Paramagnetic Spin Correlations in CaFe$_{2}$As$_{2}$ Single Crystals arXiv:1001.2804v2 [cond-mat.supr-con] 7 Jul 2010 S.O. Diallo, 1 D.K. Pratt, 1 R.M. Fernandes, 1 W. Tian, 1 J.L. Zarestky, 1 M. Lumsden, 2 T.G. Perring, 3 C.L. Broholm, 4 N. Ni, 1 S.L. Bud’ko, 1 P.C. Canfield, 1 H.-F. Li, 1 D. Vaknin, 1 A. Kreyssig, 1 A.I. Goldman, 1 and R.J. McQueeney 1 $^{1}$Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011 USA $^{2}$Oak Ridge National Laboratory, Oak Ridge, TN 37831 USA $^{3}$ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 OQX, United Kingdom $^{4}$Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218 USA (Dated: October 31, 2018) Magnetic correlations in the paramagnetic phase of CaFe 2 As 2 ( T$_{N}$ = 172 K) have been examined by means of inelastic neutron scattering from 180 K ( ∼ 1 . 05 T$_{N}$ ) up to 300 K (1 . 8 T$_{N}$ ). Despite the first-order nature of the magnetic ordering, strong but short-ranged antiferromagnetic (AFM) cor- relations are clearly observed. These correlations, which consist of quasi-elastic scattering centered at the wavevector Q AFM of the low-temperature AFM structure, are observed up to the highest measured temperature of 300 K and at high energy transfer (¯ hω > 60 meV). The L dependence of the scattering implies rather weak interlayer coupling in the tetragonal c -direction corresponding to nearly two-dimensional fluctuations in the ( ab ) plane. The spin correlation lengths within the Fe layer are found to be anisotropic, consistent with underlying fluctuations of the AFM stripe structure. Similar to the cobalt doped superconducting BaFe 2 As 2 compounds, these experimen- tal features can be adequately reproduced by a scattering model that describes short-ranged and anisotropic spin correlations with overdamped dynamics. PACS numbers: 74.70.-b,75.30.Et,78.70.Nx I. INTRODUCTION The appearance of superconductivity (SC) in doped A Fe$_{2}$As$_{2}$ materials ( A = Ca,Sr,Ba) is linked to the sup- pression of antiferromagnetic (AFM) ordering found in the parent compounds. 1–3 Other unconventional super- conductors share a similar phase diagram, suggesting that the AFM spin fluctuations may be responsible for pairing of electrons in the SC state. Certainly, the AFM fluctuation spectrum itself is directly influenced by superconductivity. 4–6 The appearance of a gap and resonance-like feature in the paramagnetic spectrum of these compounds below the superconducting tempera- ture T$_{C}$ also closely resembles 7 other unconventional su- perconductors and highlights the coupling of the iron spins with electronic charge carriers. Recent neutron scattering results elegantly show that the magnetic reso- nance can infer details about the symmetry of the super- conducting gap. 4 In order to understand the nature of the superconduct- ing pairing, details of the normal state spin fluctuations must be first understood. These spin fluctuations are expected to be unusual 8–11 since magnetic frustration in the tetragonal paramagnetic phase leads to an additional nematic 12 degree-of-freedom due to the weak net mag- netic coupling of nearest-neighbor Fe sublattices. The AFM ordering in parent A Fe$_{2}$As$_{2}$ compounds below T$_{N}$ is observed to occur either simultaneously with or after a structural transition from tetragonal to orthorhombic at T$_{S}$ . The magnetic excitations in A Fe$_{2}$As$_{2}$ in stripe AFM ordered parent compounds have been extensively studied 13–17 and indicate itinerant spin waves whose ex- citation spectrum can be adequately described by large nearest ( J$_{1}$ ) and next-nearest-neighbor ( J$_{2}$ ) in-plane ex- change constants, a substantial interlayer coupling ( J$_{c}$ ), and strong Landau damping γ . The primary role of doping is to suppress both the AFM and structural transitions, resulting in strong AFM spin fluctuations. In the context of establishing the con- nection between spin fluctuations and superconductivity, it becomes imperative to examine the evolution of these spin excitations across the entire phase diagram of doped A Fe$_{2}$As$_{2}$. There have been several theoretical and ex- perimental studies on the effects of charge doping on the spin excitations in the superconducting compounds. 18–23 In general, these studies show that the normal state spin fluctuations are quasi-two-dimensional (2D) and strongly damped while remaining peaked at Q$_{AFM}$ , the magnetic ordering wavevector of the stripe AFM state. It is un- clear if the quasi-2D nature and strong damping are fea- tures that appear only with sufficient doping, or whether these are common features of the spin fluctuations in the tetragonal phase. In order to address these questions, we examine the spin correlations that occur in the parent compound CaFe$_{2}$As$_{2}$ above the AFM ordering temperature T$_{N}$ . Inelastic neutron scattering data on CaFe$_{2}$As$_{2}$ single- crystals show that above the simultaneous first order transitions at T$_{N}$ = T$_{S}$ = 172 K, 24 the spin gap col- lapses and spin wave scattering centered at the stripe ordering wavevector Q$_{AFM}$ is replaced by short-ranged and quasi-elastic AFM correlations that extend up to at least 60 meV. Just above T$_{N}$ (at T = 180 K) the low en- ergy magnetic response is quasi-elastic with anisotropic in-plane correlations. We find the in-plane correlation length to be ξ$_{T}$$_{+}$ ≃ 8 ˚ A along the orthorhombic a -axis and ξ$_{T}$$_{−}$ ≃ 6 ˚ A along b . Weak modulations of the scat-