A new approach to solve quasicrystalline atomic structures in 3-dimensional (3D) real space is presented: The atomic pair distribution function (PDF) of face centred icosahedral Ho 9 Mg 26 Zn 65 [a(6D) = 2×5.18(3)Å] was obtained from in-house X-ray diffraction data (MoKα 1 ). Starting with rational approximant models, derived from 1/1and 2/1-Al-Mg-Zn, its local and medium range structure was refined (r < 27Å; R = 12.9%) using the PDF data. 85% of all atoms show Frank-Kasper (FK) type coordinations. Basic structural unit is the 3-shell, 104-atom Bergman cluster (d ≈ 15Å) comprising a void at its center. The clusters are interconnected sharing common edges and hexagonal faces of the 3rd shells. T he remaining space is filled by some glue atoms (9% of all atoms), yielding an almost tetrahedrally close packed structure. All Ho atoms are surrounded by 16 neighbours (FK-polyhedron "P"). Most of them (89%) are situated in the 2nd shell (pentagon dodecahedron), the other act as glue atoms. As a result and as can be expected for real matter, local atomic coordinations in quasicrystals are similar compared to common crystalline intermetallic compounds. From our results, the long range quasiperiodic structure of icosahedral Mg-Zn-RE (RE = Y and some rare earths) is anticipated to be a canonical cell tiling (CCT , after Henely) decorated with Bergman clusters.

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An unified picture for the Raman response of magnetic excitations in cuprate spin-ladder compounds is obtained by comparing calculated two-triplon Raman line-shapes with those of the prototypical compounds SrCu2O3 (Sr123), Sr14Cu24O41 (Sr14), and La6Ca8Cu24O41 (La6Ca8). The theoretical model for the two-leg ladder contains Heisenberg exchange couplings J and J ⊥ plus an additional four-spin interaction Jcyc. Within this model Sr123 and Sr14 can be described by x := J /J ⊥ = 1.5, xcyc := Jcyc/J ⊥ = 0.2, J Sr123 ⊥ = 1130 cm −1 and J Sr14 ⊥ = 1080 cm −1 . The couplings found for La6Ca8 are x = 1.2, xcyc = 0.2, and J La6Ca8 ⊥ = 1130 cm −1 . The unexpected sharp two-triplon peak in the ladder materials compared to the undoped two-dimensional cuprates can be traced back to the anisotropy of the magnetic exchange in rung and leg direction. With the results obtained for the isotropic ladder we calculate the Raman line-shape of a two-dimensional square lattice using a toy model consisting of a vertical and a horizontal ladder. A direct comparison of these results with Raman experiments for the two-dimensional cuprates R2CuO4 (R=La,Nd), Sr2CuO2Cl2, and YBa2Cu3O 6+δ yields a good agreement for the dominating two-triplon peak. We conclude that short range quantum fluctuations are dominating the magnetic Raman response in both, ladders and planes. We discuss possible scenarios responsible for the high-energy spectral weight of the Raman line-shape, i.e. phonons, the triple-resonance and multi-particle contributions.

We investigated temperature dependent Raman spectra of the one-dimensional spin-ladder compound SrCu2O3. At low temperatures a two-magnon peak is identified at 3160 ± 10 cm −1 and its temperature dependence analyzed in terms of a thermal expansion model. We find that the two-magnon peak position must include a cyclic ring exchange of J cycl /J ⊥ = 0.09 − 0.25 with a coupling constant along the rungs of J ⊥ ≈ 1215 cm −1 (1750 K) in order to be consistent with other experiments and theoretical results. PACS numbers: 78.30.-j, 75.50.Ee O (p x ) Cu (d x²-y² ) J ¡ J J cycl A

Key words Ho-Mg-Zn simple icosahedral quasicrystals, structure analysis, atomic pair distribution function (PDF). PACS 61.44.Br, 61.10.NzWe present a new complementary strategy to quasicrystalline structure determination: The local atomic structure of simple icosahedral (si) Ho 11 Mg 15 Zn 74 [a(6D) = 5.144(3)Å] in a sphere of up to r = 17Å was refined using the atomic pair distribution function (PDF) from in-house X-ray powder diffraction data (MoKα 1 , Q max = 13.5Å -1 ; R = 20.4%). The basic building block is a 105-atom Bergman-Cluster {Ho 8 Mg 12 Zn 85 }. Its center is occupied by a Zn atom -in contrast to a void in face centred icosahedral (fci) Ho 9 Mg 26 Zn 65 . The center is then surrounded by another 12 Zn atoms, forming an icosahedron (1st shell). The 2nd shell is made up of 8 Ho atoms arranged on the vertices of a cube which in turn is completed to a pentagon dodecahedron by 12 Mg atoms, the dodecahedron then being capped by 12 Zn atoms. The 3rd shell is a distorted soccer ball of 60 Zn atoms, reflecting the higher Zn content of the si phase compared to the fci phase. In our model, 7% of all atoms are situated in between the clusters. The model corresponds to a hypothetical 1/1-approximant of the icosahedral (i) phase. The local coordinations of the single atoms are of a much distorted FrankKasper type and call to mind those present in 0/1-Mg 2 Zn 11 .