approximately equal area have been found with scaling frequencies of about 10⁴ and 10⁶ Hz. It is argued that the high-frequency branch, which has some unusual structure, relates to ³ He- ⁴ He tunnelling, uninhibited by other ³ He impurities, and occurs at a rate of about 0.6 MHz for molar volume 21 cm³. The molar volume dependence of this tunneling appears to be similar to that found in pure, solid ³ He.     

Effects of 4He impurities on 3He nuclear spin-lattice relaxation in hcp solid 3He

Nuclear spin-lattice relaxation properties of hcp solid ³He with ⁴He impurities have been studied. At temperatures below the exchange plateau region, three kinds of relaxation time were observed. To analyze the data, a phenomenological four-bath model was developed, the four baths being the Zeeman bath, the phonon bath, an X-bath, and a Y-bath. The X-bath consists of the exchange bath and a part of the ⁴He-⁴He elastic interaction bath. The Y-bath is the main part of the elastic interaction bath. We measured the concentration dependence of the energy constants of all the baths, as well as the temperature and concentration dependences of the three kinds of relaxation time. The relaxation behavior corresponding to the process between the X-bath and the Y-bath could not be expressed by a single exponential function of time and the relaxation rate was strongly dependent on the concentration. This process may be related to the internal thermal equilibrium process within the elastic interaction bath. The impurity-dependent relaxation time between the X-bath and the phonon bath had a temperature dependence of T ^–n with n = 7.4±0.3.     

Influence of4He impurities on nuclear spin relaxation in solid3He

The NMR properties of solid³He, mainly the ratio of the heat capacities of exchange and Zeeman energies and the exchange-lattice relaxation times are very sensitive to the presence of⁴He impurities, while the transverse relaxation timeT ₂ does not depend on the impurity concentration when the latter remains small. These properties can be explained in two different ways. (1) We assume an enhancement of exchange interactions around⁴He impurities. We derive the consequences of such an assumption and compare them with experimental results. For two molar volumes in the bcc phase, the locally enhanced exchange is equal to approximately7J, withJ being the exchange in pure³He. (2) Guyer and Zane introduce a mass fluctuation wave to explain the excess of heat capacity and the dependence of the longitudinal relaxation time with concentration. Both these models give rise to a four-energy bath system. As in the bcc phase, the exchange-lattice relaxation time in the hcp phase decreases when × increases at low enough⁴He concentrations. ForV=18.48 cm³ we deduce the coefficient for translational diffusion from high-temperature experiments with the help of Torrey's theory for spin-lattice relaxation.This paper is based on a thesis to be submitted in partial fulfillment of the requirements for the degree ofDocteur ès Sciences in Physics at theFaculté des Sciences d'Orsay in 1970. This thesis will be registered at the CNRS under the number AO 3704.     

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.     

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.     

Pulsed NMR in the Nuclear Spin Ordered Phases of Solid 3He in a Silver Sinter

To obtain the exact spin structure of the nuclear magnetically ordered phases of solid ³He, which in the bee lattice are the U2D2 and the high field phase, both occurring below about 1 mK, we started a project of neutron scattering at the Hahn-Meitner Institut, Berlin. This experiment faces three main difficugties: to grow a single crystal within the sinter needed for cooling, to cool the solid to temperatures below 1 mK (or even much lower in the case of the hcp lattice), and to keep it there long enough, even under neutron irradiation. As a first step we have performed pulsed NMR measurements in the ordered phases of solid ³He in a Ag sinter of 700 Å particle size down to temperatures of 400 µK at various molar volumes. The samples remained in the ordered state for as long as 140 h. In the low field phase a strong reduction of the Larmor line to nearly zero intensity was observed. With a sample grown over 6 h at the megting curve around 50 bars three lines at the Larrnor frequency and on its high frequency side were observed which seem to indicate a partly crystalline U2D2 phase in our sinter. The origin of the strong intensity drop, however, is not clear and needs further investigation.     

Pressure measurement during nuclear demagnetization of BCC and HCP solid3He

Direct nuclear demagnetization is used to cool high density solid³He into the magnetically ordered phases. The pressure change in the samples is detected by a capacitive strain gauge. The entropy of the samples is removed by precooling to a temperature of 0.5 mK in a field of 2.5 T. For a bcc sample with a molar volume of 20.10 cm³/mol, two magnetic transitions have been observed. A similar experiment on an hcp sample with a molar volume of 19.65 cm³/mol is being done. Preliminary data indicates no abrupt change in the pressure as observed in the bcc sample.     

NMR in flowing superfluid 3He

The effects of flow on the NMR absorption in the A and B phases of ³He have been studied. While no flow-induced changes in the absorption were seen in the B phase, a variety of phenomena were observed in the A phase. The phenomena include the development of time-dependent satellite peaks, height reductions of the signal, and a splitting of the signal, with a fraction of the signal shifting to lower frequencies. These effects are described and discussed in light of the existing theoretical models. In addition, the NMR shift in the static B-phase liquid confined between 135-m-spaced parallel plates has been measured as a function of temperature and the angle between the magnetic field and the plates. These results are compared with previous measurements and are found to be in good agreement. Finally, two effects observed in the static liquid, the disappearance of the B-phase signal under certain conditions and the splitting of the A-phase signal, are described.Research supported by the National Science Foundation.     

Triple exchange in solid3He

In a recent paper we have used triple exchange, the cyclic permutation of three atoms, to explain the anomalous behavior of the magnetic pressure of solid³He in the presence of high magnetic fields. The results of susceptibility, pressure, melting curve, and nuclear relaxation experiments are reexamined using a spin Hamiltonian which includes triple exchange. This systematic examination points out which experiments are best suited for testing the importance of triple exchange in solid³He.Work supported by National Science Foundation Grant No. GP-22553.     

A pulsed NMR study of 3He-4He solutions

We report a study of the Leggett-Rice effect in dilute ³He-⁴He solutions at a Larmor frequency of 71 MHz. We have measured the height and phase of the spin echoes following 2-pulse NMR sequences of three solutions with ³He concentrations of 0.56%, 1.4%, and 4.0%. The theory of Leggett fits the data extremely well and yields values of the parameter M ₀ and the transverse diffusion coefficient D. We are also able to evaluate M ₀ and D by analyzing multiple spin echoes and find good consistency between the two methods. From values of /(1+F ₀ ^a ) at various concentrations, we are able to determine the scattering length for ³He quasiparticles, a, quite accurately. We find a = –0.97±0.03 Å.     

Pulsed NMR of monolayer and near-monolayer films of 3He adsorbed on Grafoil at low temperatures

Pulsed NMR measurements at 30 MHz of near-monolayer coverages of ³He on Grafoil have been made between 4.2 and 0.1 K. The time constants of the free induction decay indicate that below 4.2 K the mobility of ³He in an exact monolayer is smaller than that at lower coverages or at coverages above one monolayer, in agreement with the results found by Hegde and Daunt, by Cowan and co-workers, and by Rollefson. Furthermore, in spite of rf heating of the sample, we were able to conclude that the mobility of ³He in nearmonolayers films decreases as the temperature is decreased below 4.2 K. At 4K and 30MHz our measurements give T₁ = 1 ± 0.3 sec for coverages between 0.6 and 1.35 monolayers. This is in agreement with previous work.Supported by the National Science Foundation.     

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.     

Pulsed NMR in solid D2. II. Stimulated echo

A study of the NMR stimulated echo resulting from an r.f. three-pulse sequence is presented for hcp D₂ with para-D₂ concentrations X between 0.06 and 0.49 and over the temperature range 0.07 < T < 1.5 K. The echo has two components, a sharp one on top of a broad one, which are the signals of the I = I (p-D₂) and the I= 2 (o-D₂) spins respectively. The echo widths reflect the different degrees of molecular orientational ordering. The echo amplitudes are studied as a function of the experimental parameters in the r.f. pulse sequence. The temperature dependence of the amplitude shows the expected Curie law behavior for the I = 2 spins, but a strong deviation from this law for the I = 1 spins. This anomalous behavior is consistent with that found for the I = 1 solid echo signal. The echo decay time _E is found to be very different for both spin systems, both in magnitude and in temperature dependence. The comparison of the I=1 spin results in D₂ with those in H₂, where the molecular orientational ordering is also from quadrupolar interaction, shows substantial differences. These are discussed in terms of the spin diffusion within each NMR line, and of the cross-relaxation between the two I = 1 and I = 2 spin systems.     

Nuclear magnetic order in solid 3He

Over the past 20 years our understanding of cooperative magnetic phenomena in solid ³He has expanded greatly. Starting from the concept of atomic exchange, the author explains how early experiments led to the abandonment of the naive Heisenberg nearest neighbor antiferromagnetic Hamiltonian, in favor of a multiple exchange model. He then describes the detailed experimental picture of the spin-ordered phases which has developed over the past decade, and the successes and failures of the multiple exchange model to explain the experimental results. Today solid ³He is a powerful model magnetic system for extending our general understanding of magnetic order, and should continue to play an important role for many years to come.