9 TABLE III: The derived staggered susceptibility X$_{T}$ , relax- ational linewidth Γ T , and bulk susceptibility χ bulk , as a func- tion of temperature from 180 < T < 300 K. Temp. 180 K 220 K 250 K 300 K X$_{T}$ ( µ 2 B meV $_{−}$1 f.u. $^{$_{−}$1}$) 0.84 0.66 0.49 0.32 Γ T (meV) 10 13 17 26 χ bulk (10 $_{−}$4 emu mol $^{$_{−}$1}$) 2.41 2.40 2.39 2.37 tions at any of the other wavevectors studied, indicat- ing that the relevant spin fluctuations throughout the phase diagram are short-ranged fluctuations of the low- temperature stripe AFM ordering. In addition, we find weaker interlayer coupling immediately above T$_{N}$ in the parent compound, suggesting that the quasi-2D spin fluc- tuations are a property of the tetragonal paramagnetic phase in general, and does not necessarily occur only af- ter doping. The substantial spin fluctuations that persist above T$_{N}$ should have an effect on the bulk transport and magnetic properties of CaFe$_{2}$As$_{2}$. For example, such spin fluctua- tions are a likely source of the high resistivity found for CaFe$_{2}$As$_{2}$ between T$_{N}$ and 300 K at ambient pressure. 24 Large spin disorder scattering at ambient pressure is sup- ported by dramatic decrease of the resistivity 29,30 and disappearance of spin fluctuations 31 upon transition to the collapsed tetragonal phase under applied pressure. The bulk magnetic susceptibility of CaFe$_{2}$As$_{2}$ also dis- plays a weak, non Curie-Weiss temperature dependence above T$_{N}$ . 24 Even though Eq. (5) is strictly valid only as an expansion for momenta close the AFM ordering vector, we can use this expression for the dynamic spin susceptibility to estimate the Q = 0 bulk susceptibility as χ$_{bulk}$ = χ ( Q = 0 , ω = 0) = χ$_{0}$/ [2 π $^{2}$(1 + η/ 2) + ( ξ$_{T}$ a ) − 2 + 2 η$_{c}$ ]. For large correlation lengths, the bulk susceptibility takes on a temperature independent value of χ$_{bulk}$ ≈ χ$_{0}$/ [1 + 2 π $^{2}$(1 + η/ 2) + 2 η$_{c}$ ] = 2.43x10 − 4 emu mol − 1 f.u. − $^{1}$. This estimate has the same order of magnitude as the bulk susceptibility determined from magnetiza- tion measurements, 24 further justifying the validity of the model. The shorter correlation lengths found well above T$_{N}$ will decrease the bulk susceptibility as shown in Ta- ble III, although this effect is small for the temperatures studied. The extrapolation of Eq. (5) to other momentum val- ues also allows us to estimate the size of the fluctuating moment per iron atom The Q -integration is performed in the orthorhombic zone (containing one ellipse of scattering) defined by the ranges 0 ≤ Q$_{x}$ ( Q$_{y}$ ) ≤ 2 π a and 0 ≤ Q$_{z}$ ≤ 4 π c . The factor of 1/2 in eq. 7 converts the results from squared-moment per formula unit to squared moment per iron. If we choose a high energy cut-off of ∼ 200 meV corresponding to the upper limit of observed spin wave excitations, 16,17 we obtain √ 〈 m $^{2}$〉 ≃ 0.7 µ$_{B}$ per iron which is very close to the size of the observed ordered moment. 32 The spin fluctutations observed above the AFM order- ing temperature in CaFe$_{2}$As$_{2}$ bear a close resemblance to that of doped superconducting BaFe$_{2}$As$_{2}$. Based on the model fitting, the similarity of the spin fluctuations in the parent and superconducting compositions can be com- pared more quantitatively. The paper by Inosov et al. 23 describes the parameters for short-range spin correlations in the optimally doped superconducting composition us- ing an equation similar to (6). We can estimate the values of the model parameters at 180 K for this SC composi- tion using mean-field temperature scaling as described by Inosov et al . Also, since the model parameters described in their work assume isotropic in-plane spin correlations, we extended their model by including the anisotropy pa- rameter, η , obtained from our results (i.e. assuming η to be both temperature and composition independent). With these assumptions, we estimated the values of the model parameters for the superconducting sample with the following results at 180 K; the static susceptibility at the antiferromagnetic wavevector is X$_{T}$ = 0.18 µ 2 B meV − 1 f.u. − $^{1}$, the longitudinal correlation length is ξ$_{T}$$_{+}$ = 11 ˚ A, and the Landau damping γ = 180 meV. This can be compared to the values in CaFe$_{2}$As$_{2}$ at the same temperature as found here; X$_{T}$ = 0.9 µ 2 B meV − 1 f.u. − $^{1}$, ξ$_{T}$$_{+}$ = 8 ˚ A, and γ = 43 meV. The results show that the Landau damping parameter is much larger in the super- conducting composition, whereas the correlation lengths at 180K are similar. In comparing these numbers, it is important to also recall the differences between the two materials investigated. For instance, in the sample stud- ied by Inosov et al. , 23 the alkaline earth metal is Ba and no magnetic phase transition is present. On the other hand, in the sample analyzed here, the alkaline earth metal is Ca and, at 180K, the system is very close to a strong first-order magnetic transition. We now turn to a discussion of the physical interpre- tation of the data. The new feature observed in our results is the anisotropy of the in-plane spin fluctua- tions in the paramagnetic phase, represented by the pa- rameter η . As discussed above, Eq. (5) is based on a metallic AFM model and a proper starting point to understand this anisotropy is an electronic band model for the magnetic susceptibility. The unique band struc- ture of the iron arsenides, consisting of circular hole pockets at Q =(0, 0) and elliptical electron pockets at Q 2 D $_{AFM}$=(1/2, 1/2), combined with electron-electron in- teractions will lead to an anisotropic spin response, even in the tetragonal phase. 33,34 More physical insight can be gained by considering a phenomenological model for the collective magnetic degrees of freedom of the pnictides. 35–37 In these materials, the magnetic lattice in each iron arsenide plane can be subdivided in two in- terpenetrating antiferromagnetic sublattices, each con- 〈 m $^{2}$〉 = 1 2 3¯ h π ∫ χ ′′ ( Q , ω )(1 − e − ¯ hω/kT $_{)}$− $^{1}$d Q dω ∫ d Q . (7)