On the use of new methods and multimedia

In the STEPS project the working group WG2 studied “New teaching and learning methods” and “The use of new multimedia”. Both were surveyed in Bachelor and Master studies of all STEPS members An inventory among universities and alumni on tools, software, programming languages and the importance of transferable skills was made. A list of categorized methods, tools and transferable skills resulted. The WG2 evaluated MultiMedia (MM) with the MPTL group. In 2009 the project STEPS TWO started. The WG2 focuses on project-based and student centred learning, also trying out some best practice materials with students and teachers. We address some problems found in categorizing and evaluating methods and materials We describe some didactical aspects and conditions for an effective integration of MM

Spin and orbital excitation spectrum in the Kugel-Khomskii model

We discuss spin and orbital ordering in the twofold orbital degenerate superexchange model in three dimensions relevant to perovskite transition metal oxides. We focus on the particular point on the classical phase diagram where orbital degeneracy is lifted by quantum effects exclusively. Dispersion and damping of the spin and orbital excitations are calculated at this point taking into account their mutual interaction. Interaction corrections to the mean-field order parameters are found to be small. We conclude that quasi-one-dimensional Neel spin order accompanied by the uniform d_{3z^2-r^2}-type orbital ordering is stable against quantum fluctuations.Comment: 4 pages with 3 PS figures, 1 table, RevTeX, accepted to Phys. Rev. B. Rapid Communicatio

Spin-wave softening and Hund's coupling in ferromagnetic manganites

Using one-orbital model of hole-doped manganites, we show with the help of Holstein-Primakov transformation that finite Hund's coupling is responsible for the spin-wave softening in the ferromagnetic $B$-phase manganites. We obtain an analytical result for the spin-wave spectrum for \JH\gg t. In the limit of infinte Hund's coupling, the spectrum is the conventional nearest-neighbor Heisenberg ferromagnetic spin-wave. The o(t/\JH)-order correction is negative and thus accounts for the softening near the zone boundary.Comment: 5 pages, 3 figure

Non-perturbative corrections to mean-field behavior: spherical model on spider-web graph

We consider the spherical model on a spider-web graph. This graph is effectively infinite-dimensional, similar to the Bethe lattice, but has loops. We show that these lead to non-trivial corrections to the simple mean-field behavior. We first determine all normal modes of the coupled springs problem on this graph, using its large symmetry group. In the thermodynamic limit, the spectrum is a set of $\delta$-functions, and all the modes are localized. The fractional number of modes with frequency less than $\omega$ varies as $\exp (-C/\omega)$ for $\omega$ tending to zero, where $C$ is a constant. For an unbiased random walk on the vertices of this graph, this implies that the probability of return to the origin at time $t$ varies as $\exp(- C' t^{1/3})$, for large $t$, where $C'$ is a constant. For the spherical model, we show that while the critical exponents take the values expected from the mean-field theory, the free-energy per site at temperature $T$, near and above the critical temperature $T_c$, also has an essential singularity of the type $\exp[ -K {(T - T_c)}^{-1/2}]$.Comment: substantially revised, a section adde

Spin-Orbital Entanglement and Violation of the Goodenough-Kanamori Rules

We point out that large composite spin-orbital fluctuations in Mott insulators with $t_{2g}$ orbital degeneracy are a manifestation of quantum entanglement of spin and orbital variables. This results in a dynamical nature of the spin superexchange interactions, which fluctuate over positive and negative values, and leads to an apparent violation of the Goodenough-Kanamori rules. [{\it Published in Phys. Rev. Lett. {\bf 96}, 147205 (2006).}]Comment: 4 pages, 2 figure

Single-electron tunneling in InP nanowires

We report on the fabrication and electrical characterization of field-effect devices based on wire-shaped InP crystals grown from Au catalyst particles by a vapor-liquid-solid process. Our InP wires are n-type doped with diameters in the 40-55 nm range and lengths of several microns. After being deposited on an oxidized Si substrate, wires are contacted individually via e-beam fabricated Ti/Al electrodes. We obtain contact resistances as low as ~10 kOhm, with minor temperature dependence. The distance between the electrodes varies between 0.2 and 2 micron. The electron density in the wires is changed with a back gate. Low-temperature transport measurements show Coulomb-blockade behavior with single-electron charging energies of ~1 meV. We also demonstrate energy quantization resulting from the confinement in the wire.Comment: 4 pages, 3 figure

Orbital liquid in ferromagnetic manganites: The orbital Hubbard model for ege_g electrons

We have analyzed the symmetry properties and the ground state of an orbital Hubbard model with two orbital flavors, describing a partly filled spin-polarized $e_g$ band on a cubic lattice, as in ferromagnetic manganites. We demonstrate that the off-diagonal hopping responsible for transitions between $x^2-y^2$ and $3z^2-r^2$ orbitals, and the absence of SU(2) invariance in orbital space, have important implications. One finds that superexchange contributes in all orbital ordered states, the Nagaoka theorem does not apply, and the kinetic energy is much enhanced as compared with the spin case. Therefore, orbital ordered states are harder to stabilize in the Hartree-Fock approximation (HFA), and the onset of a uniform ferro-orbital polarization and antiferro-orbital instability are similar to each other, unlike in spin case. Next we formulate a cubic (gauge) invariant slave boson approach using the orbitals with complex coefficients. In the mean-field approximation it leads to the renormalization of the kinetic energy, and provides a reliable estimate for the ground state energy of the disordered state. Using this approach one finds that the HFA fails qualitatively in the regime of large Coulomb repulsion $U\to\infty$ -- the orbital order is unstable, and instead a strongly correlated orbital liquid with disordered orbitals is realized at any electron filling.Comment: 25 pages, 9 figure

Influences of multilocus heterozygosity on size during early life

Genetic diversity has been hypothesized to promote fitness of individuals and populations, but few studies have examined how genetic diversity varies with ontogeny. We examined patterns in population and individual genetic diversity and the effect of genetic diversity on individual fitness among life stages (adults and juveniles) and populations of captive yellow perch (Perca flavescens) stocked into two ponds and allowed to spawn naturally. Significant genetic structure developed between adults and offspring in a single generation, even as heterozygosity and allelic richness remained relatively constant. Heterozygosity had no effect on adult growth or survival, but was significantly and consistently positively related to offspring length throughout the first year of life in one pond but not the other. The largest individuals in the pond exhibiting this positive relationship were more outbred than averaged size individuals and also more closely related to one another than they were to average‐sized individuals, suggesting potential heritability of body size or spawn timing effects. These results indicate that the influence of heterozygosity may be mediated through an interaction, likely viability selection, between ontogeny and environment that is most important during early life. In addition, populations may experience significant genetic change within a single generation in captive environments, even when allowed to reproduce naturally. Accounting for the dynamic influences of genetic diversity on early life fitness could lead to improved understanding of recruitment and population dynamics in both wild and captive populations.Heterozygosity is assumed to increase the fitness of individuals throughout life, but ontogenetic variance in heterozygosity–fitness correlations (HFCs) is poorly understood. We observed significant differences in HFCs between yellow perch populations and among life stages, suggesting the influence of heterozygosity may be mediated through an interaction, likely viability selection, between ontogeny and environment that is most important during early life. Accounting for the dynamic influences of genetic diversity on early life fitness could lead to improved understanding of recruitment and population dynamics in both wild and captive populations.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/136477/1/ece32781.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136477/2/ece32781_am.pd

Making it real: exploring the potential of Augmented Reality for teaching primary school science

The use of Augmented Reality (AR) in formal education could prove a key component in future learning environments that are richly populated with a blend of hardware and software applications. However, relatively little is known about the potential of this technology to support teaching and learning with groups of young children in the classroom. Analysis of teacher-child dialogue in a comparative study between use of an AR virtual mirror interface and more traditional science teaching methods for 10-year-old children, revealed that the children using AR were less engaged than those using traditional resources. We suggest four design requirements that need to be considered if AR is to be successfully adopted into classroom practice. These requirements are: flexible content that teachers can adapt to the needs of their children, guided exploration so learning opportunities can be maximised, in a limited time, and attention to the needs of institutional and curricular requirements

Orbital dynamics in ferromagnetic transition metal oxides

We consider a model of strongly correlated $e_g$ electrons interacting by superexchange orbital interactions in the ferromagnetic phase of LaMnO$_3$. It is found that the classical orbital order with alternating occupied $e_g$ orbitals has a full rotational symmetry at orbital degeneracy, and the excitation spectrum derived using the linear spin-wave theory is gapless. The quantum (fluctuation) corrections to the order parameter and to the ground state energy restore the cubic symmetry of the model. By applying a uniaxial pressure orbital degeneracy is lifted in a tetragonal field and one finds an orbital-flop phase with a gap in the excitation spectrum. In two dimensions the classical order is more robust near the orbital degeneracy point and quantum effects are suppressed. The orbital excitation spectra obtained using finite temperature diagonalization of two-dimensional clusters consist of a quasiparticle accompanied by satellite structures. The orbital waves found within the linear spin-wave theory provide an excellent description of the dominant pole of these spectra.Comment: 13 pages, 12 figures, to appear in Phys. Rev.