Pair correlations, short range order and dispersive excitations in the quasi-kagome quantum magnet volborthite

We present spatial and dynamic information on the s=1/2 distorted kagome antiferromagnet volborthite, Cu3V2O7(OD)2.2D2O, 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 Q1=0.65(3) {\AA}^-1 and Q2=1.15(5) {\AA}^-1 emerging below 5 K. The excitation spectrum, S(Q,{\omega}), reveals two steep branches dispersing from Q1 and Q2, and a flat mode at {\omega}=5.0(2) meV. The results allow us to identify the cross-over at T*=1 K in 51V 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.