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the temperature is increased, the Lorentzian half-width grows rapidly. At T = 220 K, the spectrum weakens considerably with temperature and appears flat within the energy range measured, thus the Lorentzian widths become large and poorly defined. This rapid increase in the quasi-elastic linewidth with temperature is explained below. 

## C. Spectrum of paramagnetic spin fluctuations near Q AFM 

At temperatures just above T$_{N}$ ( T = 180 K, T/T$_{N}$ = 1.05) we used the MAPS spectrometer to perform a de- tailed survey of the spin fluctuations in the paramagnetic phase in the vicinity of Q$_{AFM}$ . For detailed modeling, the MAPS measurements were normalized in absolute scat- tering units of mb Sr − 1 meV − 1 f.u. − 1 by comparison to a vanadium standard. Data were collected at 180 K and also in the AFM ordered phase at 10 K (with an inci- dent energy of 100 meV). As in previous work, 16 we use 

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the MSLICE program 25 to visualize the data and to take one and two dimensional cuts through main crystallo- graphic symmetry directions for subsequent data analysis with the TOBYFIT suite of analysis programs described below. 26 Where possible, symmetry equivalent cuts and slices were added to improve statistics. Fig. 5 shows slices of the neutron intensity along the [ h, h ] direction as a function of energy transfer after averaging over the [ h, − h ] direction. Below T$_{N}$ , the data in the left panel of Fig. 5 show a steep plume of intensity centered at Q$_{AFM}$ arising from AFM spin waves. The sizeable exchange coupling along c leads to variations in the structure factor along L , observed as energy-dependent intensity oscilla- tions that are peaked at the AFM zone centers; ¯ hω = 12 meV ( L =1), 39 meV ( L =3), and 60 meV ( L =5). Analy- sis of the AFM spin wave spectra is described in detail in Ref. [16]. Above T$_{N}$ , the right panel of Fig. 5 indicates that the magnetic spectrum is much broader in Q , and energy dependent oscillations are much less pronounced, confirming short-ranged spin correlations within the Fe layer and a weakening of interlayer correlations. 

Fig. 6 shows the neutron intensity for several constant energy slices at T = 10 K and 180 K. The energies are chosen such that L = 1, 3, and 5, in order to measure the spin fluctuations in ( h, k )-planes containing Q$_{AFM}$ (i.e. measuring the spin correlations within the Fe layers). Be- low T$_{N}$ , Figs. 6 (a)-(c) show three constant energy slices 

