3He adsorbed on graphite is an almost ideal two-dimensional (2D) fermionic system. The 2D solid, where the interaction between the nuclear spins
S=21 is due to multiple spin exchange, has been extensively studied as a model system for strongly interacting fermions in 2D. At high densities in the second layer, three-body exchange dominates and leads to Heisenberg ferromagnetism. We report on nuclear magnetic resonance measurements at ultralow temperatures and low magnetic fields of the second layer of
3He on graphite preplated by one layer of
4He. By adding controlled amounts of
4He,
3He atoms are pushed out from the ferromagnetic domains, which become smaller and denser. We can evaluate the properties of these clusters, and control their size from a few tens to a few hundreds of atoms. These sizes are comparable to today's computing capabilities for exact numerical calculations on small clusters, and should lead to direct comparison between measurements on this model Heisenberg system and theory.
We examine the thermodynamics of a two-dimensional Fermi gas model describing adsorbed
3Hein a thin superfluid
4Hefilm. The
3Hesystem is characterized by both a hydrodynamic effective mass and a set of discrete transverse single-particle states that model the effects of the interaction with the substrate that supports the film. We show that the magnetization steps seen in experiment are a simple manifestation of the
T=0K equation of state. We prove that perfectly horizontal magnetization steps rigorously disappear at any finite temperature. We show that the thermal stability of the steps is determined by the larger of $\ensuremath{\Delta}\ensuremath{\epsilon}/2,$ one-half of the level spacing, and ${\ensuremath{\mu}}_{m}{\mathcal{H}}_{0},$ the magnetic energy. We derive the conditions under which there exist points in the phase space (termed invariant points) through which all low-temperature isotherms pass exponentially close. The invariant points appear for magnetization versus
3Hecoverage, chemical potential versus magnetization, magnetic susceptibility versus coverage, and speed of sound squared versus coverage. We compare our calculated invariant points for the magnetization versus coverage with experiment and find good agreement. We show that there exist small regions of thermodynamic phase space in which the temperature derivative of the pressure is negative. We explain these anomalous regions as the result of
3Heatoms ``spilling over'' from a full Fermi sea to an empty Fermi sea upon the application of a small increase in temperature. Through a Maxwell relation, this behavior can also be seen as in the appearance of a local peak in low-temperature entropy isotherms versus coverage. In the limit of a two state model, we calculate the specific heat and show that a Schottky peak develops in the low
3Hecoverage limit. We calculate the magnetic susceptibility and predict that it should exhibit a steplike structure versus
3Hecoverage similar to that of the magnetization. We calculate the speed of sound and show that it should exhibit zero-temperature discontinuities at the points where new Fermi seas begin to be occupied. Both the steplike structure in the magnetic susceptibility and the discontinuity-type structure in the speed of sound persist to temperatures on the order of 100 mK, and are analyzed in terms of invariant points in their respective phase diagrams. We show explicitly that, in the Fermi gas limit, the zero-field magnetic susceptibility is simply proportional to the isothermal compressibility.
The nuclear magnetic susceptibility of
3He adsorbed on the surface of graphite, plated with a monolayer of solid
4He, has been measured at surface densities less than 0.055 \AA{} $^{\mathrm{\ensuremath{-}}2}$ and at temperatures down to 6 mK. A temperature-independent susceptibility is observed at low temperatures, which is strongly enhanced over the ideal-gas value, due to quasiparticle interactions. The inferred Landau-Fermi-liquid parameters allow a comparison with microscopic theories of interacting Fermi systems.
The equation of state of two-dimensional 3He at zero temperature has been calculated using the diffusion Monte Carlo method. By means of a combination of the fixed-node and released-node techniques, it is shown that backflow correlations provide a very accurate equation of state. The results prove unambiguously the non-self-bound character of two-dimensional 3He due to its Fermi statistics. We present solid evidence that the gas phase, predicted for the two-dimensional system, can be extrapolated to the case of 3He adsorbed on a strong substrate such as graphite.
Spin polarized hydrogen and helium are being studied extensively because they are expected to exhibit quantum effects on a macroscopic scale. Here, low density properties of spin polarized hydrogen gas in two and three dimensions are studied using a quantum virial expansion. These properties include heat capacities, chemical potentials, and estimates of critical temperatures and densities for Bose-Einstein condensation in three dimensions and for a possible superfluid transition in two dimensions. The classical virial expansion and the validity of effective-range theory is also discussed. The heat capacity of adsorbed helium films of 3He, 4He and spin polarized 3He is also studied. Virial calculations with a structureless substrate approximation but with substrate mediated corrections to the Lennard-Jones potential are performed as a function of applied magnetic field and magnetization. Effects of substrate potential and geometry on the thermodynamics, low density submonolayer helium films physisorbed on rare gas plated graphite substrates are investigated using a tight-binding formalism and a lattice version of potential scattering theory. A generalization of the formalism to lattices with a basis is made and applied to the honeycomb lattice. The calculations with this theory exhibit systematic trends in the specific heat that are in qualitative agreement with presentlymore » available experimental data.« less
Abstract We investigate the thickness dependence of the Néel temperature of a thin quantum spin‐1/2 Heisenberg antiferromagnetic film as a function of the magnetic field on a simple cubic lattice. The Néel temperature TN(H, ℓ) is obtained by using the framework of the effective‐field theory for films consisting of ℓ = 2, 3, 5, 10 and ∞ (bulk) interacting layers. We present the phase diagram of T versus H in the whole range of the magnetic field for several values of ℓ. A continuous phase‐transition line separating the antiferromagnetic and ferromagnetic phases is observed. The critical temperature TN(H, ℓ) of the film is smaller than the corresponding bulk critical temperature $ T^{\rm b}_{\rm N} $ (H) ≡ TN(H, ∞) of the infinite system, which has been analyzed recently by Bublitz Filho and de Sousa [Phys. Lett. A 323, 9 (2004)]; as ℓ is increased, TN(H, ℓ) also increases and approaches $ T^{\rm b}_{\rm N} $ (H) for large values of ℓ. We have, also, studied the quantum phase transition where three critical fields were found: Hc(ℓ) = 6.224 for ℓ ≥ 3 (three‐dimensional regime), Hc(ℓ = 2) = 5.210 (intermediate regime) for ℓ = 2 and, finally, the two‐dimensional regime at ℓ = 1 with Hc(ℓ = 1) = 4.194. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)