0 0.05 0.1 0.15 0.2 0.25 ( d σ / d Ω ) mag [barns st − 1 f.u. − 1 ] 200 K (a) 15 K (b) 0 1 2 3 0.05 0.1 0.15 0.2 0.25 Q [ ˚ A − $^{1}$] 10 K (c) 0 1 2 3 Q [ ˚ A − $^{1}$] 5 K (d) Q$_{1}$ Q$_{2}$ 2 FIG. 2: (d σ /dΩ) mag for volborthite at T = 200 , 15 , 10 , 5 K. (a) (d σ /dΩ) mag mimics f ( Q ) 2 (dashed black line) for Cu $^{2+}$. (b,c) Spectral weight shifts into a broad feature around 1 . 1 − 1 . 4 ˚ A − $^{1}$. Green line is fit to Eq. (1). (d) Fit to (d σ /dΩ) mag at 5 K as described in the text (red). The green line indicates the fit at 10 K, showing the shift of spectral weight into the two sharp features at Q 1 and Q 2 . FIG. 1: Structure of volborthite. (a) Kagome planes of Cu(1) and Cu(2) octahedra (respectively blue and green) are sep- arated by V 2 O 7 columns (red). (b) Local environments of Cu 2+ in a kagome plane. Solid and dashed black lines indi- cate the two nearest neighbour exchanges, J 1 and J ′ $_{1}$. The next-nearest neighbour exchange J 2 along the b -direction is shown in orange. frustration in volborthite. Polarised diffuse neutron scattering was performed on D7 at ILL using 35 . 7 g of sample and incident en- ergy E$_{i}$ = 8 . 5 meV. Three orthogonal neutron polari- sations ( x , y , and z ) and their corresponding spin flip and non-spin flip cross sections were analysed, which allowed for isolation of the magnetic scattering cross section, (d σ /dΩ)$_{mag}$ [15]. As no energy analysis was used, the observed scattering was effectively integrated up to ω = 8 . 2 meV, thus approximating the instanta- neous structure factor, S ( Q ). Spectra were measured at T = 200 K, 15 K, 10 K, and 5 K (Fig. 2). At 200 K ∼ 2 J , the Q -dependence of (d σ /dΩ)$_{mag}$ ap- proximately follows the Cu 2+ form factor, | f ( Q ) | $^{2}$, as an- ticipated for a paramagnet. Reducing the temperature to 15 K, broad diffuse scattering develops around Q = 1 . 1 − 1 . 4 ˚ A − $^{1}$. The Q -dependence is consistent with a buildup of nearest neighbour pair correlations, described by the powder averaged structure factor (d σ /dΩ)$_{mag}$: where the second term in the parenthesis reflects the aver- age correlation 〈 S$_{0}$ · S$_{1}$ 〉 = − 0 . 25(5) between a unit spin and its Z$_{1}$ nearest neighbours at a distance r$_{Cu}$$_{−}$$_{Cu}$ ∼ 3 ˚ A. The total scattering was found to be 0 . 99(8) µ 2 B per Cu, corresponding to 33% of the full S ( S + 1).The fact that correlations are weak and confined to only nearest neigh- bours even at T/J$_{avg}$ ∼ 0 . 2 are both indicators of strong At 50 K ∼ J/ 2, S ( Q, ω ) shows only a broad response centered at Q = 1 . 1 ˚ A − 1 and extending to 5 meV, con- sistent with fluctuations in a short range correlated sys- tem. The Q -dependence extracted by integrating over the range 1 − 6 meV is indicated in the top panel of Fig. 3(b). Its form is similar to S ( Q ) at 10 K and 15 K, and can also be fitted by Eq. 1 using r ∼ 3 . 5(2) ˚ A ∼ r$_{Cu}$$_{−}$$_{Cu}$ . Acoustic phonons are observed dispersing from nuclear Bragg positions at Q > 2 ˚ A − 1 and intense phonon scat- tering is found above 7 meV, making extraction of the magnetic signal at these energies difficult. Cooling to 5 K, the low Q , low ω intensity has largely moved into two features: an intense broad flat band, centered at ω$_{f}$ = 5 . 0(2) meV, and a nearly vertical bar of scattering ( dσ d Ω )$_{mag}$ = 2 3 ( γ$_{n}$r$_{0}$ 2 µ ) 2 | f ( Q ) | 2 ( 1 + Z$_{1}$ 〈 S$_{0}$ · S$_{1}$ 〉 sin Qr Qr ) (1) As T is further decreased to first 10 K and then 5 K, the broad diffuse scattering persists, but some (14%) of the spectral weight is shifted into two sharper (though not resolution limited) peaks at Q$_{1}$ = 0 . 65(3) ˚ A − 1 and Q$_{2}$ = 1 . 15(5) ˚ A − $^{1}$. The corresponding correlation length, ξ = 24(8) ˚ A ∼ 8 r$_{Cu}$$_{−}$$_{Cu}$ , was extracted by fitting the dif- fuse scattering to (1) and the two sharper features to Lorentzians (Fig. 2(d)). The dynamical structure fac- tor, S ( Q, ω ), was investigated by inelastic neutron scat- tering on IN4 at ILL. Spectra were collected using in- cident energy E$_{i}$ = 17 . 2 meV, giving elastic Q range 0 . 65 ˚ A − 1 − 4 . 95 ˚ A − $^{1}$. Further experiments were carried out on MARI at ISIS ( E$_{i}$ = 15 meV, 0 . 45 ˚ A − $^{1}$− 4 . 95 ˚ A − 1 at ω = 0 meV). Data are summarised in Fig. 3.