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?     

Vapor Pressure and Heat Capacity Measurement of 3He Adsorbed on 18Å-Pores

We have measured the vapor pressure (0.84 K 3 He adsorbed on pores 18 Å in diameter. The results of the vapor pressure measurement indicate that ³ He film grows up to the second layer. In the first layer, the heat capacity of ³ He shows the same temperature and coverage dependence as ⁴ He, indicating a solid phase. Above a little higher coverage than second layer promotion, heat capacity isotherms for ³ He at several hundred mK increase with coverage while those for ⁴ He decrease. This large heat capacity of ³ He is the nuclear spin heat capacity of the second layer fluid ³ He.     

Slippage of 4He Films Adsorbed on Grafoil

We applied the quartz-crystal microbalance (QCM) technique to ⁴He films adsorbed on grafoil. It was found that both of nonsuperfluid ⁴He films and the inert layers underneath the superfluid film slip under a certain condition at low temperatures, and that the temperature at which these films start to slip depends on the ⁴He areal density. In addition, this slippage also depended strongly on the amplitude of the quartz crystal.     

3He Impurities in 4He Systems Adsorbed on Curved Substrates

It is shown that ³He impurities in sufficiently large ⁴He systems adsorbed onto substrates with curved geometries form surface bound states, analogous to the Andreev state on a planar liquid--vapor interface. We report the analysis performed for superfluid ⁴He adsorbed on the external surface of the nano-fullerene C₆₀ and on cylindrical nano-wires of Au. It is found that a single ³He impurity diluted into such adsorbed structures behaves as on films on planar substrates and as on pure ⁴He clusters.     

‘Heat from Above’ Heat Capacity Measurements in Liquid 4He

We have made heat capacity measurements of superfluid ⁴He at temperatures very close to the lambda point, T _λ, in a constant heat flux, Q, when the helium sample is heated from above. In this configuration the helium enters a self-organized (SOC) heat transport state at a temperature T _soc(Q), which for Q≥100 nW/cm² lies below T _λ. At low Q we observe little or no deviation from the Q=0 heat capacity up to T _SOC(Q); beyond this temperature the heat capacity appears to be sharply depressed, deviating dramatically from its bulk behaviour. This marks the formation and propagation of a SOC/superfluid two phase state, which we confirm with a simple model. The excellent agreement between data and model serves as an independent confirmation, of the existence of the SOC state. As Q is increased (up to 6 µW/cm²) we observe a Q dependent depression in the heat capacity that occurs just below T _SOC(Q), when the entire sample is still superfluid, This is due to the emergence of a large thermal resistance in the sample, which we have measured and used to model the observed heat capacity depression. Our measurements of the superfluid thermal resistivity are a factor of ten larger than previous measurements by Baddar et al.     

Heat Capacity Measurements of 3He-4He Mixture Films

We report heat capacity measurements from our on-going experiments on two-dimensional liquid ³He on superfluid ⁴He thin films absorbed on Nuclepore. The ³He coverage dependence of the heat capacity for 0.02–0.50 bulk-density layers of ³He with 3.10 bulk-density layers of ⁴He over the temperature range 40≤T≤200 mK is presented. We find the effective mass of ³He on 3.10 layers of ⁴He is greater than that on 4.33 layers of ⁴He, consistent with our previous magnetic susceptibility measurements.     

Fluctuation Effects in the Heat Capacity of 3He–4He Solid Solutions

The impurity heat capacity of solid ³ He–⁴ He mixtures is theoretically investigated both below and above phase separation temperature T _s . It is shown that at T > T _s the temperature behavior of the heat capacity is completely defined by correlation effects in the impuriton subsystem. The proposed theory is in good agreement with experimental data.     

Heat Capacity of H2 Adsorbed on Carbon Nanotube Bundles

We report on ongoing measurements of the heat capacity of H₂ adsorbed on closed-end single-wall carbon, nanotube bundles(SWNTB), for 1.5K≤T≤10K and for coverages between 0.04 and 1.4 layers. Coverages are defined from a sharp minimum in heat capacity isotherms. We determine three distinct regions corresponding to: a) Formation of lines of atoms in grooves and large interstitial sites, b) Formation of a layer over the graphite-like outside surface of the bundle, and c) Beginning of growth of the second layer. Resugts are correlated to H₂ vapor pressure isotherms and are compared to helium heat capacity measurements done on the same cell. In, neither ⁴He nor H₂ do we observe a 1-d ideal gas regime.     

Superfluidity of 4He Adsorbed on Nanoporous Activated Carbon Fibers

⁴He confined in nanoporous media is one of the most interesting nano-sized systems in the context of an interacting Bose system. In the present work, we study superfluidity of ⁴He adsorbed in nanoporous activated carbon fibers (ACFs). Up to a ⁴He coverage of n=22.6 μmol m⁻², no superfluidity is observed. Over 23.7 μmol m⁻², superfluid transition is observed at T _c ∼550 mK. With an increase in n the superfluid density enhances, but T _c is independent of n. These observations indicate that the thickness of the superfluid ⁴He films on the pore wall is restricted by a slit type pore shape of ACFs.     

Variational Monte Carlo Calculations of 4He Adsorbed on Graphite

We present the results of variational Monte Carlo calculations of the solid ⁴ He monolayer adsorbed on a corrugated graphite substrate with the shadow wave function technique. We find that the solid monolayer at the commensurate density is tightly bound to the substrate and that the presence of corrugation localizes the Helium atoms in the direction parallel to the substrate around the sites of a triangular lattice where 1/3 of the adsorption sites of graphite are occupied. We have calculated the energy per particle, the density profile of the monolayer and the static structure factor. We have also studied the system in the presence of a defect (vacancy or interstitial) and we report the results for the one-body density matrix.     

Heat Capacity of Adsorbed Helium-3 at Ultra-Low Temperatures

We report on direct measurements of the heat capacity of monolayers of ³He adsorbed on the surface of a copper cell filled with superfluid ³He. We found that at ultra low temperatures the surface ³He heat capacity dominates over the heat capacity of the bulk liquid ³He. The replacement of adsorbed ³He by ⁴He changes the heat capacity of the sample by an order of magnitude. These investigations were made in the framework of the “ULTIMA” project, a dark matter detector based on superfluid ³He in the limit of ultra low temperatures.     

Quartz Oscillator Study of Monolayer 4He and 3He - 4He Mixture Films Adsorbed on Solid H2

The superfluid transition in submonolayer and monolayer ⁴ He films and ³ He - ⁴ He mixture films on solid H ₂ has been studied using a quartz crystal microbalance technique. Kosterlitz-Thouless (KT) transitions were observed in submonolayer ⁴ He films with density greater than 0.062 ± 0.002 Å ^–2 . We determine a binding energy of ⁴ He to 0.241 Å ^–2 H ₂ of –15.7 K in the. presence of 1 monolayer of ⁴ He. At several ⁴ He coverages, a range of submonolayer ³ He coverages was studied (n ₃ 0.0567 Å ^–2 ). With each increase in the ³ He coverage, the KT transition temperature decreased. For the higher coverage mixture films studied (n ₄ 0.0726 Å ^–2 ) we observed an apparent second decoupling of the film from the quartz oscillator frequency in addition to the KT transition. We have studied the. coverage dependence of this new feature.     

Observation of Superfluid 4He Adsorbed in One-Dimensional Mesopores

To study one-dimensional (1D) quantum liquid of ⁴ He, we measured the heat capacity and performed a torsional oscillator experiment for ⁴ He adsorbed on a new mesoporous substrate whose adsorption area consists of walls of straight one-dimensional 18Å diameter tunnels. The presence of adsorbed quantum liquid was examined by the isotope effect on the heat capacity for ³ He and ⁴ He adatoms. Above a coverage n _o , the heat capacity isotherms are completely different because of the Fermi and the Bose fluids, respectively. In the torsional oscillator experiment we observed superfluid ⁴ He above n _o . The fraction of the superfluid decoupled from the motion of the substrate is 0.13, which is the same order as 0.18 for packed Pt fine powder and 0.24 for 80 Å-porous glasses. The result indicates that the superfluid state exists in the one-dimensional ⁴ He adatoms formed in the 18 Å diameter pores.     

Localization-Fermi Liquid Transition of 3He Adsorbed on 4He-Coated Hectorite

To create a phase diagram of two-dimensional (2D) ³ He fluids, we measured heat capacity of the ³ He adatoms down to 20mK as a function of the density. The ³ He adatoms are deposited on hectorite precoated with ⁴ He in the amount of 24.70mol/m ², just above the onset density for the ⁴ He super-fluid. Isotherms of the heat capacity steeply increase with the ³ He density up to n _c =2.4mol/m ². Above n _c , the heat capacity shows properties of the 2D Fermi liquids. We pointed out that the density dependence of the heat capacity is similar to those of the insulator-metal (I-M) transitions of some electron systems, e.g. Si:P. Assuming the transition from a localized state to the Fermi liquid at the density n _c , the diameter of a localization area a _H ^* was obtained as about 3.8Å using the Mott relation that the mean distance equals 2.2 a _H ^* at the transition. Effective mass and 2D spin fluctuations of the Fermi liquids are enhanced with the density by increasing correlations in the 2D liquids.     

Preliminary Heat Capacity and Vapor Pressure Measurements of 2D 4He on ZYX Graphite

We report preliminary heat capacity and vapor pressure measurements of the first and second layers of ⁴He adsorbed on ZYX graphite. ZYX is known to have much better crystallinity than Grafoil, the most commonly-used exfoliated graphite substrate, such as a ten-times larger platelet size. This allows us to distinguish different phases in 2D ⁴He much more clearly and may provide qualitatively different insights into this system. We found a significantly asymmetric density-dependence of the heat-capacity peak associated with the $\sqrt{3}\times\sqrt{3}$ phase formation comparing with that obtained with Grafoil. The 2nd-layer promotion density is determined as 11.8±0.3 nm^?2 from the heat-capacity measurement of low density samples in the 2nd layer and vapor pressure measurement.     

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.     

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.     

Heat Capacity of Low Temperature Solid 3He

We have calculated the spin wave spectra and from these the specific heats of CNAF and UUDD solid ³He at low temperatures. We compare with experiment and find good agreement even though we also find major deviations from simple T³ behavior. The calculation included the six-spin exchange terms now recognized to be important for quantitative calculations. The inclusion of these terms was made more tractable by application of an algebraic technique from nuclear theory (Random Phase Approximation) for execution of the spin wave calculation, which nevertheless involved lengthy analysis.     

Heat capacity of3He/4He mixtures

We measured the specific heat capacity of three dilute mixtures (2.6, 1.07, and 0.44%) of³He in⁴He and of pure⁴He. The⁴He contribution to the specific heat of the mixture is subtracted, leaving only the³He part. This is fitted to a theoretical expression over the whole temperature range from 10 to 700 mK. Assuming a dispersion relation of the form =² k ²(1+k ²)/2m*, the fits yield the value of and the effective mass m* of each mixture. The average value of is –0.076±0.01 A² and the effective mass in the limit of zero concentration is (2.23±0.02)m ₃. These are compared to values deduced from other measurements.     

One-Dimensional Phonon State of 4He Films Adsorbed in Straight Nanopores

We have studied heat capacities of ⁴He adsorbed in straight nanopores 1.8, 2.2, and 2.8 nm in diameter. Heat capacities of the ⁴He fluid film on the solid layer at 0.08–0.4 K show power laws close to T in 1.8 nm pores, close to T ² in 2.8 nm pores, and a crossover from T to T ² with increasing temperature in 2.2 nm pores. These heat capacities are explained by a model assuming a phonon dispersion with continuous one-dimensional (1D) states in the axial direction and discrete energy levels in the azimuthal direction. By fitting experimental data to the model, the phonon velocity along the pore axis and the energy gap for propagation in the cross section are derived. At temperatures sufficiently lower than the energy gap, where the thermal wave length of phonons is much longer than the effective pore diameter, the ⁴He fluid films show a T-linear heat capacity of 1D phonons propagating only along the pore axis. At higher temperatures, a 1D-2D crossover of phonons occurs.