8 tively fixing the width) and then vary the scale factor χ$_{0}$ to get the best fit. This procedure was performed for con- stant energy cuts at several energy transfers on both HB3 and MAPS data sets at T = 180 K. Upon convergence to reasonable values of χ$_{0}$ and ξ$_{T}$ , the whole procedure was repeated for consistency. Once the best fitted value of χ$_{0}$ was obtained at 180 K, we kept it fixed at that same value for all other temperatures and fit the data by varying only ξ$_{T}$ . strong first-order character of the magnetic transition in the parent compound CaFe$_{2}$As$_{2}$, we do not assume any particular form for temperature dependence of ξ$_{T}$ . For detailed comparison of model susceptibility in Eq. (5) to the data, we use standard inelastic neutron scat- tering computer programs that account for resolution effects. Specifically, the high energy data collected on MAPS was analyzed using TOBYFIT 26 while the low energy response measured on HB3 (up to 15 meV) was analyzed using RESLIB. 28 Our protocol was to establish the value of the temper- ature independent parameters using data sets from both HB3 and MAPS at 180 K where scattering features are more sharply defined. Data fits at subsequent tempera- tures would then only require the refinement of a single parameter, ξ$_{T}$ . Due to the interrelated nature of the fit- ting parameters, self-consistency checks were performed for model fittings on the HB3 and MAPS data sets. The in-plane anisotropy parameter η was obtained indepen- dently from the MAPS data by fitting the longitudinal (+) and transverse (-) cuts, as depicted in Fig. 8. The ob- served in-plane anisotropy is then determined from these fitted widths according to η = 2 ξ 2 T + − ξ 2 T$_{−}$ ξ 2 T $_{+}$+ ξ 2 T$_{−}$ . The temper- ature independent damping parameter, γ , was obtained from both the HB3 and MAPS energy scans at T = 180 K where we have the best signal to noise ratio. The cor- responding fits are illustrated in Figs. 4 and 7. The fits were performed by constraining the value of γ = Γ$_{T}$ ( ξ$_{T}$ a ) 2 such that the Lorentzian width Γ$_{T}$ remains fixed at 10 meV (fitting only for ξ$_{T}$ ). Once γ was determined at T = 180 K, it was held fixed in all subsequent fits. To determine η$_{c}$ at 180 K, we have performed a chi- squared analysis of fits in which only η$_{c}$ (0 ≤ η$_{c}$ ≤ 0 . 5) was allowed to vary, and other parameters held fixed. The best fits were obtained for 0 . 9 < η$_{c}$ < 0 . 11, as indi- cated in Fig. (3), which also corresponds to a minimum χ 2 value. Outside this range, χ 2 drastically increases and the fits are altered. The parameter η$_{c}$ in Eq. (5) which describes the interlayer coupling was found to be ≃ 10% at T = 180 K. The parameters χ$_{0}$ and ξ$_{T}$ were found to be strongly correlated. The prescription was used to fix ξ$_{T}$ (effec- The MAPS data was normalized to vanadium stan- dard, allowing us to report χ$_{0}$ in absolute units. In con- trast, the HB3 data was not in absolute units. Thus, the corresponding best fitted scale factor from HB3 gives a value that is proportional to the true χ$_{0}$ . Therefore the χ$_{0}$ value reported here are obtained solely from the MAPS data. In all, we arrived at the following final set of parameters at T = 180 K; γ = 43 ± 5 meV, χ$_{0}$ = 0 . 20 ± 0 . 05 µ 2 B meV − $^{1}$f.u. − $^{1}$, ξ$_{T}$$_{+}$ = 8 1 ˚ A and ξ$_{T}$$_{−}$ = 6 ± 1 . 5 ˚ A. Fits are shown as solid lines in Figs. 3, 4, 7 and 8. From these values, we estimate the average in-plane anisotropy parameter 〈 η 〉 ≃ 0.55 ± 0.36, and thus kept η fixed at this value in subsequent model fits to the higher temperature data. The corresponding value of the static correlation length ξ$_{T}$ obtained from MAPS is 7 ± 2 ˚ A, in good agreement with the low energy HB3 value of 7.9 ± 0.1 ˚ A. A summary of all of the model parameters at T = 180 K are listed in Table I. Fig. 9(a) shows the temperature dependence of the HB3 constant energy cuts along the [1 , 1 , 0] direction at 5 meV for several temperatures up to 300 K. These data were fit to determine the values of ξ$_{T}$ at different tem- peratures. The correlation length decreases by a factor of ∼ 2 from 180 K to 300 K. Similar fits were performed at constant energy cuts of 10 meV and 15 meV (not shown), giving comparable results. The results are summarized in Table II. We note that the set of parameters in Tables I and II describe the full data set at all temperatures and energy transfers exceptionally well, as can be seen by reviewing all of the fitted curves in Figs. 3, 4, 7, 8 and 9. For example, the line through the data in Fig. 4 at T = 220 K is not a fit, rather it is a model calculation based on the fixed parameters in Tables I and II. This universal agreement with the data at all measured energies and temperatures is a strong endorsement for the validity of the nearly AFM model. Despite the strong first order transition and the pos- sible influence of magnetic frustration in the tetragonal phase, we find that the spin fluctuations observed above the AFM ordering temperature in CaFe$_{2}$As$_{2}$ are peaked at Q$_{AFM}$ , the wavevector of the stripe AFM structure. We found no evidence of substantial magnetic fluctua- IV. DISCUSSION AND CONCLUSIONS A. Discussion TABLE II: Temperature evolution of the correlation length ξ$_{T}$ (in ˚ A) for several incident energies, as measured on HB-3. For a given temperature, ξ$_{T}$ appears largely independent of energy, as expected. The final column, containing the corre- lation length averaged over all energies, is the value used in subsequent model calculations. 5 meV 10 meV 15 meV < ξ$_{T}$ > ( ˚ A) 180 K 8.1 ± 0.2 7.9 ± 0.1 7.8 ± 0.3 7.9 ± 0.1 220 K 7.0 ± 0.2 7.2 ± 0.3 6.9 ± 0.2 7.0 ± 0.1 250 K 6.0 ± 0.1 6.0 ± 0.2 6.2 ± 0.2 6.1 ± 0.1 300 K 4.9 ± 0.1 4.9 ± 0.2 4.9 ± 0.2 4.9 ± 0.1