Pair Correlations, Short Range Order and Dispersive Excitations in the Quasi-Kagome Quantum Magnet Volborthite G. J. Nilsen, 1, 2, 3, ∗ F. C. Coomer, 3, † M. A. de Vries, 4 J. R. Stewart, 5 P. P. Deen, 6 A. Harrison, 3,7 and H. M. Rønnow 1 $^{1}$Laboratory for Quantum Magnetism, ICMP, Ecole Polytchnique F´ed´erale de Lausanne (EPFL), Switzerland $^{2}$Department of Chemistry and Biochemistry, Universit¨ at Bern, Freiestrasse 3, CH-3012 Bern, Switzerland $^{3}$School of Chemistry, University of Edinburgh, West Mains Road, Edinburgh, EH9 3JJ, United Kingdom $^{4}$Department of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT United Kingdom $^{5}$ISIS facility, Rutherford Appleton Laboratory, STFC, Chilton, Didcot, OX11 0DE United Kingdom $^{6}$European Spallation Source, ESS AB, P. O. Box 176, SE-22100 Lund, Sweden $^{7}$Institut Laue-Langevin, 6 rue Jules Horowitz, F-38042 Grenoble, France (Dated: September 1, 2018) We present spatial and dynamic information on the s = 1 / 2 distorted kagome antiferromagnet volborthite, Cu 3 V 2 O 7 (OD) 2 · 2D 2 O, obtained by polarized and inelastic neutron scattering. The instantaneous structure factor, S ( Q ), is dominated by nearest neighbor pair correlations, with short range order at wave vectors Q 1 = 0 . 65(3) ˚ A − 1 and Q 2 = 1 . 15(5) ˚ A − 1 emerging below 5 K. The excitation spectrum, S ( Q, ω ), reveals two steep branches dispersing from Q 1 and Q 2 , and a flat mode at ω$_{f}$ = 5 . 0(2) meV. The results allow us to identify the cross-over at T ∗ ∼ 1 K in $^{51}$V NMR and specific heat measurements as the build-up of correlations at Q 1 . We compare our data to theoretical models proposed for volborthite, and demonstrate that the excitation spectrum can be explained by spin-wave-like excitations with anisotropic exchange parameters, as also suggested by recent local density calculations. PACS numbers: 75.10.Jm, 75.10.Kt, 78.70.Nx The quantum kagome Heisenberg antiferromagnet (QKHAF) is among the most coveted targets in the quest for experimental realizations of quantum spin liq- uid ground states. The two most prominent physical real- izations of the QKHAF studied to date are the naturally occuring minerals herbertsmithite, Cu$_{3}$Zn(OH)$_{6}$Cl$_{2}$ [1] and volborthite, Cu$_{3}$V$_{2}$O$_{7}$(OH)$_{2}$ · 2H$_{2}$O [2]. The physics of herbertsmithite is arguably influenced by depletion of the kagome lattice caused by antisite mixing, possibly re- sulting in a valence bond glass state [3, 4]. In volborthite, the kagome planes are slightly distorted, but the lattice coverage is essentially complete. Since both systems de- viate from the pure QKHAF model, focus has shifted to the intriguing question of which states arise when the QKHAF is perturbed. Remarkably, a multitude of dif- ferent states have been proposed theoretically, depend- ing on the nature of the perturbation. These range from ordered states [5–9] to the aforementioned valence bond glass. Experimentally, the ground state of volborthite re- mains enigmatic, despite over 9 years of intensive study [2, 10–13]. Here we present a neutron scattering investi- gation of volborthite, employing both xyz polarised and inelastic time of flight techniques. Volborthite contains distorted kagome planes of edge sharing Cu 2+ octahedra, well separated ( ∼ 7 . 2 ˚ A) by pyrovanadate columns (V$_{2}$O$_{7}$), Fig. 1(a). There are two crystallographically distinct Cu 2+ ions. Cu(2) form chains along the b directions whileCu(1) populates the in- terchain sites. Locally, Cu(1) and Cu(2) reside in tetrag- onally and axially distorted octahedra, respectively, sug- gesting the d$_{3z}$ $^{2}$−r2 orbital being singly occupied on the Cu(1) site, with d$_{x}$ $^{2}$−y2 the magnetically active orbital for These results, however, have provided little insight to the nature of the magnetic correlations and excitations. Neutron scattering is an ideal probe for investigating these aspects, but has thus far not been employed, in main due to the large background generated by spin in- coherent scattering from $^{1}$H and $^{51}$V. We minimised this problem by replacing most of the $^{1}$H ( ∼ 98%) by $^{2}$D, which was achieved by performing the synthesis [2] us- ing deuterated reagents in an atmosphere of N$_{2}$, followed by annealing the product several times in D$_{2}$O at 95 $^{◦}$C. Phase purity of the resulting sample was verified by pow- der XRD. The concentration of paramagnetic defects, proportional to the magnitude of the Curie tail [14], was estimated to be to be < 1%. Despite a large estimated average coupling J$_{avg}$ = (2 J ′ 1 + J$_{1}$ ) / 3 = 84 K, magnetic susceptibility and spe- cific heat measurements on volborthite show no signs of long range order down to 1 . 8 K [2]. At yet lower temper- atures, muon spin rotation ( µ SR) and $^{51}$V NMR [10–12] indicate slowing down of fluctuations at T ∗ = 1 K, but with dynamics persisting to 20 mK. The state below T ∗ was interpreted as either incommensurate or short range correlated. Consistent with this, low temperature spe- cific heat studies indicate a high density of low energy modes below T ∗ [13]. Cu(2). As a consequence, there are two different nearest neighbour exchange pathways, J$_{1}$ ( r$_{Cu}$$_{(}$$_{2}$$_{)}$$_{−}$$_{Cu}$$_{(}$$_{2}$$_{)}$ = 2 . 93 ˚ A) and J ′ 1 ( r$_{Cu}$$_{(}$$_{1}$$_{)}$$_{−}$$_{Cu}$$_{(}$$_{2}$$_{)}$ = 3 . 03 ˚ A). J$_{1}$ links Cu(2) ions along the b axis. J ′ 1 connects Cu(1) and Cu(2) ions. Further- more, the edge sharing of the Cu(2) octahedra along the b direction imply the possibility of a strong next-nearest neighbour exchange, J$_{2}$ . arXiv:1001.2462v2 [cond-mat.str-el] 27 Feb 2011