Wave dispersion properties of compound finite elements

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Mixed finite elements use different approximation spaces for different dependent variables. Certain classes of mixed finite elements, called compatible finite elements, have been shown to exhibit a number of desirable properties for a numerical weather prediction model. In two-dimensions the lowest order element of the Raviart-Thomas based mixed element is the finite element equivalent of the widely used C-grid staggering, which is known to possess good wave dispersion properties, at least for quadrilateral grids. It has recently been proposed that building compound elements from a number of triangular Raviart-Thomas sub-elements, such that both the primal and (implied) dual grid are constructed from the same sub-elements, would allow greater flexibility in the use of different advection schemes along with the ability to build arbitrary polygonal elements. Although the wave dispersion properties of the triangular sub-elements are well understood, those of the compound elements are unknown. It would be useful to know how they compare with the non- compound elements and what properties of the triangular sub-grid elements are inherited? Here a numerical dispersion analysis is presented for the linear shallow water equations in two dimensions discretised using the lowest order compound Raviart-Thomas finite elements on regular quadrilateral and hexagonal grids. It is found that, in comparison with the well known C-grid scheme, the compound elements exhibit a more isotropic dispersion relation, with a small over estimation of the frequency for short waves compared with the relatively large underestimation for the C-grid. On a quadrilateral grid the compound elements are found to differ from the non- compound Raviart-Thomas quadrilateral elements even for uniform elements, exhibiting the influence of the underlying sub-elements. This is shown to lead to small improvements in the accuracy of the dispersion relation: the compound quadrilateral element is slightly better for gravity waves but slightly worse for inertial waves than the standard lowest order Raviart-Thomas element.The work of John Thuburn was funded by the Natural Environment Research Council under the 'Gung Ho' project (grant NE/1021136/1)

Spin dynamics of the bilinear-biquadratic S=1S=1 Heisenberg model on the triangular lattice: a quantum Monte Carlo study

We study thermodynamic properties as well as the dynamical spin and quadrupolar structure factors of the O(3)-symmetric spin-1 Heisenberg model with bilinear-biquadratic exchange interactions on the triangular lattice. Based on a sign-problem-free quantum Monte Carlo approach, we access both the ferromagnetic and the ferroquadrupolar ordered, spin nematic phase as well as the SU(3)-symmetric point which separates these phases. Signatures of Goldstone soft-modes in the dynamical spin and the quadrupolar structure factors are identified, and the properties of the low-energy excitations are compared to the thermodynamic behavior observed at finite temperatures as well as to Schwinger-boson flavor-wave theory.Comment: 7 pages, 8 figure

First-principles calculations of exchange interactions, spin waves, and temperature dependence of magnetization in inverse-Heusler-based spin gapless semiconductors

Employing first principles electronic structure calculations in conjunction with the frozen-magnon method we calculate exchange interactions, spin-wave dispersion, and spin-wave stiffness constants in inverse-Heusler-based spin gapless semiconductor (SGS) compounds Mn$_2$CoAl, Ti$_2$MnAl, Cr$_2$ZnSi, Ti$_2$CoSi and Ti$_2$VAs. We find that their magnetic behavior is similar to the half-metallic ferromagnetic full-Heusler alloys, i.e., the intersublattice exchange interactions play an essential role in the formation of the magnetic ground state and in determining the Curie temperature, $T_\mathrm{c}$. All compounds, except Ti$_2$CoSi possess a ferrimagnetic ground state. Due to the finite energy gap in one spin channel, the exchange interactions decay sharply with the distance, and hence magnetism of these SGSs can be described considering only nearest and next-nearest neighbor exchange interactions. The calculated spin-wave dispersion curves are typical for ferrimagnets and ferromagnets. The spin-wave stiffness constants turn out to be larger than those of the elementary 3$d$-ferromagnets. Calculated exchange parameters are used as input to determine the temperature dependence of the magnetization and $T_\mathrm{c}$ of the SGSs. We find that the $T_\mathrm{c}$ of all compounds is much above the room temperature. The calculated magnetization curve for Mn$_2$CoAl as well as the Curie temperature are in very good agreement with available experimental data. The present study is expected to pave the way for a deeper understanding of the magnetic properties of the inverse-Heusler-based SGSs and enhance the interest in these materials for application in spintronic and magnetoelectronic devices.Comment: Accepted for publ;ication in Physical Review

Superconductivity in heavy fermion compounds

We review the current state of experimental and theoretical investigations of heavy fermion superconductors. We discuss most of the Ce-based compounds like Ce122, Ce115, Ce218 and Ce131 classes and U-based superconductors like UBe_13 and UPd_2Al_3. In the former the emphasis is on the connection to quantum critical phenomena and non-Fermi liquid behaviour. Recent neutron scattering and hydrostatic pressure results on SDW/SC competition in the Ce122 system are included. For the U-compounds we discuss the significance of dual models with both localised and itinerant 5f electrons for mass enhancement and superconducting pair formation. Itinerant spin fluctuation theories for unconventional superconductivity are also reviewed.Comment: 74 pages, 29 figures. For a version of the manuscript including higher-resolution figures, see http://www.cpfs.mpg.de/~thalm/SCMaterials.pd

Monolayer honeycomb structures of group IV elements and III-V binary compounds

Using first-principles plane wave calculations, we investigate two dimensional honeycomb structure of Group IV elements and their binary compounds, as well as the compounds of Group III-V elements. Based on structure optimization and phonon mode calculations, we determine that 22 different honeycomb materials are stable and correspond to local minima on the Born-Oppenheimer surface. We also find that all the binary compounds containing one of the first row elements, B, C or N have planar stable structures. On the other hand, in the honeycomb structures of Si, Ge and other binary compounds the alternating atoms of hexagons are buckled, since the stability is maintained by puckering. For those honeycomb materials which were found stable, we calculated optimized structures, cohesive energies, phonon modes, electronic band structures, effective cation and anion charges, and some elastic constants. The band gaps calculated within Density Functional Theory using Local Density Approximation are corrected by GW0 method. Si and Ge in honeycomb structure are semimetal and have linear band crossing at the Fermi level which attributes massless Fermion character to charge carriers as in graphene. However, all binary compounds are found to be semiconductor with band gaps depending on the constituent atoms. We present a method to reveal elastic constants of 2D honeycomb structures from the strain energy and calculate the Poisson's ratio as well as in-plane stiffness values. Preliminary results show that the nearly lattice matched heterostructures of ...Comment: 12 Pages, 7 Figures, 1 Table; http://link.aps.org/doi/10.1103/PhysRevB.80.15545

Field dependent mass enhancement in Pr_{1-x}La_xOs_4Sb_12 from aspherical Coulomb scattering

The scattering of conduction electrons by crystalline electric field (CEF) excitations may enhance their effective quasiparticle mass similar to scattering from phonons. A wellknown example is Pr metal where the isotropic exchange scattering from inelastic singlet-singlet excitations causes the mass enhancement. An analogous mechanism may be at work in the skutterudite compounds Pr_{1-x}La_xOs_4Sb_12 where close to x=1 the compound develops heavy quasiparticles with a large linear specific heat coefficient. There the low lying CEF states are singlet ground state and a triplet at 8 K. Due to the tetrahedral CEF the main scattering mechanism must be the aspherical Coulomb scattering. We derive the expression for mass enhancement in this model including also the case of dispersive excitations. We show that for small to moderate dispersion there is a strongly field dependent mass enhancement due to the field induced triplet splitting. It is suggested that this effect may be seen in Pr_{1-x}La_xOs_4Sb_12 with suitably large x when the dispersion is small.Comment: 12 pages, 5 figure

Surprises on the Way from 1D to 2D Quantum Magnets: the Novel Ladder Materials

One way of making the transition between the quasi-long range order in a chain of S=1/2 spins coupled antiferromagnetically and the true long range order that occurs in a plane, is by assembling chains to make ladders of increasing width. Surprisingly this crossover between one and two dimensions is not at all smooth. Ladders with an even number of legs have purely short range magnetic order and a finite energy gap to all magnetic excitations. Predictions of this novel groundstate have now been verified experimentally. Holes doped into these ladders are predicted to pair, and possibly superconduct.Comment: Review Article, Science, TeX file, 18 pages, 6 figures available upon reques