6 through the AFM spin wave cone centered Q$_{AFM}$ . Above T$_{N}$ , Figs. 6 (d)-(f) again demonstrate that the sharp spin waves are replaced by very broad scattering in the para- magnetic phase. The paramagnetic fluctuations persist up to at least 60 meV and are notably anisotropic with an elliptical shape. This anisotropic scattering is charac- terized by transverse [ h, − h ] cuts through Q$_{AFM}$ being broader than the longitudinal [ h, h ] cuts, as illustrated in Fig. 7 where the solid lines are the resolution convo- luted fits of Eq. (5) to the experimental data, described below. This anisotropy implies that the paramagnetic fluctuations are described by two different spin correla- tion lengths within the Fe layer. An in-plane anisotropy of this type is allowed in the I4/mmm tetragonal cell, i.e. 4-fold symmetry has not been broken. The origin of this anisotropy is discussed below. Fig. 8 shows the energy dependence of the MAPS neu- tron intensity at Q$_{AFM}$ = (1 / 2 , 1 / 2 , L ) at T = 180 K after subtraction of background estimated at Q = (0 . 15 , 0 . 5 , L ). In the geometry of our time-of-flight experiment, L varies with energy transfer, however, L - dependent oscillations here and in Fig. 5 are only weakly present. After correcting for the dependence of the mag- netic form factor, the data was fit to the full susceptibility function described in Eq. 5 after convolution with the in- strumental resolution function. The model describes the MAPS data quite well, including weak L-dependent os- cillations, and gives relaxational half-width Γ$_{T}$ = 10 ± 1 meV, which is consistent with the HB3 measurements shown in Fig. 4. Fig. 9 shows HB3 scans along the [ h, h ] and L - directions through Q$_{AFM}$ = (1 / 2 , 1 / 2 , 3) and ¯ hω = 5 meV at several temperatures. Similar to Fig. 1, the In this section, we describe the theoretical model used to fit the experimental data. At temperatures below T$_{N}$ , the imaginary part of the generalized susceptibil- ity χ ′′ ( Q , ω ) for CaFe$_{2}$As$_{2}$ is well described by damped spin wave models. 15–17 Above T$_{N}$ , our neutron scatter- ing data reveal several features that have allowed us to develop a fairly detailed model of the paramagnetic exci- tations. First, the excitations are diffusive in character, at least for the measured energy scales ( < 60 meV). Sec- ond, the excitations are nearly two-dimensional, with a cuts below T$_{N}$ show sharp spin wave scattering. The measurements at several temperatures above T$_{N}$ indicate a gradual weakening of the scattering at Q$_{AFM}$ as the temperature is raised, reminiscent of Figs. 3 and 4. As noted above, the magnetic scattering along the [ h, h ] di- rection through Q$_{AFM}$ is much sharper, as shown in Fig. 3 (d), indicating much longer ranged spin correlations within the Fe layer than between layers. We see now that the weakening originates from temperature-dependent broadening of the scattering in reciprocal space, indicat- ing a gradual reduction in the spin correlation length with temperature. Similar to Fig. 3, the L − dependence of scans at Q$_{AFM}$ =(1/2, 1/2, 3) and ¯ hω = 5 meV were fit to the susceptibility in Eq. (5) for several temperatures up to 300 K and are shown as solid lines in Fig. 9(b). The description of this fitting and the interpretation of the results is now described. FIG. 9: Fits of Eq. (5) to constant energy cuts at 5 meV along h and L , as a function of increasing temperature (180 ≤ T ≤ 300 K). Circles are experimental data measured on HB3 with E$_{f}$ = 14.7 meV. Solid lines are the best fit to the data. Both the h - and L scans were fit to Eq. (5) (as shown in Fig. 3 over a wider range of h - and L ). The data at T = 140 K was fit to a spin wave model (as described in Ref. [15]), and is shown here for comparison. FIG. 8: Net magnetic neutron scattering intensity as a function of energy measured on MAPS around Q AFM = (1 / 2 , 1 / 2 , L ) after subtraction of a non-magnetic background at Q = (0 . 15 , 0 . 5 , L ). The integration ranges used in MSLICE are such that Δ h = ± 0 . 05. Lines are the best fits of Eq. (5) to the data. GLYPH<s49>GLYPH<s48> GLYPH<s50>GLYPH<s48> GLYPH<s51>GLYPH<s48> GLYPH<s52>GLYPH<s48> GLYPH<s53>GLYPH<s48> GLYPH<s54>GLYPH<s48> GLYPH<s55>GLYPH<s48> GLYPH<s48> GLYPH<s53> GLYPH<s49>GLYPH<s48> GLYPH<s49>GLYPH<s53> GLYPH<s50>GLYPH<s48> GLYPH<s50>GLYPH<s53> GLYPH<s51>GLYPH<s48> GLYPH<s76>GLYPH<s61>GLYPH<s51> GLYPH<s76>GLYPH<s61>GLYPH<s53> GLYPH<s83>GLYPH<s40>GLYPH<s81>GLYPH<s44> GLYPH<s41>GLYPH<s32>GLYPH<s40>GLYPH<s109>GLYPH<s98>GLYPH<s97>GLYPH<s114>GLYPH<s110>GLYPH<s115>GLYPH<s32>GLYPH<s109>GLYPH<s101>GLYPH<s86> GLYPH<s45>GLYPH<s49> GLYPH<s32>GLYPH<s83>GLYPH<s114> GLYPH<s45>GLYPH<s49> GLYPH<s32>GLYPH<s102>GLYPH<s46>GLYPH<s117>GLYPH<s46> GLYPH<s45>GLYPH<s49> GLYPH<s41> GLYPH<s104> GLYPH<s32>GLYPH<s40>GLYPH<s109>GLYPH<s101>GLYPH<s86>GLYPH<s41> GLYPH<s32> GLYPH<s32>GLYPH<s77>GLYPH<s65> GLYPH<s80>GLYPH<s83> GLYPH<s32> GLYPH<s32>GLYPH<s77>GLYPH<s111>GLYPH<s100>GLYPH<s101>GLYPH<s108> GLYPH<s76>GLYPH<s61>GLYPH<s49> GLYPH<s84>GLYPH<s61>GLYPH<s49>GLYPH<s56>GLYPH<s48>GLYPH<s32>GLYPH<s75> 0.25 0.5 0.75 h in [hhL] 0 500 1000 1500 Intensity (A.U.) 2.5 3 3.5 L in [1/2 1/2 L] 140 K 180 K 220 K 250 K 300 K HB-3 5 meV (a) (b) D. Theoretical Model