Helium Spin Echo Research Articles

Low-cost bidirectional coil driver with microamp precision

We describe a compact constant current power supply with µA precision designed to drive coils. The unit generates currents from −125 mA to 125 mA with a load up to 10 Ω using a precision 16-bit digital to analogue converter, driven from a microcontroller (e.g. Raspberry Pi Pico). All power for the unit is derived from the 5 V of the microcontroller. As a demonstration of the capability of the power supply, it was applied to spin manipulation in a helium spin echo system.

Surface Diffusion by Means of Stochastic Wave Functions. The Ballistic Regime

Stochastic wave function formalism is briefly introduced and applied to study the dynamics of open quantum systems; in particular, the diffusion of Xe atoms adsorbed on a Pt(111) surface. By starting from a Lindblad functional and within the microscopic Caldeira–Leggett model for linear dissipation, a stochastic differential equation (Ito^-type differential equation) is straightforwardly obtained. The so-called intermediate scattering function within the ballistic regime is obtained, which is observable in Helium spin echo experiments. An ideal two-dimensional gas has been observed in this regime, leading to this function behaving as a Gaussian function. The influence of surface–adsorbate interaction is also analyzed by using the potential of two interactions describing flat and corrugated surfaces. Very low surface coverages are considered and, therefore, the adsorbate–adsorbate interaction is safely neglected. Good agreement is observed when our numerical results are compared with the corresponding experimental results and previous standard Langevin simulations.

Molecular spin echoes; multiple magnetic coherences in molecule surface scattering experiments.

In this paper we demonstrate that a molecular beam of hydrogen molecules can be magnetically manipulated to produce multiple coherences in the molecular interference pattern. Unlike spin 1/2 magnetic beam experiments, i.e., neutron and helium spin echo, the nuclear and rotational magnetic moments in a molecule are strongly coupled. We show experimentally and theoretically that this coupling leads to multiple magnetic field conditions under which the magnetic moment of molecules travelling with different speeds can be coherently refocussed. We also demonstrate that these multiple coherence signals are extremely sensitive to the scattering event, opening up new possibilities for measuring molecule-surface interactions.

Parallel and anti-parallel echoes in beam spin echo experiments

Abstract The refocusing of velocity-dependent spin-phase is the basic phenomenon behind helium and neutron spin echo beam experiments. In this paper we present quantum and classical descriptions of the spin echo phenomenon and show that non-adiabatic transitions, such as those which take place during rotation of the magnetic field axis between the two arms of a helium spin echo setup, lead to echo conditions without reversing the magnetic field orientation between the two arms. The usual spin echo conditions, created by reversing the magnetic field orientation, do not require such non-adiabatic transitions. These two echo conditions are termed parallel and anti-parallel spin echoes, respectively. We derive the dependence of the relative intensity of the two echoes on the scattering geometry of the setup and show experimental results which verify the co-existence of the two echo conditions, the theoretically derived expressions for their relative intensity and the effect of an additional spin rotator coil introduced within the non-adiabatic transition region.

Quantum surface diffusion in Bohmian mechanics

Surface diffusion of small adsorbates is analyzed in terms of the so-called intermediate scattering function and dynamic structure factor, observables in experiments using the well-known quasielastic Helium atom scattering and Helium spin echo techniques. The linear theory applied is an extension of the neutron scattering due to van Hove and considers the time evolution of the position of the adsorbates in the surface. This approach allows us to use a stochastic trajectory description following the classical, quantum and Bohmian frameworks. Three different regimes of motion are clearly identified in the diffusion process: ballistic, Brownian and intermediate which are well characterized, for the first two regimes, through the mean square displacements and Einstein relation for the diffusion constant. The Langevin formalism is used by considering Ohmic friction, moderate surface temperatures and small coverages. In the Bohmian framework, analyzed here, the starting point is the so-called Schrödinger-Langevin equation which is a nonlinear, logarithmic differential equation. By assuming a Gaussian function for the probability density, the corresponding quantum stochastic trajectories are given by a dressing scheme consisting of a classical stochastic trajectory followed by the center of the Gaussian wave packet, and issued from solving the Langevin equation (particle property), plus the time evolution of its width governed by the damped Pinney differential equation (wave property). The Bohmian velocity autocorrelation function is the same as the classical one when the initial spread rate is assumed to be zero. If not, in the diffusion regime, the Brownian-Bohmian motion shows a weak anomalous diffusion.

The dynamics of benzene on Cu(111): a combined helium spin echo and dispersion-corrected DFT study into the diffusion of physisorbed aromatics on metal surfaces.

We use helium spin-echo spectroscopy (HeSE) to investigate the dynamics of the diffusion of benzene adsorbed on Cu(111). The results of these measurements show that benzene moves on the surface through an activated jump-diffusion process between the adsorption sites on a Bravais lattice. Density Functional Theory (DFT) calculations with van der Waals (vdW) corrections help us understand that the molecule diffuses by jumping through non-degenerate hollow sites. The results of the calculations shed light on the nature of the binding interaction between this prototypical aromatic molecule and the metallic surface. The highly accurate HeSE experimental data provide a quantitatively stringent benchmark for the vdW correction schemes applied to the DFT calculations and we compare the performances of several dispersion interaction schemes.

Structure and dynamics investigations of a partially hydrogenated graphene/Ni(111) surface

Using helium-3 atom scattering, we have studied the adsorption kinetics, the structure and the diffusional dynamics of atomic hydrogen on the surface of a graphene monolayer on Ni(111). Diffraction measurements reveal a 4° rotated rectangular hydrogen overstructure. Hydrogen adsorption and desorption exhibit activation barriers of Ea=(89±7) meV and Ed=(1.8±0.2) eV, respectively. Helium-3 spin-echo measurements showed no decay of the spatial correlation function (or intermediate scattering function) within the time range of the spectrometer. Hence, we are able to set lower limits for a possible hydrogen surface diffusion rate.

Energy Dissipation during Diffusion at Metal Surfaces: Disentangling the Role of Phonons versus Electron-Hole Pairs.

Helium spin echo experiments combined with abinitio based Langevin molecular dynamics simulations are used to quantify the adsorbate-substrate coupling during the thermal diffusion of Na atoms on Cu(111). An analysis of trajectories within the local density friction approximation allows the contribution from electron-hole pair excitations to be separated from the total energy dissipation. Despite the minimal electronic friction coefficient of Na and the relatively small mass mismatch to Cu promoting efficient phononic dissipation, about (20±5)% of the total energy loss is attributable to electronic friction. The results suggest a significant role of electronic nonadiabaticity in the rapid thermalization generally relied upon in adiabatic diffusion theories.

Coupling between diffusion and orientation of pentacene molecules on an organic surface.

The realization of efficient organic electronic devices requires the controlled preparation of molecular thin films and heterostructures. As top-down structuring methods such as lithography cannot be applied to van der Waals bound materials, surface diffusion becomes a structure-determining factor that requires microscopic understanding. Scanning probe techniques provide atomic resolution, but are limited to observations of slow movements, and therefore constrained to low temperatures. In contrast, the helium-3 spin-echo (HeSE) technique achieves spatial and time resolution on the nm and ps scale, respectively, thus enabling measurements at elevated temperatures. Here we use HeSE to unveil the intricate motion of pentacene admolecules diffusing on a chemisorbed monolayer of pentacene on Cu(110) that serves as a stable, well-ordered organic model surface. We find that pentacene moves along rails parallel and perpendicular to the surface molecules. The experimental data are explained by admolecule rotation that enables a switching between diffusion directions, which extends our molecular level understanding of diffusion in complex organic systems.

How Atomic Steps Modify Diffusion and Inter-adsorbate Forces: Empirical Evidence from Hopping Dynamics in Na/Cu(115).

We followed the collective atomic-scale motion of Na atoms on a vicinal Cu(115) surface within a time scale of pico- to nanoseconds using helium spin echo spectroscopy. The well-defined stepped structure of Cu(115) allows us to study the effect that atomic steps have on the adsorption properties, the rate for motion parallel and perpendicular to the step edge, and the interaction between the Na atoms. With the support of a molecular dynamics simulation we show that the Na atoms perform strongly anisotropic 1D hopping motion parallel to the step edges. Furthermore, we observe that the spatial and temporal correlations between the Na atoms that lead to collective motion are also anisotropic, suggesting the steps efficiently screen the lateral interaction between Na atoms residing on different terraces.

Jumping, Rotating, and Flapping: The Atomic-Scale Motion of Thiophene on Cu(111).

Self-assembled monolayers of sulfur-containing heterocycles and linear oligomers containing thiophene groups have been widely employed in organic electronic applications. Here, we investigate the dynamics of isolated thiophene molecules on Cu(111) by combining helium spin-echo (HeSE) spectroscopy with density functional theory calculations. We show that the thiophene/Cu(111) system displays a rich array of aperiodic dynamical phenomena that include jump diffusion between adjacent atop sites over a 59-62 meV barrier and activated rotation around a sulfur-copper anchor, two processes that have been observed previously for related systems. In addition, we present experimental evidence for a new, weakly activated process, the flapping of the molecular ring. Repulsive inter-adsorbate interactions and an exceptionally high friction coefficient of 5 ± 2 ps(-1) are also observed. These experiments demonstrate the versatility of the HeSE technique, and the quantitative information extracted in a detailed analysis provides an ideal benchmark for state-of-the-art theoretical techniques including nonlocal adsorbate-substrate interactions.

Electronic Structure and Bonding of an Ionic Molecular Adsorbate: c-C5H5 on Cu{111}

Self-assembled monolayers containing conjugated π systems find application in organic electronics to functionalize and modify the electronic properties of metals and metal oxides. Isolated cyclopentadienyl is an aromatic molecular anion similar in size to benzene that, unlike benzene, adsorbs quite strongly even on coinage metal surfaces. In this study, the electronic structure, bonding, and minimum energy configuration of cyclopentadienyl (c-C5H5 or Cp) adsorbed on Cu{111} are calculated via first-principles density functional theory (DFT). The Cu{111} surface has been modeled within a (2√3 × 2√3)R30° cell, and the adsorbed Cp has been found to reside preferentially on the hollow sites, with a binding energy of 1.73 eV. Electronic population analysis reveals a net charge transfer of ∼1.1 electrons from the metal to the Cp, indicating that the adsorption is dominated by ionic bonding. The surface diffusion barrier between two adjacent hollow sites was calculated to be 55 meV, in good agreement with previously reported measurements by helium spin echo (HeSE) spectroscopy. It was found that lateral interactions do not significantly influence the binding energy and mobility of the adsorbate. The physical–chemical properties of this strongly bound but weakly mutually interacting molecular adsorbate suggest that Cp could become a model system for ionically adsorbed molecular adsorbates.

Measuring surface phonons with a 3He spin echo spectrometer: a two-dimensional approach

The helium spin echo spectrometer is a powerful apparatus for measuring surfacedynamics and can be used in several different modes of operation. In this paperwe present the first two-dimensional measurements of the wavelength intensitymatrix, offering a new approach for studying surface phonons. The approach thatwe present is completely independent of the incident beam energy distributionand hence can be used to study inelastic scattering with ultra-high resolution.The additional insights obtained by using this new approach and its technicaldifficulties are discussed, and a comparison with other existing methods is given.

Surface dynamics and friction of K/Cu(001) characterized by helium-3 spin-echo and density functional theory

Helium-3 spin-echo measurements of K/Cu(001) are presented, the diffusional surface dynamics of the system at low coverages and on picosecond time scales. Langevin molecular-dynamics simulations are used, together with a potential-energy surface derived from density functional theory calculations, to provide further understanding of the experimental data. An anisotropic potential with a corrugation of 35--64 meV and a friction parameter of $1/4.5\text{ }{\text{ps}}^{\ensuremath{-}1}$ are found to give a good fit to the data for the lower coverages with the adsorbate interactions modeled with a dipole-dipole repulsion. Additionally, at the highest coverage, $\ensuremath{\theta}=0.084$, a component of motion is observed perpendicular to the surface, analogous to that recently found for Na/Cu(001).

Linewidths in bound state resonances for helium scattering from Si(111)–(1 × 1)H

Helium-3 spin-echo measurements of resonant scattering from the Si(111)–(1 × 1)H surface, in the energy range 4–14 meV, are presented. The measurements havehigh energy resolution yet they reveal bound state resonance features withuniformly broad linewidths. We show that exact quantum mechanical calculationsof the elastic scattering, using the existing potential for the helium/Si(111)–(1 × 1)H interaction, cannot reproduce the linewidths seen in the experiment. Furthercalculations rule out inelastic and other mechanisms that might give rise to losses from theelastic scattering channels. We show that corrugation in the attractive part of theatom–surface potential is the most likely origin of the experimental lineshapes.

Molecular dynamics simulations of the diffusion of benzene sub-monolayer films on graphite basal plane surfaces

A classical molecular dynamics study of the diffusive motion of benzene molecules on graphite basal planes has been performed in the sub-monolayer coverage regime. Atomistic calculations were performed using the second generation forcefield COMPASS as well as the general purpose forcefields Dreiding and Universal. The COMPASS based calculations show evidence for a Brownian nature of the diffusion with a very small diffusion activation barrier of 11 ± 2 meV in agreement with recent helium and neutron spin-echo spectroscopy data [Fouquet P, Hedgeland H, Jardine AP, Alexandrowicz G, Allison W, Ellis J. Measurements of molecule diffusion on surfaces using neutron and helium spin echo. Physica B 2006;385–386:269-71]. Reasonable agreement is also found for the general purpose forcefields if screened charges are used in the description of the Coulombic non-bond interaction. The less computationally intensive Dreiding forcefield was shown to give a good qualitative description of the diffusion validating its applicability for future large scale calculation, i.e., for long times or enlarged systems. A potential energy surface (PES) has been established for the translational and rotational diffusive motion. The PES shows a peculiar dependence of the lateral diffusion barriers on the rotation angle of the benzene molecule which leads to a preferential selection of certain rotational states in the MD trajectories.

Studying the microscopic nature of diffusion with helium-3 spin-echo

Helium-3 spin-echo (3HeSE) is a powerful, new experimental technique for studying dynamical phenomena at surfaces with ultra-high energy resolution. Resolution is achieved by using the 3He nuclear spin as an internal timer, to enable measurement of the energy changes of individual atoms as they scatter. The technique yields a measurement of surface correlation in reciprocal space and real time, and probes the nanometre length scales and picosecond to nanosecond timescales that are characteristic of many important atomistic processes. In this article we provide an introductory description of the 3HeSE technique for quasi-elastic scattering measurements and explain how it can be used to obtain unique insights into the motion of adsorbates. We illustrate the technique by reviewing recent measurements, starting with simple hopping and then showing how correlations, arising from adsorbate interactions, can be observed. The final measurements demonstrate how the absence of such correlations, when expected, are used to question the conventional description that attributes the coverage dependence of surface processes entirely to pairwise forces between adsorbates. The emphasis throughout is on the characteristic signatures of adsorbate motion that can be seen in the data, without recourse to a detailed theoretical analysis. Numerical simulations using the Langevin equation are used to illustrate generic behaviour and to provide a quantitative analysis of the experiment.