7 tal dynamical magnetic susceptibility per formula unit as that of a two-dimensional metallic AFM in the para- magnetic phase, 23,27 which we have extended to include the effects of an in-plane anisotropy of the magnetic in- teractions. weak modulation of the scattered intensities along L . Fi- nally, broad scattering is observed within the Fe layers that is anisotropically distributed around Q$_{AFM}$ . We are thus forced to define two in-plane spin correlation lengths in order to fully describe the quasi-2D spin fluctuations. Considering these facts, we start by writing the to- The parameter ξ$_{T}$ defines the magnetic correlation length at temperature T in units of ˚ A, χ$_{0}$ is the staggered sus- ceptibility, and γ denotes the damping coefficient origi- nating from the spin decay into particle-hole excitations. The dimensionless parameter η is used to represent the anisotropy of the in-plane correlation lengths. The vector $^{q}$| | = ( q$_{x}$, q$_{y}$ ) = 2 π a ( h, k ) is a 2D vector defined relative to Q 2 D AFM = 2 π a (1 / 2 , 1 / 2) and a = √$_{2}$$_{a}$$_{0}$ is the lattice con- stant of the tetragonal cell with a$_{0}$ the nearest neighbor Fe-Fe distance. We can define two correlation lengths in directions longitudinal ( q$_{x}$ = q$_{y}$ denoted (+) scan) to Q 2 D AFM with a value ξ$_{T}$$_{+}$ = ξ$_{T}$ (1 + η $_{2}$) 1 / 2 and trans- verse ( q$_{x}$ = − q$_{y}$ denoted (-) scan) to Q 2 D AFM with value ξ$_{T}$$_{−}$ = ξ$_{T}$ (1 η $_{2}$) 1 / $^{2}$. Thus, we must have 0 ≤ η < 2 in order for these correlation lengths to be meaningful, which we found indeed to be the case. The effect of weak interlayer AFM coupling J$_{c}$ on total dynamic susceptibility can be written as where the scattering vector is defined as Q = Q$_{AFM}$ + $^{q}$| | + q$_{z}$ k . This expression can be motivated using the 1 /N approach for the action of the collective magnetic degrees of freedom employed in Refs. $^{35,37}$. Taking the imaginary part of Eq. (4), we obtain the expression perature, making ξ$_{T}$ the only temperature dependent pa- rameter in the model. However, one can introduce effec- tive temperature dependent parameters X$_{T}$ = χ$_{0}$ ( ξ$_{T}$ a ) 2 and Γ$_{T}$ = γ ( a ξ$_{T}$ ) $^{2}$. With these definitions, the dynam- ical susceptibility along the longitudinal direction at, q = ( q √$_{2}$ , q √$_{2}$ , L = 1 ) , or in the 2D limit where J$_{c}$ = 0 can be written as, At q = 0, this model reduces to the quasi-elastic Lorentzian lineshape used to describe the susceptibility in Eq. (2). In the context of the iron arsenides, Eq. (6) was first used successfully by Inosov et al. 23 to describe the Co- doped BaFe$_{2}$As$_{2}$ superconducting compound. In their work, Inosov et al. 23 assumed a mean-field behavior for the correlation length ξ$_{T}$ ∝ ( T − T$_{N}$ ) 1 / $^{2}$. Here, given the which we used to fit our inelastic neutron scattering data. Here, the parameter η$_{c}$ = J$_{c}$χ$_{0}$ controls the strength of the interlayer spin correlations and we have substituted q$_{z}$ = 2 π ( L − 1) /c . A physical motivation for this ex- pression and an interpretation of these parameters in the context of the iron arsenides is given later in section IV. As we are only able to define η from a single MAPS data set at 180 K, we make the assumption that the pa- rameters χ$_{0}$ , γ , J$_{c}$ and η in Eq. (5) do not depend on tem- TABLE I: Best fit parameters of Eq. (5) obtained self consis- tently from both HB-3 and MAPS at temperature T =180 K. The parameter χ 0 was solely obtained from the MAPS data which were normalized in absolute units. $_{χ}$− 1 2 $_{D}$( Q 2 D AFM + $^{q}$| | , ω ) = $_{χ}$− 1 0 [ ( q 2 || + ηq$_{x}$q$_{y}$ ) a 2 + ( ξ$_{T}$ /a $_{)}$− 2 − i ¯ hω/γ ] . (3) $_{χ}$− $^{1}$( Q$_{AFM}$ + q , ω ) = $_{χ}$− 1 2 $_{D}$( Q 2 D $_{AFM}$+ $^{q}$| | , ω )+2 J$_{c}$ sin $^{2}$( q$_{z}$c/ 4) (4) χ ′′ ( Q , ω ) = ¯ hωγχ$_{0}$ (¯ hω ) 2 + γ 2 [ ( q 2 + ηq$_{x}$q$_{y}$ ) a 2 + ( ξ$_{T}$ a ) − 2 + η$_{c}$ (1 + cos( πL )) ] $_{2}$, (5) χ ′′ 2 $_{D}$( Q 2 D AFM + q , ω ) = ¯ hω Γ$_{T}$ X$_{T}$ (¯ hω ) 2 + Γ 2 $_{T}$(1 + q $^{2}$ξ 2 $_{T$_{+}$}$) 2 (6) γ ξ$_{T}$ χ 0 η η$_{c}$ (meV) ( ˚ A ) ( µ$_{B}$ 2 meV $_{−}$1 f.u. $^{$_{−}$1}$) 43 ± 5 7.9 ± 0.10 0.2 ± 0.05 0.55 ± 0.36 0.20 ± 0.02