Heat Capacity of the Second Layer of 3He Adsorbed on Graphite Pre-plated with a 4He Monolayer

The second solid layer of ³He on graphite is a highly frustrated magnetic system, as a resugt of its triangular symmetry and the importance of ring exchange (mugtiple spin exchange). This is predicted to lead to a quantum spin liquid ground state. Experiments in which the first paramagnetic solid layer is replaced by ⁴He have been undertaken by several groups, allowing more precise measurements of the second layer magnetisation in an attempt to infer the spin gap of the putative spin liquid phase. We report the first measurements of the influence of such pre-plating on the second layer heat capacity, in the vicinity of the commensurate solid phase. We find the differences in heat capacity of the two systems to be significant. The effective exchange constant is reduced by pre-plating by a factor of order 2/3. In addition the value of the heat capacity at its maximum is significantly reduced by approximately 20%. Can these differences be accounted for within a model of intra-layer mugtiple spin exchange on a triangular lattice?     

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.     

Surface Magnetism of 3He in Grafoil

We report the magnetic susceptibility of ³He in Grafoil filled with pure liquid³He at 27.6 bar and at temperatures down to 0.1 mK with a cw NMR method. It is composed of two contributions: from the bulk liquid and from the adsorbed layer of ³He on the Grafoil surface. The latter shows a well-known strong ferromagnetic tendency and can be fitted to a Curie–Weiss law in the high temperature region. The obtained Weiss temperature is surprisingly large compared with the previous ones.     

Nuclear Magnetism of Two Dimensional Solid 3He Adsorbed on Plated Graphite

Nuclear spin exchange in the low density two dimensional quantum solid formed by ³ He adsorbed on graphite plated by a bilayer of HD has been studied by heat capacity and magnetization measurements. The low densities result in a frustrated magnet with significantly larger effective exchange constants than observed in the antiferromagnetic second layer of ³ He on bare graphite. Promotion to a fluid overlayer occurs at 6.8 nm ^–2. A ferromagnetic anomaly is observed in magnetization measurements at 10 nm ^–2 with an effective exchange constant of 1.0 mK, about half the value observed at the corresponding anomaly on bare graphite.     

Static Structure Factor of Two-Dimensional Liquid 3He Adsorbed on Graphite

Liquid ³He is a model system for strongly correlated Fermi liquids. For this reason, many X-ray and neutron scattering experiments have been performed to understand the structure and dynamics of this quantum fluid. We have recently shown that two-dimensional liquid ³He sustains long-lived zero-sound excitations at large wave-vectors (Godfrin et al., Nature, 483:576, 2012). Here we show that its static structure factor can be obtained with reasonable accuracy by integrating the experimental S(Q,ω) over a suitable energy range. A good agreement is found between the static structure factor deduced from the experiment and theoretical models: Quantum Monte Carlo simulations and Dynamical Many Body Theory (DMBT). At high wave-vectors, the experimental values are underestimated because of the limited accessible phase space; nevertheless, even at atomic wave-vectors a semi-quantitative agreement is observed with the theoretical predictions.     

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     

Large Boundary Magnetism and Superfluidity of Liquid 3He in Nanometer-sized Porous Alumina

Continuous-wave NMR measurements were performed for liquid ³He in porous alumina with nominal pore size of 20 nm in diameter, at temperatures down to 0.3 mK. The signal is composed of two contributions: from the liquid and from the boundary solid layer of ³He on the alumina’s surface. The latter shows a well-known ferromagnetic tendency and signal intensities can be fitted to a Curie-Weiss law in the high temperature region. The obtained Weiss temperatures are 0.18 and 0.50 mK at 7.5 and 28 bar, respectively. ⁴He coverage (4 monolayers) completely eliminates boundary signal between 7.5 bar and 32.5 bar. The residual liquid signal shows frequency shift and broadening below superfluid transition temperatures depending on liquid pressures. The obtained P-T phase diagram well resembles that of bulk liquid ³He in spite of the very narrow pore-size comparable to the coherence length of superfluid ³He.      

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.     

Absolute Value of the Surface Tension of Liquid 4He

In 1985 Iino et al. [J. Low Temp. Phys. 61, 155 (1985)] measured the surface tension of liquid ⁴ He by the surface-wave resonance method, and reported that the surface tension at 0K is 354 N/m. Recently, Roche et al. [J. Low Temp. Phys. 106, 565 (1997)] obtained the absolute value at 0K to be 375 N/m from the dispersion relation of a capillary wave at a micron wavelength. There is a 6% discrepancy between those two values. To determine the meniscus effects for the surface waves and the absolute value of the surface tension, we measured the resonance frequencies of the surface wave in two parallelepiped cavities with different widths. By comparing the same wave number of the two cavities, it was found that the resonance frequencies are shifted to be slightly smaller by the meniscus effects. The absolute value of the surface tension, which was obtained by eliminating these effects by using the resonance frequencies of the two cavities, was in agreement with that of Iino et al.     

Large Mass Enhancement in 3He Monolayer Fluids Adsorbed on Graphite Preplated with 4He

A fluid monolayer of ³He adsorbed on a graphite surface is an ideal twodimensional (2D) Fermi system. We have observed very large mass enhancement of the quasiparticles (m*/m=20±5) in preliminary heat-capacity measurements for high density ³He fluids adsorbed on graphite preplated with a ⁴He monolayer (³He/⁴He/gr). This could be divergence of m* toward the critical density for the 4/7 phase with a triangular lattice, which is a registered phase commensurate against the first layer. The observed m* is larger than those reported for other 2D ³He systems, e.g., m*/m=13 for ³He/HD/HD/gr system, presumably because of the higher critical density. The apparent divergence of m* toward the different Critical densities strongly suggests the Mott–Hubbard type transition between the 2D Fermi fluid phase and the registered phase under a strong onsite hard core repulsion between the 3He atoms.     

Anomalous Resonance Phenomena in Two-Dimensional Electrons on the Surface of 3He-4He Liquid Mixtures

No Heading We report on anomalous resonance phenomena observed in a two-dimensional electron system on ³He-⁴He liquid mixtures. The resonance is observed in a Corbino conductivity measurement, in which a magnetic field B is applied prependicular to the electron sheet. We have detected the resonances for ³He concentrations n₂ from 0.475% to 10.20%, and at temperatures below 800 mK. The resonance frequency f_r is inversely proportional to B. In a preliminary study we found that f_r and the resonance amplitude increases when the electron sheet is not parallel to the electrode, and this made the understanding difficult. Here we have made the systematic measurement keeping the parallelism between the electrons and the electrode. We have observed the resonance only at n₃ > 0.475%. This fact finally leads us to conclude that adding ³He atoms to liquid ⁴He induces the nonuniformity in local electron density, and hence the resonance.PACS numbers: 73.20.–r, 67.60.–g     

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.     

Preliminary Heat-Capacity Measurements of 2D Solid 3He Adsorbed on Graphite Preplated with 4He

We describe preliminary resugts of heat capacity measurements of the 4/7 phase in two dimensional ³He adsorbed on graphite preplated with a ⁴He monolayer in a temperature range between 0.17 and 20 mK. In zero magnetic field, we observed a double-peak structure similar to that reported previously for the same phase in a different system (³He/³He/gr) in which the gapless quantum spin-liquid ground state is proposed. The exchange interaction deduced from the high temperature data is by a factor of 30% smaller than the previous one, presumably because of the smaller lattice constant for the ³He/⁴He/gr system. The present resugt provides strong evidence that such a peculiar temperature dependence of heat capacity is characteristic of the 4/7 phase. Application of magnetic fields up to 0.65 T on this phase does not seem to change appreciably the higher temperature broad peak at around 1.4 mK.     

Dynamic Surface Properties of Liquid 3He Probed by Surface State Electrons

Two-dimensional (2D) electrons floating on the liquid He surface is a powerful tool to study the dynamic surface properties of both normal and superfluid ³ He. From the mobility measurement an evidence is found for the existence of ripplons on liquid ³ He at least above 140 mK. When the 2D electrons form a Wigner solid (WS) at low temperatures, they are accompanied with surface depression under each lattice site. Low frequency mobility of the WS probes the scattering of quasiparticles from the surface depression. The damping of high frequency magnetophonon resonances of the WS is dominated by the scattering of electrons from surface excitations. A comparative measurement on both ³ He and ⁴ He shows a prominent difference in the surface properties of ³ He from ⁴ He below 70 mK.     

4He Impurity Effect on the Positive Ion Mobility in Liquid 3He

The behaviour of ⁴ He impurities has been investigated through positive ion mobility measurements in liquid ³ He at milliKelvin temperatures. In spite of the enormous surface area of the cell, the influence of ⁴ He lasted for hundreds of hours at temperatures of 20 mK. However below 10 mK, the ⁴ He impurities were quickly frozen out on the cell walls and we were free from the impurity problem. Nevertheless the multiple ion signal occasionally appeared even at a few mK, although it disappeared for a number of ionization pulses.     

Theory of the Surface Tension Maximum of Liquid 3He

Recently Matsumoto et al. performed very precise measurements of the surface tension of liquid ³He, (T), at low temperatures and found that (T) exhibits a small maximum at about 100 mK. Existing theories are unable to explain this anomaly. On the basis of a local approximation for the entropy in which the Fermi liquid effect is included, we can evaluate the variation of (T), (T)=(T)–(0), as a function of T and of the number density (or the interaction strength). It is found that (T) consists of two terms; a T² term and T⁴ ln T term. We predict that, for the density of real liquid ³He, exhibits a tiny minimum and a small but relatively larger maximum. This prediction explains qualitatively and quantitatively all salient features of the observed (T).     

Fermi Liquid Properties of 3He-4He Mixtures

We calculate microscopically the spectrum of a ³ He impurity atom moving in ⁴ He, determine the Fermi-Liquid interaction between ³ He atoms and then calculate the pressure and concentration dependence of the effective mass and the magnetic susceptibility. The long wavelength limit of the spectrum defines the hydrodynamic effective mass. When k 1.7Å^–1 the motion of the impurity is damped due to the decay into a roton and a low energy impurity mode. The calculations of the Fermi-Liquid interaction are based on correlated basis functions (CBF); the relevant matrix elements are determined by the Fermi hypernetted-chain theory. Our theoretical effective masses agree well with recent measurements, ^1,2 but our analysis suggests a new extrapolation to the zero-concentration limit. With that effective mass we also find a good agreement with the measured ³ Landau parameter F ₀ ^a .     

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.