Lanthanide contraction and magnetism in the heavy rare earth elements

The heavy rare earth elements crystallize into hexagonally close packed (h.c.p.) structures and share a common outer electronic configuration, differing only in the number of 4f electrons they have. These chemically inert 4f electrons set up localized magnetic moments, which are coupled via an indirect exchange interaction involving the conduction electrons. This leads to the formation of a wide variety of magnetic structures, the periodicities of which are often incommensurate with the underlying crystal lattice. Such incommensurate ordering is associated with a 'webbed' topology of the momentum space surface separating the occupied and unoccupied electron states (the Fermi surface). The shape of this surface-and hence the magnetic structure-for the heavy rare earth elements is known to depend on the ratio of the interplanar spacing c and the interatomic, intraplanar spacing a of the h.c.p. lattice. A theoretical understanding of this problem is, however, far from complete. Here, using gadolinium as a prototype for all the heavy rare earth elements, we generate a unified magnetic phase diagram, which unequivocally links the magnetic structures of the heavy rare earths to their lattice parameters. In addition to verifying the importance of the c/a ratio, we find that the atomic unit cell volume plays a separate, distinct role in determining the magnetic properties: we show that the trend from ferromagnetism to incommensurate ordering as atomic number increases is connected to the concomitant decrease in unit cell volume. This volume decrease occurs because of the so-called lanthanide contraction, where the addition of electrons to the poorly shielding 4f orbitals leads to an increase in effective nuclear charge and, correspondingly, a decrease in ionic radii.     

A second generation human haplotype map of over 3.1 million SNPs

We describe the Phase II HapMap, which characterizes over 3.1 million human single nucleotide polymorphisms (SNPs) genotyped in 270 individuals from four geographically diverse populations and includes 25-35% of common SNP variation in the populations surveyed. The map is estimated to capture untyped common variation with an average maximum r2 of between 0.9 and 0.96 depending on population. We demonstrate that the current generation of commercial genome-wide genotyping products captures common Phase II SNPs with an average maximum r2 of up to 0.8 in African and up to 0.95 in non-African populations, and that potential gains in power in association studies can be obtained through imputation. These data also reveal novel aspects of the structure of linkage disequilibrium. We show that 10-30% of pairs of individuals within a population share at least one region of extended genetic identity arising from recent ancestry and that up to 1% of all common variants are untaggable, primarily because they lie within recombination hotspots. We show that recombination rates vary systematically around genes and between genes of different function. Finally, we demonstrate increased differentiation at non-synonymous, compared to synonymous, SNPs, resulting from systematic differences in the strength or efficacy of natural selection between populations.     

Evolution and diversity of subduction zones controlled by slab width

Subducting slabs provide the main driving force for plate motion and flow in the Earth's mantle, and geodynamic, seismic and geochemical studies offer insight into slab dynamics and subduction-induced flow. Most previous geodynamic studies treat subduction zones as either infinite in trench-parallel extent (that is, two-dimensional) or finite in width but fixed in space. Subduction zones and their associated slabs are, however, limited in lateral extent (250-7,400 km) and their three-dimensional geometry evolves over time. Here we show that slab width controls two first-order features of plate tectonics-the curvature of subduction zones and their tendency to retreat backwards with time. Using three-dimensional numerical simulations of free subduction, we show that trench migration rate is inversely related to slab width and depends on proximity to a lateral slab edge. These results are consistent with retreat velocities observed globally, with maximum velocities (6-16 cm yr(-1)) only observed close to slab edges (<1,200 km), whereas far from edges (>2,000 km) retreat velocities are always slow (<2.0 cm yr(-1)). Models with narrow slabs (< or =1,500 km) retreat fast and develop a curved geometry, concave towards the mantle wedge side. Models with slabs intermediate in width ( approximately 2,000-3,000 km) are sublinear and retreat more slowly. Models with wide slabs (> or =4,000 km) are nearly stationary in the centre and develop a convex geometry, whereas trench retreat increases towards concave-shaped edges. Additionally, we identify periods (5-10 Myr) of slow trench advance at the centre of wide slabs. Such wide-slab behaviour may explain mountain building in the central Andes, as being a consequence of its tectonic setting, far from slab edges.     

Adaptive subwavelength control of nano-optical fields

Adaptive shaping of the phase and amplitude of femtosecond laser pulses has been developed into an efficient tool for the directed manipulation of interference phenomena, thus providing coherent control over various quantum-mechanical systems. Temporal resolution in the femtosecond or even attosecond range has been demonstrated, but spatial resolution is limited by diffraction to approximately half the wavelength of the light field (that is, several hundred nanometres). Theory has indicated that the spatial limitation to coherent control can be overcome with the illumination of nanostructures: the spatial near-field distribution was shown to depend on the linear chirp of an irradiating laser pulse. An extension of this idea to adaptive control, combining multiparameter pulse shaping with a learning algorithm, demonstrated the generation of user-specified optical near-field distributions in an optimal and flexible fashion. Shaping of the polarization of the laser pulse provides a particularly efficient and versatile nano-optical manipulation method. Here we demonstrate the feasibility of this concept experimentally, by tailoring the optical near field in the vicinity of silver nanostructures through adaptive polarization shaping of femtosecond laser pulses and then probing the lateral field distribution by two-photon photoemission electron microscopy. In this combination of adaptive control and nano-optics, we achieve subwavelength dynamic localization of electromagnetic intensity on the nanometre scale and thus overcome the spatial restrictions of conventional optics. This experimental realization of theoretical suggestions opens a number of perspectives in coherent control, nano-optics, nonlinear spectroscopy, and other research fields in which optical investigations are carried out with spatial or temporal resolution.