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ing from the sample holder, with little or no magnetic contribution. We can use the intensity at (002) and (003) as an estimate for this phonon background. In Fig. 2(b), the temperature dependence at Q$_{AFM}$ = (1 / 2 , 1 / 2 , 1) and also (1 / 2 , 1 / 2 , 0) is shown. The intensity at Q$_{AFM}$ increases from low temperatures as expected for the in- creasing Bose population factor of the low lying spin wave modes. At T$_{N}$ , there is a sharp drop in the intensity con- sistent with the first-order transition to the paramagnetic state. The paramagnetic intensity decreases above T$_{N}$ and is nearly at background by 300 K. At (1 / 2 , 1 / 2 , 0) the intensity is nearly at background level below T$_{N}$ , in- creases sharply at the transition, and decreases slowly at higher temperatures. 

The L − dependence of the paramagnetic scattering is consistent with weak antiferromagnetic correlations be- tween layers atop a constant magnetic background, as illustrated in Fig. 2(b). Figs. 3(a) and (c) show the L - dependence of the scattering at ¯ hω = 10 meV and along the (1 / 2 , 1 / 2 , L ) direction for T = 300 K and 180 K, respectively. The L -dependence displays sinusoidal vari- ation with maxima at odd values of L . The lines shown correspond to fits to the dynamic susceptibility and will be described in detail below. The intensity drops by a factor of 2 between 180 K and 300 K indicating the grad- ual evolution of the system to less correlated quasi-2D spin fluctuations similar to the reduction in intensity for 

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cuts along the [ h, h, 3] direction shown in Figs. 3 (b) and (d). The temperature dependence of Al phonons is primarily responsible for the increase in background be- tween 180 K and 300 K. However, the constant magnetic background itself is also weakly temperature dependent as inferred from Fig. 2 (a). We return to this in section III C. 

In all, the surveys of magnetic scattering intensities above T$_{N}$ in the ( hhL ) and ( h 0 L ) planes indicate that the AFM spin correlations are restricted to the vicinity of Q$_{AFM}$ , the wavevector of the stripe ordered phase. One essential difference in the paramagnetic phase is an in- crease in the c -axis anisotropy and tendency towards 2D spin fluctuations, as indicated by the weakly modulated rod of scattering along L . This is entirely analogous to the behavior of AFM spin fluctuations in the optimally doped superconductors, where interlayer correlations are very weak $^{5,23}$. 

Fig. 4 depicts the dynamical structure factor χ ′′ ( Q$_{AFM}$ , ω ) / ¯ hω at Q$_{AFM}$ = (1 / 2 , 1 / 2 , 3) and ¯ hω < 22 meV for temperatures above and below T$_{N}$ . In order to obtain χ ′′ from the raw data, a non-magnetic background was estimated by measurements at Q = (0 . 35 , 0 . 35 , 3) and subtracted. Below T$_{N}$ , the low energy magnetic spectrum consists of spin waves with a sizeable spin gap of 7 meV (see Ref. 15). Just above T$_{N}$ , the gap collapses and the spin wave scattering is replaced by gapless, dif- fusive excitations. At 180 K, the diffusive excitations can be fit to a quasi-elastic Lorentzian form, 

with an energy linewidth of Γ$_{T}$ = 10 ± 1 meV. The parameter A is an arbitrary intensity scale factor. As 

## B. Energy dependence 

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