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taining one iron per unit cell. These two sublattices are only loosely coupled, because the local magnetic field produced by one sublattice on the other vanishes in the completely ordered state. To dominant order, the only couplings between the two sublattices that are allowed by symmetry are the biquadratic term − g ( m$_{1}$ · m$_{2}$ ) 2 and the momentum-dependent quadratic term ηq$_{x}$q$_{y}$ m$_{1}$ · m$_{2}$ . Evaluation of the spin-spin correlation function using this two-sublattice model leads to Eq. (5). Within this de- scription, the anisotropy of the correlation length results from an inter-sublattice coupling. 

This phenomenological model can be motivated by either an itinerant 38 or a localized moment picture $^{9}$. Indeed, the short correlation lengths encountered in the paramagnetic phase suggest a minimum description where only the short-range interactions are kept. One then has the so-called frustrated J$_{1}$ - J$_{2}$ model, with an- tiferromagnetic nearest-neighbor exchange interaction J$_{1}$ and next-nearest neighbor exchange J$_{2}$ . The anisotropy parameter η becomes simply the ratio between the two exchange constants, η = J$_{1}$/J$_{2}$ , and J$_{2}$ is related to the bare susceptibility χ$_{0}$ of Eq. (5) through χ$_{0}$ = 2 /J$_{2}$ . This also allows us to equate the interlayer coupling parameter η$_{c}$ with the ratio 2 J$_{c}$/J$_{2}$ . 

The exchange ratios in the paramagnetic phase can be compared directly to the values in the orthorhom- bic AFM ordered phase as obtained from measurements of spin waves 16,17 (see also Fig. 6) From the observed anisotropy of the in-plane correlation lengths, we can de- termine J$_{1}$/J$_{2}$ = 0 . 55 ± 0 . 36 in the tetragonal phase, im- plying that J$_{1}$ is indeed antiferromagnetic. In the AFM ordered orthorhombic phase, there are distinct nearest- neighbor exchange interactions, J$_{1}$$_{a}$ and J$_{1}$$_{b}$ and the ex- perimentally determined ratio 16,17 ( J$_{1}$$_{a}$ + J$_{1}$$_{b}$ ) / 2 J$_{2}$ ≈ 0 . 6 − 1 is similar in magnitude to the exchange ratio in the paramagnetic phase and within the error bars. Thus, the relative strength of the average exchange in- teractions in the Fe plane do not appear to be strongly affected by the structural transition. The value of this ra- tio J$_{1}$/J$_{2}$ < 2 places the paramagnetic phase of CaFe$_{2}$As$_{2}$ in a regime of frustrated magnetism within the J$_{1}$ − J$_{2}$ model and consistent with the presence of spin nematic correlations. 35–37 Taking the fitted value of χ$_{0}$ and con- sidering the Fe moment to be ∼ 1 µ$_{B}$ , one can use the relation χ$_{0}$ ∼ 2 /J$_{2}$ to estimate the the effective next- nearest neighbor exchange J$_{2}$ ≈ 10 meV, which can be compared with the value of 25-35 meV obtained from fits to the spin wave dispersion in the ordered phase. 

With regard to the 2 D nature of the spin fluctuations above T$_{N}$ , we can estimate the relative strength of the interlayer coupling in the paramagnetic phase through the parameter η$_{c}$ . The resulting exchange ratio J$_{c}$/J$_{2}$ = 0 . 1 ± 0 . 01, is lower than the ratio J$_{c}$/J$_{2}$ ≈ 0 . 15 − 0 . 25 in the ordered AFM state $^{17}$, implying that the fluctua- tions have a more two-dimensional character above T$_{N}$ . This result is consistent with angle-resolved photoemis- sion spectroscopy (ARPES), 39 which showed that the band structure dispersion of CaFe$_{2}$As$_{2}$ is quasi-2D above 

<img src='content_image/431109.jpg'>

T$_{N}$ but 3D below T$_{N}$ . 

At last, we would like to mention that the existence of anisotropic in-plane correlation lengths has a sim- ple physical interpretation within the frustrated J$_{1}$ − J$_{2}$ model. The magnetically ordered phase consists of di- agonal stripes with the magnetic moments ordered fer- romagnetically along one diagonal and antiferromagneti- cally along the correspondent orthogonal diagonal, as il- lustrated in Fig. 10. The direction longitudinal to Q$_{AFM}$ points along chains of antiferromagnetic spins while the transverse direction points along ferromagnetic chains. Since J$_{1}$ and J$_{2}$ are antiferromagnetic couplings, the nearest-neighbor bonds along the transverse direction are frustrated, leading to a shorter correlation length when compared to the correlation length associated to the un- frustrated bonds along the longitudinal direction. Thus, the data are consistent with nanoscale regions of dynamic AFM stripe/nematic correlations. 

In conclusion, paramagnetic excitations in CaFe$_{2}$As$_{2}$ ( T$_{S}$ = T$_{N}$ = 172 K) have been investigated in the tem- perature range from 180 K ( ∼ 1 . 05 T$_{N}$ ) up to 300 K (1 . 8 T$_{N}$ ). Above T$_{N}$ = 172 K, the spin gap collapses and antiferromagnetic spin wave scattering is replaced by in-plane anisotropic short-ranged AFM correlations that extend to high energy (¯ hω < 60 meV) and tempera- ture ( T < 300 K). The paramagnetic excitations are ob- 

## B. Summary 

