Effects of anisotropy in spin molecular-orbital coupling on effective spin models of trinuclear organometallic complexes

We consider layered decorated honeycomb lattices at two-thirds filling, as realized in some trinuclear organometallic complexes. Localized $S=1$ moments with a single-spin anisotropy emerge from the interplay of Coulomb repulsion and spin molecular-orbit coupling (SMOC). Magnetic anisotropies with bond dependent exchange couplings occur in the honeycomb layers when the direct intracluster exchange and the spin molecular-orbital coupling are both present. We find that the effective spin exchange model within the layers is an XXZ + 120$^\circ$ honeycomb quantum compass model. The intrinsic non-spherical symmetry of the multinuclear complexes leads to very different transverse and longitudinal spin molecular-orbital couplings, which greatly enhances the single-spin and exchange coupling anisotropies. The interlayer coupling is described by a XXZ model with anisotropic biquadratic terms. As the correlation strength increases the systems becomes increasingly one-dimensional. Thus, if the ratio of SMOC to the interlayer hopping is small this stabilizes the Haldane phase. However, as the ratio increases there is a quantum phase transition to the topologically trivial `$D$-phase'. We also predict a quantum phase transition from a Haldane phase to a magnetically ordered phase at sufficiently strong external magnetic fields.Comment: 22 pages, 11 figures. Final version of paper to be published in PRB. Important corrections to appendix

Heisenberg and Dzyaloshinskii-Moriya interactions controlled by molecular packing in tri-nuclear organometallic clusters

Motivated by recent synthetic and theoretical progress we consider magnetism in crystals of multi-nuclear organometallic complexes. We calculate the Heisenberg symmetric exchange and the Dzyaloshinskii-Moriya antisymmetric exchange. We show how, in the absence of spin-orbit coupling, the interplay of electronic correlations and quantum interference leads to a quasi-one dimensional effective spin model in a typical tri-nuclear complex, Mo$_3$S$_7$(dmit)$_3$, despite its underlying three dimensional band structure. We show that both intra- and inter-molecular spin-orbit coupling can cause an effective Dzyaloshinskii-Moriya interaction. Furthermore, we show that, even for an isolated pair of molecules the relative orientation of the molecules controls the nature of the Dzyaloshinskii-Moriya coupling. We show that interference effects also play a crucial role in determining the Dzyaloshinskii-Moriya interaction. Thus, we argue, that multi-nuclear organometallic complexes represent an ideal platform to investigate the effects of Dzyaloshinskii-Moriya interactions on quantum magnets.Comment: This update incorporates the corrections described in a recently submitted erratum. Changes are confined to sections IV.A and B. The conclusions of the paper are unchanged. 12 + 4 pages, 9 figure

Spin-orbit coupling in {Mo3_3S7_7(dmit)3_3}

Spin-orbit coupling in crystals is known to lead to unusual direction dependent exchange interactions, however understanding of the consequeces of such effects in molecular crystals is incomplete. Here we perform four component relativistic density functional theory computations on the multi-nuclear molecular crystal {Mo$_3$S$_7$(dmit)$_3$} and show that both intra- and inter-molecular spin-orbit coupling are significant. We determine a long-range relativistic single electron Hamiltonian from first principles by constructing Wannier spin-orbitals. We analyse the various contributions through the lens of group theory. Intermolecular spin-orbit couplings like those found here are known to lead to quantum spin-Hall and topological insulator phases on the 2D lattice formed by the tight-binding model predicted for a single layer of {Mo$_3$S$_7$(dmit)$_3$}

Late Pleistocene and Holocene palaeoenvironments in and around the middle Caspian basin as reconstructed from a deep-sea core

This article has been made available through Open Access by the Brunel Open Access Publishing Fund.Late Pleistocene and/or Holocene high-resolution palynological studies are available for the south basin of the Caspian Sea (CS), the world's largest lake. However, the north and middle basins have not been the object of high-resolution palynological reconstructions. This new study presents the pollen, spores and dinoflagellate cysts records obtained from a 10m-long sediment core recovered in the middle basin, which currently has brackish waters and is surrounded by arid and semi-arid vegetation.An age-depth model built based on six radiocarbon dates on ostracod shells indicates that the sequence spans the period from 14.47 to 2.43cal.kaBP. The present palaeoenvironmental study focuses on the top 666cm, or from 12.44 to 2.43cal.kaBP.At the vegetation level, the Younger Dryas is characterised by an open landscape dominated by desert vegetation composed by Amaranthaceae with shrubs and salt-tolerant plants. However, although the Early Holocene is also characterised by desert vegetation, it is enriched in various shrubs such as Ephedra and Calligonum, but tree expansion is not important at the Holocene onset. After a major shift at 8.19cal.kaBP, the Middle Holocene displays now both the character of desert and of steppe, although some trees such as Quercus and Corylus slightly spread. The Late Holocene records steppe vegetation as dominant, with more tree diversity.Regarding the lacustrine signal, the dinocyst assemblage record fluctuates between slightly brackish conditions highlighted by Pyxidinopsis psilata and Spiniferites cruciformis, and more brackish ones - similar to the present day - with the dominance of Impagidinium caspienense. The Late Pleistocene is characterised by low salinities, related to the Khvalynian highstand. From 11.56cal.kaBP, slightly more saline waters are reconstructed with an increase of I.caspienense for a period of 1000 years, which could be attributed to the Mangyshlak lowstand. From 10.55cal.kaBP, low salinity conditions return with remains such as Anabaena and Botryococcus abundant until 8.83cal.kaBP, followed by a slow, progressive decrease of P. psilata and S. cruciformis until 4.11cal.kaBP, which is the main assemblage change at lacustrine scale. Since then, higher salinities, similar to the present one, are reconstructed. Finally, Lingulodinium machaerophorum starts its development only at 2.75cal.kaBP, in the Late Holocene.The present research revealed fundamental differences from previously published sea-level curves, in that a 6000yr-long highstand suggested by low salinities is shown between 10.55 and 4.11cal.kaBP. Amongst other arguments, using a comparison to a similar palynological regard but in the south basin, a N-S salinity gradient that is the reverse of the present one across the CS, suggests that the Amu Darya was flowing in the CS. Hence the CS levels during the Late Pleistocene and Holocene were influenced by a combination of precipitation over the high European latitudes and the indirect influence of the Indian summer monsoon over the Pamirs. © 2014.This study has been conducted within the European Contract INCO-Copernicus “Understanding the Caspian Sea erratic fluctuations” n IC15-CT96-0112. This was funded by the Centre National de la Recherche Scientifique within the framework of the INSUDYTEC (DYnamique de la Terre et du Climat) Program (France)

New two-colour light curves of Q0957+561: time delays and the origin of intrinsic variations

We extend the gr-band time coverage of the gravitationally lensed double quasar Q0957+561. New gr light curves permit us to detect significant intrinsic fluctuations, to determine new time delays, and thus to gain perspective on the mechanism of intrinsic variability in Q0957+561. We use new optical frames of Q0957+561 in the g and r passbands from January 2005 to July 2007. These frames are part of an ongoing long-term monitoring with the Liverpool robotic telescope. We also introduce two photometric pipelines that are applied to the new gr frames of Q0957+561. The transformation pipeline incorporates zero-point, colour, and inhomogeneity corrections to the instrumental magnitudes, so final photometry to the 1-2% level is achieved for both quasar components. The two-colour final records are then used to measure time delays. The gr light curves of Q0957+561 show several prominent events and gradients, and some of them (in the g band) lead to a time delay between components of 417 +/- 2 d (1 sigma). We do not find evidence of extrinsic variability in the light curves of Q0957+561. We also explore the possibility of a delay between a large event in the g band and the corresponding event in the r band. The gr cross-correlation reveals a time lag of 4.0 +/- 2.0 d (1 sigma; the g-band event is leading) that confirms a previous claim of the existence of a delay between the g and r band in this lensed quasar. The time delays (between quasar components and between optical bands) from the new records and previous ones in similar bands indicate that most observed variations in Q0957+561 (amplitudes of about 100 mmag and timescales of about 100 d) are very probably due to reverberation within the gas disc around the supermassive black hole.Comment: 13 pages, 9 figures. Accepted for publication in A&

Bounded and unbounded polynomials and multilinear forms: Characterizing continuity

In this paper we prove a characterization of continuity for polynomials on a normed space. Namely, we prove that a polynomial is continuous if and only if it maps compact sets into compact sets. We also provide a partial answer to the question as to whether a polynomial is continuous if and only if it transforms connected sets into connected sets. These results motivate the natural question as to how many non-continuous polynomials there are on an infinite dimensional normed space. A problem on the \emph{lineability} of the sets of non-continuous polynomials and multilinear mappings on infinite dimensional normed spaces is answered.Comment: 8 page