4 FIG. 5: (Color online). Magnetic excitations in CaFe 2 As 2 mea- sured on the MAPS spectrometer with an incident energy of E$_{i}$ = 100 meV at T = 10 K (left panel) and 180 K (right panel). The data shows magnetic intensity as a function of the [ h, h ] di- rection and the energy transfer after averaging over the transverse [ h, − h ] direction in the range 0.4 < h < 0.6. Given the fixed crystal orientation with incident beam along L , the L component of the wave vector varies with the energy transfer as indicated. Excita- tions below T$_{N}$ are consistent with steep spin waves and diffuse magnetic excitations are observed above T$_{N}$ at T = 180 K. FIG. 4: (Color online) The dynamic magnetic susceptibility of CaFe 2 As 2 as a function of energy at Q AFM = (1 / 2 , 1 / 2 , 3) for T = 140 K (blue solid squares), T = 180 K (grey solid circles) and T = 220 K (red solid diamonds). Above the magneto-structural transition T$_{N}$ = T$_{S}$ = 172 K, a broad magnetic spectrum is ob- served as quasi-elastic response near Q AFM . Data taken at T = 180 K were fit to a Lorentzian form given in Eq. (2) convoluted with the instrumental resolution (black solid line). The Lorentzian half- width Γ$_{T}$ at T = 180 K is 10 meV. At T = 220 K, we estimate the energy linewidth to be ∼ 13 meV using the expression Γ$_{T}$ = γ ( a ξ$_{T}$ ) 2 and the fitted value of γ (temperature independent Landau damp- ing defined in the text) and that of the correlation length ξ$_{T}$ at 220 K. The calculated Lorentzian scattering at T = 220 K is shown as a red solid line. In contrast, sharp spin waves having an energy gap Δ of ∼ 7 meV are observed in the ordered phase at T = 140 K. cuts along the [ h, h, 3] direction shown in Figs. 3 (b) and (d). The temperature dependence of Al phonons is primarily responsible for the increase in background be- tween 180 K and 300 K. However, the constant magnetic background itself is also weakly temperature dependent as inferred from Fig. 2 (a). We return to this in section III C. In all, the surveys of magnetic scattering intensities above T$_{N}$ in the ( hhL ) and ( h 0 L ) planes indicate that the AFM spin correlations are restricted to the vicinity of Q$_{AFM}$ , the wavevector of the stripe ordered phase. One essential difference in the paramagnetic phase is an in- crease in the c -axis anisotropy and tendency towards 2D spin fluctuations, as indicated by the weakly modulated rod of scattering along L . This is entirely analogous to the behavior of AFM spin fluctuations in the optimally doped superconductors, where interlayer correlations are very weak $^{5,23}$. ing from the sample holder, with little or no magnetic contribution. We can use the intensity at (002) and (003) as an estimate for this phonon background. In Fig. 2(b), the temperature dependence at Q$_{AFM}$ = (1 / 2 , 1 / 2 , 1) and also (1 / 2 , 1 / 2 , 0) is shown. The intensity at Q$_{AFM}$ increases from low temperatures as expected for the in- creasing Bose population factor of the low lying spin wave modes. At T$_{N}$ , there is a sharp drop in the intensity con- sistent with the first-order transition to the paramagnetic state. The paramagnetic intensity decreases above T$_{N}$ and is nearly at background by 300 K. At (1 / 2 , 1 / 2 , 0) the intensity is nearly at background level below T$_{N}$ , in- creases sharply at the transition, and decreases slowly at higher temperatures. The L − dependence of the paramagnetic scattering is consistent with weak antiferromagnetic correlations be- tween layers atop a constant magnetic background, as illustrated in Fig. 2(b). Figs. 3(a) and (c) show the L - dependence of the scattering at ¯ hω = 10 meV and along the (1 / 2 , 1 / 2 , L ) direction for T = 300 K and 180 K, respectively. The L -dependence displays sinusoidal vari- ation with maxima at odd values of L . The lines shown correspond to fits to the dynamic susceptibility and will be described in detail below. The intensity drops by a factor of 2 between 180 K and 300 K indicating the grad- ual evolution of the system to less correlated quasi-2D spin fluctuations similar to the reduction in intensity for Fig. 4 depicts the dynamical structure factor χ ′′ ( Q$_{AFM}$ , ω ) / ¯ hω at Q$_{AFM}$ = (1 / 2 , 1 / 2 , 3) and ¯ hω < 22 meV for temperatures above and below T$_{N}$ . In order to obtain χ ′′ from the raw data, a non-magnetic background was estimated by measurements at Q = (0 . 35 , 0 . 35 , 3) and subtracted. Below T$_{N}$ , the low energy magnetic spectrum consists of spin waves with a sizeable spin gap of 7 meV (see Ref. 15). Just above T$_{N}$ , the gap collapses and the spin wave scattering is replaced by gapless, dif- fusive excitations. At 180 K, the diffusive excitations can be fit to a quasi-elastic Lorentzian form, with an energy linewidth of Γ$_{T}$ = 10 ± 1 meV. The parameter A is an arbitrary intensity scale factor. As χ ′′ ( Q$_{AFM}$ , ω ) ¯ hω = A (¯ hω ) 2 + Γ 2 T (2) B. Energy dependence