Artificial square ice and related dipolar nanoarrays

We study a frustrated dipolar array recently manufactured lithographically by Wang in order to realize the square ice model in an artificial structure. We discuss models for thermodynamics and dynamics of this system. We show that an ice regime can be stabilized by small changes in the array geometry; a different magnetic state, kagome ice, can similarly be constructed. At low temperatures, the square ice regime is terminated by a thermodynamic ordering transition, which can be chosen to be ferro- or antiferromagnetic. We show that the arrays do not fully equilibrate experimentally, and identify a likely dynamical bottleneck.     

Superinelastic electron transfer: electron trapping in H2O ice via the N-2((2)Pi(g)) resonance

We present measurements on the trapping of 0-3 eV electrons in H2O ice films covered with a submonolayer of N2 molecules. At the energy of the N-2((2)Pi(g)) shape resonance, the absolute cross section for electron trapping in ice is approximately 5.5 x 10(-16) cm(2), similar to that for vibrational excitations of gaseous N2 via the resonance. This result, indicating that nearly all electrons from autoionization of N-2((2)Pi(g)) are transferred to electron traps in ice, is explained by superinelastic electron transfer from N-2((2)Pi(g)) into preexisting traps in polar ice, leaving N2 in high vibrational excited states.     

A simulation study on the magnetic ordering in an artificial geometrically frustrated lattice

A Monte Carlo simulation on the magnetic ordering of the artificial geometrically frustrated square lattice shows that the system exhibits the spin ice state and the disorder state for strong and weak dipolar interactions. We demonstrate that the long-range dipolar interactions are significant for the short-range spin ice state.     

Orientational defects in ice Ih: an interpretation of electrical conductivity measurements

We present a first-principles study of the structure and energetics of Bjerrum defects in ice Ih and compare the results to experimental electrical conductivity data. While the DFT result for the activation energy is in good agreement with experiment, we find that its two components have quite different values. Aside from providing new insight into the fundamental parameters of the microscopic electrical theory of ice, our results suggest the activity of traps in doped ice in the temperature regime typically assumed to be controlled by the free migration of L defects.     

Optical forces arising from phase gradients

We demonstrate both theoretically and experimentally that phase gradients in a light field can be used to create a new category of optical traps complementary to the more familiar intensity-gradient traps known as optical tweezers. We further show that the work done by phase-gradient forces is path dependent and briefly discuss some ramifications of this nonconservativity.     

Direct evidence for a dynamical ground state in the highly frustrated Tb(2)Sn(2)O(7) pyrochlore

mSR experiments have been performed on a powder sample of the "ordered spin ice" Tb(2)Sn(2)O(7) pyrochlore. At base temperature (T=35 mK), the muon relaxation is found to be of dynamical nature, which demonstrates that strong fluctuations persist below the ferromagnetic transition (T(C)=0.87 K). Hints of long-range ordering appear as oscillations of the muon polarization when an external field is applied and also as a hysteretic behavior below T(C). We propose that dynamics results from fluctuations of clusters of correlated spins with the ordered spin ice structure.     

Operator ordering, ellipticity and spurious solutions in k · p calculations of III-nitride nanostructures

We analyze the ellipticity of the standard k · p wurtzite model for the symmetrized and the Burt–Foreman operator ordering. We find that for certain situations the symmetrized Hamiltonian is unstable, leads to unplausible results and can cause spurious solutions. We show that the operator ordering in wurtzite must be completely asymmetric to be stable. The asymmetric operator ordering is elliptic and consequently no spurious solutions are obtained. Therefore we recommend the use of a complete asymmetric operator ordering for nitride device simulation.     

Is Pauling’s Hypothesis Violated in the Hexagonal Modification of Ice?

The effect of long-range dipole interaction on the fulfilment of Pauling’s hypothesis concerning the degeneracy of proton configurations satisfying the ice rules is studied for the case of hexagonal ice. It is shown that the ice rules imply a significant reduction of the contributions to the ground state energy from the next-nearest neighbors. The ground state energy of proton subsystem as a function of quasimomentum ceases to change if more than a hundred primitive unit cells in each direction are taken into account. The final amplitude of the energy changes are about 70 K. The analysis reveals the proton ordering in hexagonal ice with the simple unit cell of the oxygen sublattice is impossible. However, that does not exclude proton ordering with a more complex cell caused by distortion of the hexagonal oxygen lattice.     

Magnetic relaxation in rare-earth oxide pyrochlores

A theory of magnetic relaxation is developed for geometrically frustrated three-dimensional magnets that can be described by an antiferromagnetic Ising model. These magnetic materials are exemplified by some of the recently synthesized rare-earth oxide pyrochlores, such as Dy₂Ti₂O₇, Ho₂Ti₂O₇, or Yb₂Ti₂O₇. A model based on an analogy between the spin ordering in Ising magnets and proton ordering in ice is proposed. In this model, magnetic point defects treated as noninteracting quasiparticles characterized by well-defined energies, mobilities, and effective magnetic charges play a fundamental role analogous to that of ion defects in the physics of ice or by electrons and holes in semiconductors. The proposed model is used to derive expressions for magnetic susceptibility as a function of frequency and temperature.     

Optical vortex beam shaping by use of highly efficient irregular spiral phase plates for optical micromanipulation

Optical dark traps such as Laguerre-Gaussian beams, modulated optical vortices, and high-order Bessel beams have been used in the micromanipulation of microparticles. Such optical traps are highly versatile, as they are able to trap both high- and low-index microparticles as well as to set them into rotation by use of the orbital angular momentum of light. Holography has been widely used to modulate the shape of an optical vortex for new optical traps. We show that, by designing the shape of a spiral phase plate and using electron-beam lithography for fabrication, one can modulate the amplitude and the phase of an optical vortex with respect to the specific shape of the spiral phase plate as required. Furthermore, to the best of our knowledge this is the first report of transferring orbital angular momentum from a spiral phase plate to an absorptive microparticle in an experiment. Hence, with this technique, optical dark traps can easily be designed and fabricated.     

Analysis of a fully packed loop model arising in a magnetic Coulomb phase

The Coulomb phase of spin ice, and indeed the I(c) phase of water ice, naturally realize a fully packed two-color loop model in 3D. We present a detailed analysis of the statistics of these loops: we find loops spanning the system multiple times hosting a finite fraction of all sites while the average loop length remains finite. We contrast the behavior with an analogous 2D model. We connect this body of results to properties of polymers, percolation and insights from Schramm-Loewner evolution processes. We also study another extended degree of freedom, called worms, which appear as "Dirac strings" in spin ice. We discuss implications of these results for the efficiency of numerical cluster algorithms, and address implications for the ordering properties of a broader class of magnetic systems, e.g., with Heisenberg spins, such as CsNiCrF(6) or ZnCr(2)O(4).     

Proper Effect Algebras Admitting No States

We show that there is even a finite proper effect algebra admitting no states. Further, every lattice effect algebra with an ordering set of valuations is an MV effect algebra (consequently it can be organized into an MV algebra). An example of a regular effect algebra admitting no ordering set of states is given. We prove that an Archimedean atomic lattice effect algebra is an MV effect algebra iff it admits an ordering set of valuations. Finally we show that every nonmodular complete effect algebra with trivial center admits no order-continuous valuations.     

Microfabricated ion traps

Ion traps offer the opportunity to study fundamental quantum systems with a high level of accuracy highly decoupled from the environment. Individual atomic ions can be controlled and manipulated with electric fields, cooled to the ground state of motion with laser cooling and coherently manipulated using optical and microwave radiation. Microfabricated ion traps hold the advantage of allowing for smaller trap dimensions and better scalability towards large ion trap arrays also making them a vital ingredient for next generation quantum technologies. Here we provide an introduction into the principles and operation of microfabricated ion traps. We show an overview of material and electrical considerations which are vital for the design of such trap structures. We provide guidance on how to choose the appropriate fabrication design, consider different methods for the fabrication of microfabricated ion traps and discuss previously realised structures. We also discuss the phenomenon of anomalous heating of ions within ion traps, which becomes an important factor in the miniaturisation of ion traps.     

Probing the electron delocalization in liquid water and ice at attosecond time scales

We determine electron delocalization rates in liquid water and ice using core-hole decay spectroscopy. The hydrogen-bonded network delocalizes the electrons in less than 500 as. Broken or weak hydrogen bonds--in the liquid or at the surface of ice--provide states where the electron remains localized longer than 20 fs. These asymmetrically bonded water species provide electron traps, acting as a strong precursor channel to the hydrated electron.     

Potential-based reduced Newton algorithm for nonlinear multiphase flow in porous media

We present a phase-based potential ordering that is an extension of the Cascade ordering introduced by Appleyard and Cheshire [John R. Appleyard, Ian M. Cheshire, The cascade method for accelerated convergence in implicit simulators, in: European Petroleum Conference, 1982, pp. 113–122]. The proposed ordering is valid for both two-phase and three-phase flow, and it can handle countercurrent flow due to gravity and/or capillarity. We show how this ordering can be used to reduce the nonlinear algebraic system that arises from the fully-implicit method (FIM) into one with only pressure dependence. The potential-based reduced Newton algorithm is then obtained by applying Newton’s method to this reduced-order system. Numerical evidence shows that our potential-based reduced Newton solver is able to converge for time steps that are much larger than what the standard Newton’s method can handle. In addition, whenever standard Newton converges, so does the reduced Newton algorithm, and the number of global nonlinear iterations required for convergence is significantly reduced compared with the standard Newton’s method.     

An Extension of Gleason's Theorem for Quantum Computation

We develop a synthesis of Turing's paradigm of computation and von Neumann's quantum logic to serve as a model for quantum computation with recursion, such that potentially non-terminating computation can take place, as in a quantum Turing machine. This model is based on the extension of von Neumann's quantum logic to partial states, defined here as sub-probability measures on the Hilbert space, equipped with the natural point-wise partial ordering. The sub-probability measures allow a certain probability for the non-termination of the computation. We then derive an extension of Gleason's theorem and show that, for Hilbert spaces of dimension greater than two, the partial order of sub-probability measures is order isomorphic with the collection of partial density operators, i.e. trace class positive operators with trace between zero and one, equipped with the usual partial ordering induced from positive operators. We show that the expected value of a bounded observable with respect to a partial state can be defined as a closed bounded interval, which extends the classical definition of expected value.     

Tuning the metal-insulator transition in manganite films through surface exchange coupling with magnetic nanodots

In strongly correlated electronic systems, the global transport behavior depends sensitively on spin ordering. We show that spin ordering in manganites can be controlled by depositing isolated ferromagnetic nanodots at the surface. The exchange field at the interface is tunable with nanodot density and makes it possible to overcome dimensionality and strain effects in frustrated systems to greatly increasing the metal-insulator transition and magnetoresistance. These findings indicate that electronic phase separation can be controlled by the presence of magnetic nanodots.     

Magnetic dipolar ordering on geometrically frustrated brick-shaped lattices

The magnetic ordering of frustrated arrays of nanoscale islands can be strongly influenced by the array patterns. We theoretically present three kinds of artificial geometrically frustrated systems with different brick-shaped geometries, defined as brick-shaped lattices, and investigate their magnetic dipolar ordering at the ground state using the Monte Carlo method. The simulated results show that the magnetic ordering of three brick-shaped frustrated lattices depends strongly on the strength of dipolar interactions, depending on the lattice spacing. It is found that the long-range dipolar interactions tend to suppress the long-range ordered state and induce the short-range quasi-ice state at each vertex of the lattices. In addition, the correlations for neighboring spin pairs are closely related to not only the dipolar coupling strength but also the geometry of the lattices.     

Proton ordering in ice at an ice-metal interface

The structure of the proton sublattice of ice at an ice-metal interface is analyzed by solving the Ginzburg-Landau equation for an order parameter describing the proton ordering under an appropriate boundary condition [1, 2]. When the interaction between protons and the substrate is weak, the ice rules that govern proton order are weaker at the interface as compared to bulk ice, but to a lesser extent than at the free ice surface. In the case of strong proton-substrate interaction (clean interface and/or high conductivity of the substrate), the ice rules are stronger at the interface as compared to bulk ice, which corresponds to a more ordered proton sublattice. The latter case corresponds to a lower concentration of defects in the proton sublattice, which determine important properties of ice, such as adhesion, electrical conductivity, plasticity, and electric field distribution near the interface. A qualitative correlation is described between electrical properties of the substrate and mechanical properties of the interface, including adhesion and friction.