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Physical Review B

Ferromagnetic nanoclusters in two-dimensional He3

Eddy Collin, Christopher Bäuerle, Yu. M. Bunkov, Henri Godfrin

Published Mar 23, 2006• 8 citations
Publisher

Abstract

$^{3}\mathrm{He}$ adsorbed on graphite is an almost ideal two-dimensional (2D) fermionic system. The 2D solid, where the interaction between the nuclear spins $S=\frac{1}{2}$ 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 $^{3}\mathrm{He}$ on graphite preplated by one layer of $^{4}\mathrm{He}$. By adding controlled amounts of $^{4}\mathrm{He}$, $^{3}\mathrm{He}$ 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.

DOI
10.1103/physrevb.73.125421

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3He^{3}\mathrm{He}3He adsorbed on graphite is an almost ideal two-dimensional (2D) fermionic system. The 2D solid, where the interaction between the nuclear spins S=12S=\frac{1}{2}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^{3}\mathrm{He}3He on graphite preplated by one layer of 4He^{4}\mathrm{He}4He. By adding controlled amounts of 4He^{4}\mathrm{He}4He, 3He^{3}\mathrm{He}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.
The nuclear magnetic susceptibility of 3He^{3}\mathrm{He}3He adsorbed on the surface of graphite, plated with a monolayer of solid 4He^{4}\mathrm{He}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.
We provide evidence for a finite-temperature ferromagnetic transition in two dimensions as H -->0 in thin films of 3He on graphite, a model system for the study of two-dimensional magnetism. We perform pulsed and cw NMR experiments at fields of 0.03-0.48 mT on 3He at areal densities of 20.5-24.2 atoms/nm(2). At these densities, the second layer of 3He has a strongly ferromagnetic tendency. With decreasing temperature, we find a rapid onset of magnetization that becomes independent of the applied field at temperatures in the vicinity of 1 mK. Both the dipolar field and the NMR linewidth grow rapidly as well, which is consistent with a large (order unity) polarization of the 3He spins.
Advances with trapped ultracold atoms intensified interest in simulating complex physical phenomena, including quantum magnetism and transitions from itinerant to non-itinerant behavior. Here we show formation of antiferromagnetic ground states of few ultracold fermionic atoms in single and double well (DW) traps, through microscopic Hamiltonian exact diagonalization for two DW arrangements: (i) two linearly oriented one-dimensional, 1D, wells, and (ii) two coupled parallel wells, forming a trap of two-dimensional, 2D, nature. The spectra and spin-resolved conditional probabilities reveal for both cases, under strong repulsion, atomic spatial localization at extemporaneously created sites, forming quantum molecular magnetic structures with non-itinerant character. These findings usher future theoretical and experimental explorations into the highly correlated behavior of ultracold strongly repelling fermionic atoms in higher dimensions, beyond the fermionization physics that is strictly applicable only in the 1D case. The results for four atoms are well described with finite Heisenberg spin-chain and cluster models. The numerical simulations of three fermionic atoms in symmetric DWs reveal the emergent appearance of coupled resonating 2D Heisenberg clusters, whose emulation requires the use of a t – J -like model, akin to that used in investigations of high T c superconductivity. The highly entangled states discovered in the microscopic and model calculations of controllably detuned, asymmetric, DWs suggest three-cold-atom DW quantum computing qubits.
Using the density-matrix renormalization group method and quantum Monte Carlo simulation, we studied numerically the energy spectrum and thermodynamics of the quantum Heisenberg spin model for narrow graphene nanoribbons and their derivatives with periodically embedded heteroatoms. For several nanoribbon structures we found macroscopic ground state spin, gapless lowest excitation spectra and intermediate magnetization plateaus at low temperatures. We also studied the lowest energy states of frustrated systems formed by triangular graphitic clusters connected by bridged ions of transition metals. On the base of many-body perturbation theory and the exact diagonalization method, we showed the possibility of spin switching for this model due to the change the corresponding coupling parameters.
The superfluid response of nanoscale size quasi-2D He-4 droplets adsorbed on a graphite substrate is investigated by computer simulations. It is found that clusters comprising as few as 7 atoms are stable at temperatures lower than < 0.15 K. Clusters of ~20 atoms or less are liquid-like and ~100% superfluid. As the size is increased, the central region crystallizes, forming the commensurate C_1/3 phase, with a surface sliver of superfluidity evolving into a perimetral 1D Luttinger liquid with increasing cluster size. The relevance to quasi-2D molecular spectroscopy and to transverse quantum superfluidity is discussed.
Nuclear magnetic susceptibility measurements of the 3He^{3}\mathrm{He}3He in dilute 3He^{3}\mathrm{He}3He-4He^{4}\mathrm{He}4He mixture films are presented. At low 3He^{3}\mathrm{He}3He coverages (d3<0.1{d}_{3}<0.1d3​<0.1 layer), the 3He^{3}\mathrm{He}3He behaves approximately as a 2D ideal Fermi gas. For larger submonolayer 3He^{3}\mathrm{He}3He coverages, the low-temperature susceptibility is enhanced, increasing with increasing amounts of 3He^{3}\mathrm{He}3He, contrary to the 2D ideal Fermi-gas model. No evidence for a phase transition in the 3He^{3}\mathrm{He}3He is seen.