Nuclear susceptibility of liquid He3—I

An accurate study of the nuclear molar susceptibility of liquid He ³ has been made. Particularly emphasized was the comparison of in the liquid with that in solid He ³ . The experimental results of this work define a three-dimensional surface T/C versus temperatureT and molar volumeV between 0.35 and 2.2° K and between 26 and 37 cm ³ /mole. HereC is the molar Curie constant of solid He ³ , assumed to beN _A µ ² /k _B T, where is the nuclear magnetic moment and N _A Avogadro's number. The measurements were accomplished using a carefully designed pulsed NMR set, and sample-and-hold circuitry with a digital voltmeter for readout. Most of the measurements were made at fixed temperature relative to a sample of bcc solid He ³ , usually at a density of 22.50 cm ³ /mole. These data were complemented by measurement of versusT at fixed pressure. Except at the highest temperatures, the scatter in the values was about 0.3%, and the results are estimated to be accurate within ±0.5%. At sufficiently high temperatures, the susceptibility is found to tend asymptotically towards Curie's law by comparison with solid He ³ . The deviation from Curie's law, to temperatures near 0.5° K, could be empirically written as (1–T/C)=bT ^d whereb andd are density-dependent parameters. Comparison with theories and previous measurements of the nuclear susceptibility are made. Below 1° K, the present results are about midway between those of Beal and Hatton ⁹ and those of Thomson, Meyer, and Adams. ⁸ Research supported by a grant from the National Science Foundation and from the AROD. The results have been presented as an Abstract inBull. Am. Phys. Soc. 14, 601 (1969), submitted in partial fulfillment for the Ph.D. in physics by J. R. Thompson, May 1969.     

Nuclear susceptibility of liquid He3—II

Pulsed NMR measurements of the nuclear susceptibility of liquid He³ at various molar volumes are presented over the temperature range between 0.035 and 1°K. The scatter in the data is about 0.2%, while the absolute accuracy is estimated to be about ±1%. At temperaturesT such that ₀ T/C0.35 the susceptibility data can empirically be represented by the expression =₀[1–(x₀ T/C)²]. Here ₀ is the extrapolated molar susceptibility atT=0 for a given volume, assuming the expression to be valid below 35 m°K.C is the molar Curie constant and is a factor that appears to be somewhat dependent on molar volume and whose average value is found experimentally to be about 0.53. This result compares with the theoretical prediction by Béal-Monadet al. who used the paramagnon model for liquid He³ and obtained the expression given above with a value of =0.58. However, the observed apparentT ²dependence of the susceptibility is over a greater temperature range than the theory would lead one to expect, and this point is discussed. The experimental results are also compared with a molecular-field approach by Goldstein, who proposed a representation of the susceptibility by a universal curve T/C=f(₀ T/C), wheref is the function for the ideal gas. In spite of some systematic discrepancies, a scaled presentation of the data is in good overall agreement with the calculated curve. The data disagree with the Stoner model of a Fermi gas with interactions. Finally, the values of ₀ are compared with those of previous work.Research supported by grants from the National Science Foundation and from the Army Research Office (Durham).     

Nuclear susceptibility of liquid3He-4He solutions along the demixing line

Pulsed NMR measurements of the nuclear magnetic susceptibility of liquid³He-⁴He solutions at saturated vapor pressure are presented. They extend over the whole temperature range between 50 mK and 825 mK, for both concentrations of the coexisting dilute and³He-rich phases. The results have been compared to those obtained with pure³He, and the temperature dependence of the ratio of molar susceptibilities of coexisting phases is derived. The consequences on the efficiency of fractional distillation as a method to enhance nuclear polarization are discussed.     

Nuclear spin relaxation in normal liquid 3He in contact with magnetic substrates

We investigate the theory of longitudinal nuclear spin relaxation in the normal state of liquid ³He when the nuclear spins of the ³He are coupled to electronic moments in a substrate. We begin by deriving a general form for the relaxation rate in terms of spin correlation functions of the fluid and those of the spins in the substrate. The expression is applied to models which have formed the basis of recent theoretical discussions of the magnetic Kapitza conductance observed at very low temperature. We place considerable emphasis on the differences in the relaxation rate when the two spin systems are coupled by dipolar interactions and when they are coupled by isotropic interactions of exchange character. There are striking qualitative differences between these two cases in the model calculations. We also examine the general structure of the expressions for the nuclear relaxation rate and magnetic contribution to the Kapitza conductance to form model-insensitive conclusions about their temperature variation in special regimes of temperature. Finally, the results of our calculations are compared with the limited data available.Research supported in part by NATO Research Grant No. 1196.Laboratoire associé au CNRS.     

Nuclear cooling of hcp solid3He

Nuclear adiabatic demagnetization has successfully been done for hcp solid³He with exchange interaction of the order of 10 K. Isochoric pressure change during the demagnetization is compared with that for bcc sample with a similar exchange interaction. The bcc sample showed a clear pressure change during the demagnetization at the upper and the lower critical fields, while the hcp one had no pressure change down to zero magnetic field. These results give a strong evidence that the ground state in hcp³He is ferromagnetic.     

Nuclear magnetic relaxation of3He gas. I. Pure3He

Longitudinal relaxation timesT ₁ have been measured in³He gas, using pulsed NMR, for number densities between 3 × 10²³ and 6 × 10²⁵ spins m^–3 and temperatures between 0.6 and 15 K. 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 wall coating of solid molecular hydrogen was found to delay the formation of a³He monolayer on cooling, andT ₁ measurements were consistent with a binding energy of 13 K for a³He atom to a hydrogen surface. At temperatures below 2 K a completed³He monolayer forms on the H₂ coating. No variation of the areal density of monolayer completion with bulk number density at fixed temperature could be observed and the completed³He monolayer is thought to be a dense fluid. Baking the Pyrex sample cells under vacuum and using an rf discharge in³He gas to clean the walls before sealing in the sample gas were found to increase the observed T₁'s by up to three orders of magnitude. Once a³He monolayer has formed on the H₂ surface in these cleaned, sealed cells, the dipolar interaction between adsorbed spins is thought to be the dominant source of longitudinal relaxation. The data are consistent with a dipolar relaxation model with a correlation time of 2 × 10^–9 sec. This time is long compared to the value of 10^–11 or 10^–12 sec in the 3D fluid. This suggests that if the surface phase is a 2D fluid and the dipolar mechanism is indeed the dominant one, then the atoms in the 2D fluid are less mobile than in three dimensions. This is consistent with recent susceptibility measurements.     

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.     

Vibrating-wire measurements in vacuum,liquid3He and liquid3He-4He mixtures

In order to overcome the 200µK - barrier in the refrigeration of liquid ³ He- ⁴ He mixtures we have constructed an experimental cell using only pure materials to minimize possible origins for heat leaks into the liquid. With this arrangement we were able to cool a saturated6.8%- mixture to a temperature of 150µK. A vibrating wire which was immersed in pure ³ He floating on top of the phase-separated mixture was used as a thermometer. This wire was calibrated in a second experiment with pure ³ He only in the cell. In superfluid ³ He-B at T0.15 mK the damping of the wire due to the quasiparticles becomes very small, and we observe typical characteristics of the vacuum damping of the wire which was extensively examined before filling any liquid into the cell.     

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.     

Specific heat of amorphous3He films and confined liquid3He

We have measured the heat capacities of³He films and liquid³He in porous Vycor glass at 10 to 600 mK. With increasing the film thickness from 1 to 3 atomic layers, the specific heat evolves gradually from that typical to solid to that of liquid³He. At about 2 atomic layers, however, its low-temperature part is nearly temperature-independent; we interpret this as a result of gradual freezing of spins in an amorphous solid³He film with decreasing the temperature. The contribution of liquid³He in the center of the Vycor pores can be described as the specific heat of bulk liquid³He at corresponding pressures in the range 0 to 28 bar. The thickness of amorphous solid on the pore walls increases with external pressure roughly linearly. Preplating the walls with⁴He allows to determine the positions of³He atoms contributing to the surface specific heat at 10 to 50 mK. In addition, the contribution from the specific heat of³ He -⁴He mixing at 100 to 600 mK is discussed as a function of pressure and amount of⁴He.0n leave from ISSP Acad. Sci. of Russia, Chernogolovka, Russia     

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     

Nuclear Magnetic Properties of Solid 3He Films

A brief review on the thermodynamic properties of ³ He films adsorbed on graphite is presented. The second solid layer of ³ He adsorbed on graphite is a particularly interesting two-dimensional system of localized identical spin- fermions, which evolves from antiferromagnetism to ferromagnetism as a function of increasing density. This striking behavior is interpreted within a generalized Heisenberg model including competing ring-exchange interactions. While ferromagnetic three-particle exchange dominates at the highest densities, higher order antiferromagnetic ring-exchange processes become significant at low densities leading to highly frustrated antiferromagnetic or ferromagnetic phases. At low temperature, the frustrated antiferromagnetic and ferromagnetic states may correspond to unique examples of new quantum phases as suggested by recent theoretical results. The relevance of this ring-exchange model for other systems of localized fermions is also discussed.     

Finite-amplitude acoustic waves in liquid3He and4He

Finite-amplitude acoustic waves have been propagated in liquid³He and⁴He. The acoustic cell has been operated at 83, 250, and 420 MHz and down to 17 mK. Our measurements of the anharmonic effects are in agreement with theoretical predictions and with previous experimental work that investigated a restricted temperature range.     

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).     

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 .     

Nuclear magnetic ordering in BCC solid 3He

Applying the cluster expansion method to an antiferromagnetic bcc solid ³He, we calculate the Néel temperature T _sc. The result shows that in the case of J ₂/J ₁ 0.3–0.5, K _F/J ₁ 0.5, and J ₁ –0.5 mK, whose values were determined with a Hamiltonian including four-spin exchange to obtain a good fit with the experimental results, the transition to the normal antiferromagnetic phase at about 2 mK, which was anticipated by the molecular field approximation, does not occur. Using the same method, the paramagnetic susceptibility was also calculated.Work supported in part by the Mitsubishi Foundation.     

Binding energy of one4He impurity in liquid3He

A variational microscopic calculation of the binding energy of a⁴He impurity (_i) in homogeneous liquid³He at zero temperature is presented. Starting on an extended Jastrow-Slater wave function including three-body correlations, the expression for _I is derived and the appropriated FHNC formalism for this problem is reviewed. In the framework of the Average Correlation Approximation (ACA), it is proved that it is possible to obtain the chemical potential of the impurity only from liquid³He magnitudes with a good accuracy. Our results are consistent with both a recent experimental determination of _I at zero pressure and the non-solubility of⁴He in³He. However, numerical uncertainties preclude a firm conclusion about the latter property.     

Nuclear Magnetism of Submonolayer Solid 3He on Graphite

Submonolayer solid ³ He adsorbed on graphite has been studied with NMR measurement down to the order of 0.1 mK. The magnetization curves are well fitted to the Curie-Weiss law in the whole investigated density region (5.0 nm ^–2 - 8.5 nm ^–2 ). The obtained Weiss temperatures are found to be positive at a commensurate phase and an incommensurate one. However they are negative in the intermediate density region, which suggests the existence of an antiferromaynetic phase also in the Submonolayer. The change from an antiferro to a ferromagnetic behavior at around 7.3 nm ^–2 is similar to that of the second layer, and can be explained by a multiple spin exchange model. Therefore the ferromagnetic behavior in the second layer is not necessarily due to the liquid overlayer. While the ferromagnetic behavior at the phase is not reproduced by a simple density dependence of competing multiple exchange interactions and indicates the importance of the corrugation potential from the graphite substrate.