Derivation of effective spin models from a three band model for CuO_2-planes

The derivation of effective spin models describing the low energy magnetic properties of undoped CuO_2-planes is reinvestigated. Our study aims at a quantitative determination of the parameters of effective spin models from those of a multi-band model and is supposed to be relevant to the analysis of recent improved experimental data on the spin wave spectrum of La_2CuO_4. Starting from a conventional three-band model we determine the exchange couplings for the nearest and next-nearest neighbor Heisenberg exchange as well as for 4- and 6-spin exchange terms via a direct perturbation expansion up to 12th (14th for the 4-spin term) order with respect to the copper-oxygen hopping t_pd. Our results demonstrate that this perturbation expansion does not converge for hopping parameters of the relevant size. Well behaved extrapolations of the couplings are derived, however, in terms of Pade approximants. In order to check the significance of these results from the direct perturbation expansion we employ the Zhang-Rice reformulation of the three band model in terms of hybridizing oxygen Wannier orbitals centered at copper ion sites. In the Wannier notation the perturbation expansion is reorganized by an exact treatment of the strong site-diagonal hybridization. The perturbation expansion with respect to the weak intersite hybridizations is calculated up to 4th order for the Heisenberg coupling and up to 6th order for the 4-spin coupling. It shows excellent convergence and the results are in agreement with the Pade approximants of the direct expansion. The relevance of the 4-spin coupling as the leading correction to the nearest neighbor Heisenberg model is emphasized.Comment: 27 pages, 10 figures. Changed from particle to hole notation, right value for the charge transfer gap used; this results in some changes in the figures and a higher value of the ring exchang

Symmetries and Triplet Dispersion in a Modified Shastry-Sutherland Model for SrCu_2(BO_3)_2

We investigate the one-triplet dispersion in a modified Shastry-Sutherland Model for SrCu_2(BO_3)_2 by means of a series expansion about the limit of strong dimerization. Our perturbative method is based on a continuous unitary transformation that maps the original Hamiltonian to an effective, energy quanta conserving block diagonal Hamiltonian H_{eff}. The dispersion splits into two branches which are nearly degenerated. We analyse the symmetries of the model and show that space group operations are necessary to explain the degeneracy of the dispersion at k=0 and at the border of the magnetic Brillouin zone. Moreover, we investigate the behaviour of the dispersion for small |k| and compare our results to INS data.Comment: 9 pages, 8 figures accepted by J. Phys.: Condens. Matte

On the Origin of the Non-Fermi Liquid Behavior of SrRuO_{3}

Motivated by the unusual features observed in the transport properties of the ferromagnetic "bad metal" $SrRuO_{3}$, we construct a model incorporating essential features of the realistic structure of this nearly cubic material. In particular, we show how the $t_{2g}$orbital {\it orientation} in the perfectly cubic structure determines the peculiar structure of the hybridization matrix, and demonstrate how the local non-Fermi liquid features arise when interactions are switched on. we discuss the effect of the slight deviation from the cubic structure (at low-$T$) qualitatively. The model provides a consistent explanation of the features observed recently in the optical response of $SrRuO_{3}$.Comment: 4 pages. Submitted to Physical Review Letter

Promoting learner autonomy through multiliteracy skills development in cross-institutional exchanges

This contribution presents findings from two empirical case studies, which followed a task-based telecollaborative learning format. Participants included student teacher trainees, tutors, and language learners from colleges/universities in Germany, Poland, the United Kingdom, and the United States. The projects aimed at promoting learner autonomy through awareness raising of modes and meaning-making online and multiliteracy skills development based on hands-on analysis of web resources and social networking tools. It was hoped that this awareness would foster the teachers' own autonomy in virtual learning environments and enable them to design tasks which—in turn—would promote learner autonomy as understood by Palfreyman (2006): the informed use of a range of interacting resources in context. We argue that this awareness is reflected in enhanced multimodal communicative competence, i.e., “the ability to understand the combined potential of various modes for making meaning” (Royce, 2002, p. 92), and multiliteracy, with the latter allowing teachers and learners to realize the potential of blended and online only settings for language acquisition purposes. Ideally then, while becoming gradually more versed in multimodality and multiliteracy, learners can also take over more control and self-direct their own learning when working online (Benson, 2001) which are also characteristics of autonomy