Penrose Matching Rules from Realistic Potentials in a Model System

We exhibit a toy model of a binary decagonal Al-Co quasicrystal -- closely related to actual structures -- in which realistic pair potentials yield a ground state which appears to perfectly implement Penrose's matching rules, for Hexagon-Boat-Star (HBS) tiles of edge 2.45 A. The second minimum of the potentials is crucial for this result.Comment: 7 pp, 2 figures; proc. "Quasicrystals: Silver Jubilee" (Tel Aviv, 2007), Phil. Mag. in pres

Novel Properties of Frustrated Low Dimensional Magnets with Pentagonal Symmetry

In the context of magnetism, frustration arises when a group of spins cannot find a configuration that minimizes all of their pairwise interactions simultaneously. We consider the effects of the geometric frustration that arises in a structure having pentagonal loops. Such five-fold loops can be expected to occur naturally in quasicrystals, as seen for example in a number of experimental studies of surfaces of icosahedral alloys. Our model considers classical vector spins placed on vertices of a subtiling of the two dimensional Penrose tiling, and interacting with nearest neighbors via antiferromagnetic bonds. We give a set of recursion relations for this system, which consists of an infinite set of embedded clusters with sizes that increase as a power of the golden mean. The magnetic ground states of this fractal system are studied analytically, and by Monte Carlo simulation.Comment: 7 pages, 7 figures, contribution to ICQ11 (Sapporo, Japan 2010) conference proceeding

The "Coulomb phase" in frustrated systems

The "Coulomb phase" is an emergent state for lattice models (particularly highly frustrated antiferromagnets) which have local constraints that can be mapped to a divergence-free "flux". The coarse-grained version of this flux or polarization behave analogously to electric or magnetic fields; in particular, defects at which the local constraint is violated behave as effective charges with Coulomb interactions. I survey the derivation of the characteristic power-law correlation functions and the pinch-points in reciprocal space plots of diffuse scattering, as well as applications to magnetic relaxation, quantum-mechanical generalizations, phase transitions to long-range-ordered states, and the effects of disorder.Comment: 30 pp, 5 figures (Sub. to Annual Reviews of Condensed Matter Physics

Order by disorder and spiral spin liquid in frustrated diamond lattice antiferromagnets

Frustration refers to competition between different interactions that cannot be simultaneously satisfied, a familiar feature in many magnetic solids. Strong frustration results in highly degenerate ground states, and a large suppression of ordering by fluctuations. Key challenges in frustrated magnetism are characterizing the fluctuating spin-liquid regime and determining the mechanism of eventual order at lower temperature. Here, we study a model of a diamond lattice antiferromagnet appropriate for numerous spinel materials. With sufficiently strong frustration a massive ground state degeneracy develops amongst spirals whose propagation wavevectors reside on a continuous two-dimensional ``spiral surface'' in momentum space. We argue that an important ordering mechanism is entropic splitting of the degenerate ground states, an elusive phenomena called order-by-disorder. A broad ``spiral spin-liquid'' regime emerges at higher temperatures, where the underlying spiral surface can be directly revealed via spin correlations. We discuss the agreement between these predictions and the well characterized spinel MnSc2S4

Clusters, phason elasticity, and entropic stabilisation: a theory perspective

Personal comments are made about the title subjects, including: the relation of Friedel oscillations to Hume-Rothery stabilisation; how calculations may resolve the random-tiling versus ideal pictures of quasicrystals; and the role of entropies apart from tile-configurational.Comment: IOP macros; 8pp, 1 figure. In press, Phil. Mag. A (Proc. Intl. Conf. on Quasicrystals 9, Ames Iowa, May 2005

Fracture of complex metallic alloys: An atomistic study of model systems

Molecular dynamics simulations of crack propagation are performed for two extreme cases of complex metallic alloys (CMAs): In a model quasicrystal the structure is determined by clusters of atoms, whereas the model C15 Laves phase is a simple periodic stacking of a unit cell. The simulations reveal that the basic building units of the structures also govern their fracture behaviour. Atoms in the Laves phase play a comparable role to the clusters in the quasicrystal. Although the latter are not rigid units, they have to be regarded as significant physical entities.Comment: 6 pages, 4 figures, for associated avi file, see http://www.itap.physik.uni-stuttgart.de/~frohmut/MOVIES/C15.LJ.011.100.av

The importance of the weak: Interaction modifiers in artificial spin ices

The modification of geometry and interactions in two-dimensional magnetic nanosystems has enabled a range of studies addressing the magnetic order, collective low-energy dynamics, and emergent magnetic properties, in e.g. artificial spin ice structures. The common denominator of all these investigations is the use of Ising-like mesospins as building blocks, in the form of elongated magnetic islands. Here we introduce a new approach: single interaction modifiers, using slave-mesospins in the form of discs, within which the mesospin is free to rotate in the disc plane. We show that by placing these on the vertices of square artificial spin ice arrays and varying their diameter, it is possible to tailor the strength and the ratio of the interaction energies. We demonstrate the existence of degenerate ice-rule obeying states in square artificial spin ice structures, enabling the exploration of thermal dynamics in a spin liquid manifold. Furthermore, we even observe the emergence of flux lattices on larger length-scales, when the energy landscape of the vertices is reversed. The work highlights the potential of a design strategy for two-dimensional magnetic nano-architectures, through which mixed dimensionality of mesospins can be used to promote thermally emergent mesoscale magnetic states.Comment: 17 pages, including methods, 4 figures. Supplementary information contains 16 pages and 15 figure

Extensive degeneracy, Coulomb phase and magnetic monopoles in an artificial realization of the square ice model

Artificial spin ice systems have been introduced as a possible mean to investigate frustration effects in a well-controlled manner by fabricating lithographically-patterned two-dimensional arrangements of interacting magnetic nanostructures. This approach offers the opportunity to visualize unconventional states of matter, directly in real space, and triggered a wealth of studies at the frontier between nanomagnetism, statistical thermodynamics and condensed matter physics. Despite the strong efforts made these last ten years to provide an artificial realization of the celebrated square ice model, no simple geometry based on arrays of nanomagnets succeeded to capture the macroscopically degenerate ground state manifold of the corresponding model. Instead, in all works reported so far, square lattices of nanomagnets are characterized by a magnetically ordered ground state consisting of local flux-closure configurations with alternating chirality. Here, we show experimentally and theoretically, that all the characteristics of the square ice model can be observed if the artificial square lattice is properly designed. The spin configurations we image after demagnetizing our arrays reveal unambiguous signatures of an algebraic spin liquid state characterized by the presence of pinch points in the associated magnetic structure factor. Local excitations, i.e. classical analogues of magnetic monopoles, are found to be free to evolve in a massively degenerated, divergence-free vacuum. We thus provide the first lab-on-chip platform allowing the investigation of collective phenomena, including Coulomb phases and ice-like physics.Comment: 26 pages, 10 figure

Topology by Design in Magnetic nano-Materials: Artificial Spin Ice

Artificial Spin Ices are two dimensional arrays of magnetic, interacting nano-structures whose geometry can be chosen at will, and whose elementary degrees of freedom can be characterized directly. They were introduced at first to study frustration in a controllable setting, to mimic the behavior of spin ice rare earth pyrochlores, but at more useful temperature and field ranges and with direct characterization, and to provide practical implementation to celebrated, exactly solvable models of statistical mechanics previously devised to gain an understanding of degenerate ensembles with residual entropy. With the evolution of nano--fabrication and of experimental protocols it is now possible to characterize the material in real-time, real-space, and to realize virtually any geometry, for direct control over the collective dynamics. This has recently opened a path toward the deliberate design of novel, exotic states, not found in natural materials, and often characterized by topological properties. Without any pretense of exhaustiveness, we will provide an introduction to the material, the early works, and then, by reporting on more recent results, we will proceed to describe the new direction, which includes the design of desired topological states and their implications to kinetics.Comment: 29 pages, 13 figures, 116 references, Book Chapte

Collapse of a giant iceberg in a dynamic Southern Ocean marine ecosystem: In situ observations of A-68A at South Georgia

Large icebergs (>20 km long) are responsible for most of the freshwater discharged into the Southern Ocean. We report on in situ and satellite observations made during the break-up phase around South Georgia of the giant tabular iceberg A-68A. The in situ measurements were obtained during a 4-day visit by a research vessel in February 2021, where physical, chemical and biological measurements were made at a range of distances away from the main and subsidiary icebergs. These results were compared to a far-field station 133 km away. Up�stream of the iceberg field, water column structure was similar to ambient water although there was evidence of iceberg-associated phytoplankton as a likely remnant of the passage of the icebergs. Nevertheless, enhancement of primary productivity along the path of the icebergs was not resolved in either in situ or monthly mean satellite observations. There was a considerable brash-ice field moving ahead of the icebergs which limited the number of downstream sampling stations. One downstream station within 2 km of iceberg A-68P showed several ice-melt influenced features that distinguished it from most other stations. Firstly, there was a strong stratified meltwater influenced layer that reached to around 120 m. This had the effect of deepening underlying water masses, with the core of the temperature minimum layer around 50 m deeper than elsewhere. Secondly, there was evidence of rapid downward displacement of both particulate material and certain phytoplankton taxa that may be a further result of this water mass deepening. Thirdly, macronutrient profiles were altered, with concentrations of nitrate, silicic acid and phosphate characteristic of deeper layers being found closer to the surface and a dilution of the ambient nutrient pool just above the iceberg draft that we ascribe to meltwater released from basal melting. Meanwhile, nutrient recycling processes associated with organic matter remineralisation were also modified by the physical restructuring of the water column and biotic components. Finally, the ice-associated phytoplankton taxa Pseudo-nitszchia/Nitszchia, found in both upstream and downstream locations, were abundant at this < 2 km-distant station through melting out from the iceberg and subsequent rapid growth. Overall, we resolved alterations to water column structure, nutrient profiles and phytoplankton community composition at fine to medium scales around the iceberg field. Nevertheless, although there may have been longer term and larger scale impacts, the dynamic oceanographic environment, including the presence of a strong oceanographic front and shelf-edge processes, dominated during the collapse of A-68A