5 100 200 300 200 300 400 Intensity (A.U.) 0.25 0.5 0.75 h in [hhL] 100 200 300 -0.4 -0.2 0 0.2 0.4 [1/2+  1/2-  L] 60 meV 12 meV 39 meV T=180 K L=1 L=3 L=5 (+) (-) FIG. 6: (Color online). Constant energy slices (Δ E = ± 5 meV) through the excitation spectrum of CaFe 2 As 2 in the ( h, k ) plane at T = 10 K and 180 K, as observed on MAPS. Energy slices are chosen to correspond to odd values of L . Intensity shown is in absolute units (mbarn Sr $_{−}$1 meV $_{−}$1 per formula unit). Below T$_{N}$ , well defined spin waves are observed around Q AFM (see also Ref. [16]). Above T$_{N}$ , strong but short-range magnetic correlations remain around Q AFM and extend up to at least 60 meV. Solid lines in panel (c) show the directions along which the cuts in Fig. 7 are taken, with (+) designating longitudinal cuts and (-) transverse cuts. FIG. 7: Longitudinal (+) and transverse (-) constant-energy cuts measured around Q = Q AFM =(1 / 2 , 1 / 2 , L ) on the MAPS spec- trometer. The cuts are taken at ¯ hω =12, 39 and 60 meV, which correspond to L = 1 , 3 and 5, respectively. Solid lines are best fits of Eq. (6) to the data. Dotted lines indicate the fitted background, and the dashed lines show the instrumental resolution function. 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. 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 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 C. Spectrum of paramagnetic spin fluctuations near Q AFM