Helical screw type magnetic structure of the multiferroic CaMn7O12 with low Cu-doping

The modulated crystal structure and modulated magnetic ordering of the multiferroic CaCu x Mn7−x O12 is studied by analysing neutron and synchrotron-radiation (SR) powder diffraction data with a model based on the magnetic superspace group R31′(00γ)ts. Both atomic position modulations and magnetic modulations are described with the modulation vector (0, 0, q). The magnetic ordering is a screw-type circular helix where the magnetic moments are perpendicular to the c direction. The temperature dependence of the modulation vector length and the ordered magnetic moments of Mn3+ and Mn4+ ions is given between T = 50 K and the Néel temperature T N ≃ 90 K. The atomic position modulation length L p and the magnetic modulation length L m fulfil the relation L m = 2L p at all temperatures between 50 K and T N.

ON THE NUMBER OF METASTABLE STATES IN A STRIPE GLASS

We estimate the number of metastable states of a self generated stripe glass, relevant for the formation of glassy doped Mott insulators. Using replica bound states, we demonstrate that the configurational entropy is the difference between the entropy of the stripe liquid and of an amorphous stripe solid with phonon-type excitations. Using simple scaling laws we then determine the relationship between the modulation length and the configurational entropy.

Low Temperature Synthesis of MO2C/W2C Superlattices via Ultra-Thin Modulated Reactants

We report here a synthesis method of preparing carbide superlattices using ultra-thin modulated reactants. Initial investigations into the synthesis of the binary systems, Mo2C and W2C using ultra-thin modulated reactants revealed that both can be formed at relatively low temperature(500 and 600°C respectively). DSC and XRD data suggested a two step reaction pathway involving interdiffusion of the initial modulated reactant followed by crystallization of the final product, if the modulation length is on the order of 10 Å. This information was used to form Mo2C/W2C superlattices using the structure of the ultra-thin modulated reactant to control the final superlattice period. Relatively large superlattice modulations were kinetically trapped by having several repeat units of each binary within the total repeat of the initial reactant. DSC and XRD data again are consistent with a two step reaction pathway leading to the formation of carbide superlattices.

Water waves, nonlinear Schrödinger equations and their solutions

Equations governing modulations of weakly nonlinear water waves are described. The modulations are coupled with wave-induced mean flows except in the case of water deeper than the modulation length scale. Equations suitable for water depths of the order the modulation length scale are deduced from those derived by Davey and Stewartson [5] and Dysthe [6]. A number of ases in which these equations reduce to a one dimensional nonlinear Schrödinger (NLS) equation are enumerated.Several analytical solutions of NLS equations are presented, with discussion of some of their implications for describing the propagation of water waves. Some of the solutions have not been presented in detail, or in convenient form before. One is new, a “rational” solution describing an “amplitude peak” which is isolated in space-time. Ma's [13] soli ton is particularly relevant to the recurrence of uniform wave trains in the experiment of Lake et al.[10].In further discussion it is pointed out that although water waves are unstable to three-dimensional disturbances, an effective description of weakly nonlinear two-dimensional waves would be a useful step towards describing ocean wave propagation.