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.     

Nuclear magnetic susceptibility of solid3He with4He impurities

The nuclear magnetic susceptibility of bcc solid³He with a small concentration of⁴He is calculated in the high-temperature approximation. The exchange Hamiltonian used for the system is that obtained from a Hubbard-like cell model developed in earlier work. A brief discussion is also given of our general approach to the study of the magnetic properties of impure solid³He as compared to other approaches to the problem.     

Anomalous nuclear spin lattice relaxation of3He adsorbed on porous material

Measurements of the nuclear spin lattice relaxation times of³He adsorbed on porous material for a wide range of temperatures (0.33<T<1.5 K) and applied magnetic fields (3.75<H<25 kG) indicate that the relaxation time of the adsorbed atoms is anomalously short with respect to the minimum allowable value for internuclear dipolar interactions, and the observed temperature and field dependence establishes that paramagnetic impurities on the surface do not play a major role in the relaxation process. Comparison with the relaxation rates of¹²⁹Xe adsorbed on Vycor glass suggests that the relaxation is intimately related to the mobility of the³He adatoms.     

Anomalous nuclear spin relaxation in liquid 3He-4He mixtures near the lambda transition

The longitudinal nuclear spin relaxation time T ₁ was measured for liquid ³He-⁴He mixtures under saturated vapor pressure in an epoxy sample chamber in which the wall effect is emphasized. The molar concentration of ³He was 0.12, 0.20, 0.35, 0.45, and 1.00. The temperature was regulated to better than 5 K in the range 1.2–2.1 K. A decrease of T ₁ was clearly observed several millikelvins below T (the superfluid transition temperature). T ₁ had a cusp like temperature dependence as a whole where the temperature is far from. T . This anomalous behavior of T ₁ is discussed.Work based on part of a dissertation submitted to the University of Tsukuba in partial fulfillment of the degree of Doctor of Science by one of the authors (T.K.).     

Dynamics of3He impurities in4He films

Using a microscopic theory we calculate the binding energy of³ He impurities in films of⁴ He absorbed to a graphite substrate. Without adjustable parameters, we obtain excellent agreement with the experimental binding energies for the ground state of the He impurity. By introducing a timedependent variational wave function, the impurity atom acquires a hydrodynamic effective mass for its motion parallel to the surface due to hydrodynamic backflow, and the excited states have a finite lifetime. When these effects are included, both the energy of the first excited state of the impurity, and the effective mass of the ground state, agree well with experimental data.A comparison with recent density functional results is carried out. It is shown that the substrate bound states on strong potentials are spurious and due to the inappropriate treatment of the effective mass within that theory.     

Anomalous spin-lattice relaxation in solid3He

Nuclear spin-lattice relaxation measurements have been carried out in bcc and hcp solid³He at low temperatures. The observed relaxation rates are anomalously high and indicate that a typical sample has a substructure of small domains at whose boundaries rapid spin-lattice equilibrium takes place. Experiments on the sample anisotropy show that these domains cannot be crystallites and we believe that they may be determined by stacking faults or small-angle grain boundaries. The magnetic field dependence of the spin diffusion coefficient and the effects of dissolved⁴He are also investigated.     

Effects of3He impurities on the4He solid-liquid interface

Using crystallization waves we have measured the interfacial stiffness, , and the temperature dependence of the growth resistance, (Km)^–1, of the⁴He solid-liquid interface in the presence of³He impurities. For the purest⁴He sample, (Km)^–1 is consistent at the lowest temperatures with the assumption that the growth velocity is limited by the scattering of ballistic phonons from the moving interface. At higher concentrations of³He, we observe that (Km)^–1 increases exponentially with temperature below 0.25 K. We observe that decreases with increasing³He concentration.     

Hydrogen isotope and3He impurities in liquid4He

Recently Reynolds, Hayden and Hardy(J. Low Temp. Phys. 84,87 (1991)) analyzed atomic deuterium lifetimes in a cell with walls covered by a saturated⁴He film. They were able to determine the deuterium chemical potential in⁴He and also discussed the possibility of estimating its effective mass. These measurements inspired our attempt to understand the properties of hydrogen isotope impurities in liquid⁴He using the extended Jastrow-Feenberg theory based on the correlated wave function. We present results for hydrogen isotope chemical potentials in the bulk⁴He as a function of density. The accuracy of the method is tested by calculating the chemical potential of the³He impurity. We find a good agreement with existing measurements. We also calculate the effective masses of the hydrogen impurities. For deuterium we predict a value,m _eff=4m _D .     

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.     

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.     

Anomalous nuclear spin relaxation of adsorbed helium-3

Within the framework of a general theory of two-dimensional NMR we are able to elucidate certain anomalous features of spin relaxation in adsorbed and porous systems. We explain the linear dependence of relaxation time on applied magnetic field, and this is demonstrated to be related to the relative insensitivity ofT ₁to temperature. We also show thatT ₁remains field dependent on the “fast” side of theT ₁minimum.     

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.     

Resonant spikes of the nuclear spin qubits relaxation rate in quantum-Hall systems with magnetic impurities

The magnetic field dependence of the local phononassisted nuclear spin qubit relaxation rate in 2DES with magnetic impurities is studied theoretically. For weak and strong scattering limits under a strong magnetic field, we show that the magnetic field dependence of T/sub 1//sup -1/ exhibits giant spikes, due to the energy matching of the electron Zeeman splitting with the energy spacing between the vibrational mode energies. The localized mode is created by the lattice distortion around the impurity. This resonance phenomenon could be used as a local probe for studying the localized vibrational modes and their coupling to electrons and for the resonant manipulation of the nuclear spin qubits.     

The spin diffusion coefficient of3He in3He-4He solutions

The transport properties of³He in³He-⁴He solutions with molar concentrations of 5, 9, 14, and 24% have been studied for 0.9 KT2.5 K. The spin diffusion coefficientD _s and the longitudinal relaxation timeT ₁ were measured by the spin-echo method for temperatures both above and below the solution lambda temperatureT . The spin-echo method measures the diffusion coefficient for magnetizationD _s, which differs from the usual diffusion coefficient for particlesD belowT .D _s depends on the³He-³He scattering cross section _FF and the³He-roton/phonon cross section _FB, whileD depends only on _FB. The distinction betweenD _s andD is elaborated in terms of a simple mutual-friction model for diffusion. The two scattering mechanisms are clearly evident in the behavior ofD _s as a function of concentrationx and temperature. The contribution due to the³He-³He scattering is inversely proportional tox, indicating that the³He can be treated in first approximation as a classical gas (the Pomeranchuk model). The predictions of various theoretical models are compared with the results, where possible, but most of the previous theoretical work is not applicable to the concentration range and temperatures of these measurements.Supported in part by the National Science Foundation and the U.S. Office of Naval Research.     

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.     

Pulsed NMR study in nuclear ordered solid3He

The nuclear spin dynamics in nuclear spin ordered solid³He in low magnetic fields on the melting curve has been studied by pulsed NMR down to 0.6 mK. The free induction decay signals (FID) were measured in single crystals of solid³He at three operating frequencies of 920, 1380, and 1840 kHz. The FIDs were nonexponential and dependent on the rf pulse strength _p H ₁ t _w , where is the gyromagnetic ratio,H ₁ is the rf field strength, andt _w is the pulse width. At small _p they decayed almost linearly in time with a small exponential tail at the end. When _p was further increased they became shorter and neither exponential nor linear in time. At large _p they decayed very rapidly and sometimes could not be observed at all because of the dead time of the NMR detection system. Such behavior of the FID was observed in many different single crystals in the given temperature range at 920 kHz. Tsubota and Tsuneto have shown by solving the nonlinear equations of motion numerically that the motion of the nuclear spin becomes chaotic when the tipping angle exceeds a critical value. Comparing their result with our experimental results, we concluded that some of the results of the rapid decay of the FID at large _p might be attributed to the onset of the chaotic motion. At 1840 kHz it is expected that the nonlinear effects in the equations of motion become less effective than that at 920 kHz. In fact, at this operating frequency the FIDs even at large _p and the tipping angle-dependent frequency shift could be observed. These frequency shifts were in rather good agreement with Namaizawa's theory provided an effective tipping angle was taken into account.     

Moment calculation of vacancy-induced spin diffusion in bcc solid3He

The self-diffusion constant in bcc solid ³ He is calculated in the temperature regime where an atom changes place with a neighboring vacancy more often than flip-flops are induced through the Pauli exchange interaction. The calculation is based on the method of moments and describes vacancies with a model of fictitious spinS=1. The scattering of phonons by vacancies impedes the quantum tunneling of vacancies: the quantitative discussion of this effect shows that its relation with the lifetime of vacancy waves is not simple.     

Nuclear spin ordering of solid3He in applied magnetic fields

The effects of a magnetic field on nuclear spin ordering in solid³He have been observed through the influence of the field on the solid entropy. By making use of the Clausius-Clapeyron equation, the³He melting temperature as a function of pressure was determined in several magnetic fields from 0 to 1.2 T from measurements of the latent heat of solidification in a Pomeranchuk cell. The solid entropy as a function of temperature was then calculated from the melting curve slope in each field by again utilizing the Clausius-Clapeyron equation. The solid ordering manifested itself as a substantial reduction in entropy occurring over a narrow temperature interval. A portion of the magnetic phase diagram of solid³He was established by plotting the ordering temperature versus field. In low fields the reduction in entropy occurs over a very narrow temperature interval, and the ordering temperature is depressed by the field. Above about 0.41 T, however, the ordering region is broadened and moves to significantly higher temperatures with increasing fields. The behavior in low fields is tentatively interpreted as a magnetic phase transition from the paramagnetic to an ordered phase, while the effect in higher fields is believed to represent paramagnetic ordering of the nuclear spins by the applied field.Work supported in part by the National Science Foundation.     

Dipolar anisotropy effects in the spin relaxation of adsorbed3He monolayers

Nuclear magnetic relaxation times and their anisotropy with respect to field direction are computed for adsorbed monolayer and submonolayer ³ He films. We considerT ₁ andT ₂ for fluid and solid systems with motion via diffusion and tunneling, respectively, andT ₂ for the rigid lattice system. Calculations for the fluid system are carried out via a modification of Torrey theory and for the solid system by the method of moments. The rigid lattice fourth moment is computed to check the Gaussian approximation for the line shape. The results provide explanations of and predictions for experiments on Vycor and Grafoil substrates. Possible complications implied by our results for experiments on liquid ³ He in the millidegree region are discussed.Work supported in part by the Science Research Council (D.J.C. and B.C.) and the National Science Foundation (W.J.M.) under Grant GH 34504A1.     

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.