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.     

Thermal Relaxation of 3He Solid Films Adsorbed on Graphite

No Heading The thermal conductivity between the ³He solid films and the graphite substrate was measured by the relaxation method between 100 K and 1 mK. The areal-density depedence of the thermal conductivity shows behavior similar to that of the exchange frequency J both in the submonolayer and in the second layer. These facts indicate that heat is transferred by magnetic mechanisms in the ³He solid film itself. They also imply that the ³He solid film is thermally connected with the graphite substrate only at some local spots.PACS numbers: 67.70.+n, 67.80.Gb     

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.     

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.     

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.     

Low Temperature Magnetization of Two Dimensional 3He on Three Layers of HD Preplated Graphite

We have measured the low temperature magnetization of submonolayer ³He on three layers of HD preplated graphite. NMR measurement has been performed by progressively adding ⁴He to the system, to prevent ³He atoms from being trapped in substrate heterogeneities and to change the areal density of ³He. The exchange constant (J) is found to have a similar density dependence to that for two layers of HD preplated one. The magnetization in the antiferromagnetic region increases gradually down to 100 K and shows no evidence corresponding to a spin gap.     

NMR Measurements of 2D 3He Adsorbed on ZYX Exfoliated Graphite

We describe first successful usage of ZYX exfoliated graphite to cool adsorbed two dimensional (2D) ³He to ugtra low temperatures (ULT). ZYX has much better characteristics as an adsorption substrate such as larger crystallite (platelet) size and smaller mosaic angle than Grafoil, a widely used exfoliated graphite in ULT experiments. In spite of the relatively small surface area of ZYX, we could perform a nuclear magnetization measurement of paramagnetic 2D solid ³He with continuous wave NMR below 10 mK. The data follow nicely the Curie law down to 200 µK. This indicates that ZYX can be used in experiments to study detailed density dependences of low temperature properties of 2D ³He including possible BCS transitions. We also show a preliminary resugt of pulsed NMR measurements of high density 2D fluid ³He adsorbed on ZYX preplated with a ⁴He monolayer.     

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.     

Thermal Relaxation in 3He Solid Films on Graphite

The thermal conductance (κ) between ³He solid films and graphite substrates is measured in weak magnetic fields of 0, 150, 300, and 600 Oe by a relaxation method. κ is markedly reduced in a magnetic field of 150 Oe and shows complicated magnetic-field-dependent variations. Previous measurements have revealed that heat flows along ³He solid films over a long distance and then flows into the graphite substrate at some local spots. The reduction in κ in magnetic field indicates an increase in the length of the thermal flow path and a decrease in the number of local spots through which heat is transferred to the graphite substrate. These suggest the important role of magnetic impurities present in the graphite substrate. The temperature-dependent variation in the ratio of κ and heat capacity (C), κ/C, is nearly unchanged when the magnetic field increases from 150 to 600 Oe, while κ shows complicated variations. κ/C shows a clear minimum at a temperature around 1 mK, which depends on the areal density of ³He. Above and below this temperature, heat transfer is thought to take place along the solid ³He film, respectively by phonons and spin excitations.     

Dynamical Response of Liquid 3He Films Adsorbed on Solid Substrates

Within the general framework of linear response theory, we investigate the excitation spectrum of ³He films adsorbed on substrates. Starting from the quasiparticle spectrum and the effective interaction derived in a finite range density functional scheme, we analyze the properties of the particle-hole (ph) excitations as well as the collective modes in the Random Phase Approximation. On the one hand, the most important features of the ph spectrum, originated in the band structure of the single particle spectrum together with the fermionic character of the quasiparticles, are clearly exhibited when the free response to a probe parallel or transverse to the film is considered. On the other hand, for any film, the collective spectrum presents various branches which, in many situations, can be associated with predominantly intraband longitudinal transitions or with almost pure interband transitions. Analyzing the RPA response of a monolayer on substrates of very different adsorbing power (cesium and graphite) we can interpret the nature of the existing collective excitations and determine the influence of the geometrical features of the film on the effective quasiparticle interaction responsible of these oscillations.     

Magnetization Curve of Two-Dimensional Anti-ferromagnetic Solid 3He on Graphite

Two-dimensional anti-ferromagnetic solid ³He on graphite, so called 4/7 phase, is a highly frustrated magnetic system and its ground state is considered to be a gapless spin liquid. Then how is the behavior in high magnetic fields? We tried to observe the magnetization curve at around 1 mK in high magnetic fields up to 10 T, using a Faraday-type magnetometer. To eliminate a large background signal from graphite as a substrate and copper as a thermal link, a double gradient coil system is employed to produce opposite field gradients in two regions equidistant from the field center. Preliminary results of the 4/7 phase on graphite show no saturated magnetization even at 1 mK and 10 T, suggesting the existence of magnetization plateau.     

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.     

Strongly Correlated Two Dimensional Fluid 3He

A two dimensional system of strongly correlated fermions can be realised by a fluid monolayer of ³ He adsorbed on an atomically flat surface. We report extensive measurements of the heat capacity, c, of ³ He adsorbed on graphite plated with two layers of hydrogen deuteride (HD) over a closely spaced grid of coverages in the temperature range l-80mK. The quasiparticle effective mass ratio, inferred from the linear temperature coefficient of the heat capacity, increases from near unity at low densities and appears to diverge approaching localisation. The maximum value of m*/m we are able to unambiguously extract from the data is 13 at a density 5 nm ^–2. At this density c/T is temperature independent only below 5mK. The behaviour of m*/m and F ₀ ^a , inferred from magnetization data, are consistent with the model of almost-localised fermions. We can track the evolution of strong finite temperature deviations from Fermi liquid behaviour as the density of the film and hence m*/m are increased. At sufficiently low temperature this correction is of T ² form going over to a large TlnT deviation for T > 0.05 T _F *, as predicted for 2D spin fluctuations. Thus in this system non-Fermi liquid behaviour extends to very low temperatures in the strongly correlated, large m */m, limit.     

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?     

Magnetization Curve of Second Layer Anti-Ferromagnetic Solid 3He on Graphite

Two dimensional anti-ferromagnetic solid ³He on graphite in the so called 4/7 phase is a highly frustrated quantum spin system and its ground state is considered to be a gapless spin liquid. To investigate the detailed magnetic behavior, the magnetization curve has been measured below 1 mK in high magnetic fields, by use of NMR over a wide frequency range up to 84 MHz. The magnetization of the 4/7 phase seems to have a plateau at half the saturation magnetization, which is not inconsistent with results obtained with a double gradient Faraday magnetometer.      

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.     

Calorimetric Study of the Desorption and Phases of 3He And 4He Adsorbed on Two Layers of H2-plated Graphite Above 0.2K

We have conducted new heat capacity studies of films of ³ He and ⁴ He adsorbed on 2.15 layers of hydrogen plating exfoliated graphite for temperatures T > 0.2K and coverages (n) over the entire first layer and beginning of the second layer. Low-density ³ He films show two-dimensional Fermi fluid behavior with no liquid-vapor condensation below 0.9K. We have mapped the n-T melting tine and estimated monolayer completion density using heat capacity isotherms. By fitting ³ He films' desorption specific heats to a theoretical model, we have calculated the ³ He binding energy (21.3K to 21. 7K) and compare it to a previous measurement for ⁴ He films on the same substrate (25.1K to 25.5K).     

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.     

Heat Capacity of 3He Solid Film on Graphite in Magnetic Fields

Heat capacities of a submonolayer ³He solid film adsorbed on a graphite surface are measured in magnetic fields up to 400 Oe. The measured heat capacity shifts to higher temperatures with an increasing magnetic field. The amplitudes of the shifts are twenty times larger than the magnitude of the Zeeman energy, which is anomalously large. With regard to the origin of these large shifts, the reduction of frustrations and the weakening of the competition between multiple spin exchange interactions are discussed.     

Pulsed Nuclear Magnetic Resonance on 3He Adsorbed on Bare and 4He Preplated MCM-41 Using DC SQUID Detection

We report low field DC SQUID NMR measurements down to 1.5 K of ³He adsorbed in the pores of the mesoporous molecular sieve MCM-41. In the first experiment measurements were made on ³He adsorbed onto the bare pore walls of MCM-41 with coverages ranging from $n_{^{3}\mathrm{He}}=0.86n_{1}$ to full pores at $n_{^{3}\mathrm{He}}=1.79n_{1}$ , where n ₁ is the coverage for monolayer completion. A second experiment was performed with low ³He coverages ( $n_{^{3}\mathrm{He}}\sim0.01n_{1}$ ) on ⁴He preplated pores, where a crossover to a quasi-1D state is expected to occur at temperatures sufficiently below 700 mK. In both experiments relaxation times T ₁ and T ₂ ^* were measured as a function of temperature and coverage at frequencies from 80 to 240 kHz. The frequency dependence of the linewidth in the pure ³He experiment is extremely weak therefore T ₂ ^* ≈T ₂. The 1.5 K isotherm shows a small minimum in T ₂ ^* at a coverage corresponding to monolayer completion. In the experiment with ⁴He preplating there was no significant change in T ₁ or T ₂ ^* when the ³He coverage was doubled from $n_{^{3}\mathrm{He}}=0.01n_{1}$ to 0.02n ₁ at a ⁴He preplating of $n_{^{4}\mathrm{He}}=1.05n_{1}$ . This suggests that the relaxation times are dominated by single particle effects in the low density regime.