Paramagnetic spin correlations in ${\text{CaFe}}_2{\text{As}}_2$ single crystals

Magnetic correlations in the paramagnetic phase of ${\text{CaFe}}_2{\text{As}}_2\left(T_N=172\text{K}\right)$ have been examined by means of inelastic neutron scattering from 180 K $\left(\sim 1.05T_N\right)$ up to 300 K $\left(1.8T_N\right)$. Despite the first-order nature of the magnetic ordering, strong but short-ranged antiferromagnetic (AFM) correlations are clearly observed. These correlations, which consist of quasielastic scattering centered at the wave vector ${\mathbf{Q}}_{\text{AFM}}$ of the low-temperature AFM structure, are observed up to the highest measured temperature of 300 K and at high energy transfer $\left(\hslash \omega >60\text{meV}\right)$. The $L$ dependence of the scattering implies rather weak interlayer coupling in the tetragonal $c$ direction corresponding to nearly two-dimensional fluctuations in the $\left(ab\right)$ 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 ${\text{BaFe}}_2{\text{As}}_2$ compounds, these experimental features can be adequately reproduced by a scattering model that describes short-ranged and anisotropic spin correlations with overdamped dynamics.

Figure 1

(Color online) Summary of scans performed at $T=10\text{K}$, 140 K (empty symbols), and 180 K (filled symbols) on HB3 $\left(E_f=41.2\text{meV}\right)$ and HB-1A with spectrometer configurations described in the text. (a) shows $\left(hhL\right)$ plane in reciprocal space where the scans at HB3 were performed. (b)–(f) show the various cuts investigated, as indicated in (a). (g) and (h) show the scans performed in the $\left(h0L\right)$ plane using HB1A. No diffuse magnetic scattering was observed in the $\left(h0L\right)$ plane. The magnetic signal is only observed centered at wave vectors $\mathbf{Q}={\mathbf{Q}}_{\text{AFM}}$.

Figure 2

(Color online) Temperature evolution of the neutron-scattering signal measured on HB3 at $\hslash \omega =10\text{meV}$. (a) Background estimate measured away from ${\mathbf{Q}}_{\text{AFM}}$ at (002) (solid symbols) and (003) (open symbols) showing no anomaly at $T_N$. Solid lines are linear fits to the temperature-dependent intensity. (b) Intensity at ${\mathbf{Q}}_{\text{AFM}}=\left(1/2,1/2,1\right)$ and (1/2,1/2,0). The solid line is the nonmagnetic background estimate obtained from averaging the fits at (002) and (003), shown in panel (a).

Figure 3

(Color online) $L$ and $h$ dependences of the scattering at $\hslash \omega =10\text{meV}$ measured on the HB3 instrument with $E_f=41.2\text{meV}$. The scans are performed along the $\left(1/2,1/2,L\right)$ and $\left(h,h,3\right)$ directions for temperatures [(a) and (b)] $T=300\text{K}$ and [(c) and (d)] $T=180\text{K}$. The solid lines in (a) and (c) correspond to fits to the dynamical susceptibility described in Eq. (5). The solid lines in (b) and (d) are guide to the eye, and based on Lorentzian fits to the data. The dashed line is an estimate of background scattering. Panels (c) and (d) show the sharper magnetic scattering at 180 K.

Figure 4

(Color online) The dynamic magnetic susceptibility of ${\text{CaFe}}_2{\text{As}}_2$ as a function of energy at ${\mathbf{Q}}_{\text{AFM}}=\left(1/2,1/2,3\right)$ for $T=140\text{K}$ (blue solid squares), $T=180\text{K}$ (gray solid circles), and $T=220\text{K}$ (red solid diamonds). Above the magneto-structural transition $T_N=T_S=172\text{K}$, a broad magnetic spectrum is observed as quasielastic response near ${\mathbf{Q}}_{\text{AFM}}$. Data taken at $T=180\text{K}$ were fit to a Lorentzian form given in Eq. (2) convoluted with the instrumental resolution (black solid line). The Lorentzian half-width ${\Gamma }_T$ at $T=180\text{K}$ is 10 meV. At $T=220\text{K}$, we estimate the energy linewidth to be $\sim 13\text{meV}$ using the expression ${\Gamma }_T=\gamma {\left(\frac{a}{{\xi }_T}\right)}^2$ and the fitted value of $\gamma$ (temperature-independent Landau damping defined in the text) and that of the correlation length ${\xi }_T$ at 220 K. The calculated Lorentzian scattering at $T=220\text{K}$ is shown as a red solid line. In contrast, sharp spin waves having an energy gap $\Delta$ of $\sim 7\text{meV}$ are observed in the ordered phase at $T=140\text{K}$.

Figure 5

(Color online) Magnetic excitations in ${\text{CaFe}}_2{\text{As}}_2$ measured on the MAPS spectrometer with an incident energy of $E_i=100\text{meV}$ at $T=10\text{K}$ (left panel) and 180 K (right panel). The data shows magnetic intensity as a function of the $\left[h,h\right]$ direction and the energy transfer after averaging over the transverse $\left[h,-h\right]$ 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. Excitations below $T_N$ are consistent with steep spin waves and diffuse magnetic excitations are observed above $T_N$ at $T=180\text{K}$.

Figure 6

(Color online) Constant energy slices $\left(\Delta E=\pm 5\text{meV}\right)$ through the excitation spectrum of ${\text{CaFe}}_2{\text{As}}_2$ in the $\left(h,k\right)$ plane at $T=10$ and 180 K, as observed on MAPS. Energy slices are chosen to correspond to odd values of $L$. Intensity shown is in absolute units ($\text{mbar}\text{ns}{\text{Sr}}^{-1}{\text{meV}}^{-1}$ per formula unit). Below $T_N$, well-defined spin waves are observed around ${\mathbf{Q}}_{\text{AFM}}$ (see also Ref. 16). Above $T_N$, strong but short-range magnetic correlations remain around ${\mathbf{Q}}_{\text{AFM}}$ and extend up to at least 60 meV. Solid lines in panel (c) show the directions along which the cuts in Fig. 7 are taken with $(+)$ designating longitudinal cuts and $(-)$ transverse cuts.

Figure 7

Longitudinal $(+)$ and transverse $(-)$ constant-energy cuts measured around $\mathbf{Q}={\mathbf{Q}}_{\text{AFM}}=\left(1/2,1/2,L\right)$ on the MAPS spectrometer. The cuts are taken at $\hslash \omega =12$, 39, and 60 meV, which correspond to $L=1$, 3, and 5, respectively. Solid lines are best fits of Eq. (6) to the data. Dotted lines indicate the fitted background and the dashed lines show the instrumental resolution function.

Figure 8

Net magnetic neutron-scattering intensity as a function of energy measured on MAPS around ${\mathbf{Q}}_{\text{AFM}}=\left(1/2,1/2,L\right)$ after subtraction of a nonmagnetic background at $\mathbf{Q}=\left(0.15,0.5,L\right)$. The integration ranges used in MSLICE are such that $\Delta h=\pm 0.05$. Lines are the best fits of Eq. (5) to the data.

Figure 9

Fits of Eq. (5) to constant energy cuts at 5 meV along $h$ and $L$, as a function of increasing temperature $\left(180\le T\le 300\text{K}\right)$. Circles are experimental data measured on HB3 with $E_f=14.7\text{meV}$. Solid lines are the best fit to the data. Both the $h$ and $L$ scans were fit to Eq. (5) (as shown in Fig. 3 over a wider range of $h$ and $L$). The data at $T=140\text{K}$ was fit to a spin-wave model (as described in Ref. 15) and is shown here for comparison.

Figure 10

(Color online) Schematic of the anisotropic scattering in the Fe layer at ${\mathbf{Q}}_{\text{AFM}}$. The inset shows roughly the extent of spin correlations in the layer which result in anisotropic scattering at ${\mathbf{Q}}_{\text{AFM}}$. Correlations transverse to ${\mathbf{Q}}_{\text{AFM}}$ are shorter due to the frustrating effect of antiferromagnetic $J_1$ interactions on ferromagnetic bonds (shown in red) whereas $J_1$ strengthens correlations along the antiferromagnetic bonds extending in the longitudinal direction.