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

Abstract

We present spatial and dynamic information on the $s=1/2$ distorted kagome antiferromagnet volborthite, Cu${}_{3}$V${}_{2}$O${}_{7}$(OD)${}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2$D${}_{2}$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 ${Q}_{1}=0.65(3)$ \AA{}${}^{\ensuremath{-}1}$ and ${Q}_{2}=1.15(5)$ \AA{}${}^{\ensuremath{-}1}$ emerging below 5 K. The excitation spectrum, $S(Q,\ensuremath{\omega})$, reveals two steep branches dispersing from ${Q}_{1}$ and ${Q}_{2}$, and a flat mode at ${\ensuremath{\omega}}_{f}=5.0(2)$ meV. The results allow us to identify the crossover at ${T}^{*}\ensuremath{\sim}1$ K in ${}^{51}$V NMR and specific-heat measurements as the buildup of correlations at ${Q}_{1}$. We compare our data to theoretical models proposed for volborthite, and also demonstrate that the excitation spectrum can be explained by spin-wave-like excitations with anisotropic exchange parameters, as suggested by recent local-density calculations.