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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 

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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. 

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 

## D. Theoretical Model 

