Anisotropic and quasipropagating spin excitations in superconducting $\text{Ba}{\left({\text{Fe}}_{0.926}{\text{Co}}_{0.074}\right)}_2{\text{As}}_2$

Inelastic neutron scattering from superconducting (SC) $\text{Ba}{\left({\text{Fe}}_{0.926}{\text{Co}}_{0.074}\right)}_2{\text{As}}_2$ reveals anisotropic and quasi-two-dimensional (2D) magnetic excitations close to ${\mathbf{Q}}_{\text{AFM}}=\left(\frac{1}{2}\frac{1}{2}\right)$ - the 2D antiferromagnetic (AFM) wave vector of the parent ${\text{BaFe}}_2{\text{As}}_2$ compound. The correlation length anisotropy of these low-energy fluctuations is consistent with spin nematic correlations in the $J_1\text{−}{J}_2$ model with $J_1/J_2\sim 1$. The spin resonance at $\sim 8.3\text{meV}$ in the SC state displays the same anisotropy. The anisotropic fluctuations experimentally evolve into two distinct maxima only along the direction transverse to ${\mathbf{Q}}_{\text{AFM}}$ above $\sim 80\text{meV}$ indicating unusual quasipropagating excitations.

Figure 1

(Color online) (a) A single Fe layer showing a local spin configuration corresponding to ${\mathbf{Q}}_{\text{AFM}}=\left(\frac{1}{2}\frac{1}{2}\right)$ and NN (NNN) exchange interactions $J_1$ $\left(J_2\right)$. The tetragonal and Fe lattice unit cells are shown as dashed squares. Overview of the ${\mathbf{Q}}_{ab}=\mathbf{Q}-\left(\mathbf{Q}\cdot \hat{\mathbf{c}}\right)\hat{\mathbf{c}}$ dependence at 4 K measured on ARCS with (b) $E_{\text{i}}=50\text{meV}$ and $\hslash \omega =20\pm 4\text{meV}$ and (c) $E_{\text{i}}=250\text{meV}$ and $\hslash \omega =75\pm 15\text{meV}$. An empty sample-holder background was subtracted. The dashed lines in [(b) and (c)] show the Brillouin-zone boundary of the Fe square lattice.

Figure 2

(Color online) Energy and wave-vector dependences around ${\mathbf{Q}}_{ab}=\left(\frac{1}{2}\frac{1}{2}\right)$ [(a) and (c)–(f)] in the SC state and (b) in the normal state. (a) and (b) show the $\mathbf{Q}=\left(HK0\right)$ dependence at the resonance energy $\sim 8\text{meV}$ with the same intensity scale from HB-3. [(c)–(f)] Integrated data over (c) 17–24 meV, (d) 40–50 meV, (e) 70–80 meV, and (f) 100–136 meV with (c) $E_{\text{i}}=50\text{meV}$ and [(d)–(f)] 250 meV averaged over two quadrants from ARCS. An empty sample-holder background was subtracted.

Figure 3

(Color online) [(a)–(e)] LO and [$\left({\text{a}}^{\prime }\right)$–$\left({\text{e}}^{\prime }\right)$] TR scans (circles) around ${\mathbf{Q}}_{ab}=\left(\frac{1}{2}\frac{1}{2}\right)$ with $E_{\text{i}}=250\text{meV}$ and energy transfers as indicated at 4 K from ARCS. The approximate $L$ (r.l.u.) ranges are [(a) and $\left({\text{a}}^{\prime }\right)$] [6.4, 7.5], [(b) and $\left({\text{b}}^{\prime }\right)$] [4.6, 5.8], [(c) and $\left({\text{c}}^{\prime }\right)$] [3.2, 3.8], [(d) and $\left({\text{d}}^{\prime }\right)$] [2.7, 3.2], and [(e) and $\left({\text{e}}^{\prime }\right)$] [2.2, 2.7]. The solid lines are fits of [(a)–(e) and $\left({\text{c}}^{\prime }\right)$–$\left({\text{e}}^{\prime }\right)$] the diffusive model and [$\left({\text{a}}^{\prime }\right)$ and $\left({\text{b}}^{\prime }\right)$] the ballistic model. The dashed lines are calculated with [$\left({\text{a}}^{\prime }\right)$ and $\left({\text{b}}^{\prime }\right)$] the diffusive model and [$\left({\text{c}}^{\prime }\right)$–$\left({\text{e}}^{\prime }\right)$] the ballistic model with fitted parameters held fixed. The horizontal bars in (a), $\left({\text{a}}^{\prime }\right)$, (e), and $\left({\text{e}}^{\prime }\right)$ represent the expected $q$ resolutions. (f) compares the width of single Lorentzian fits along LO (circles) and TR (triangles) directions to the HWHM of the diffusive model (lines). $\left({\text{f}}^{\prime }\right)$ compares the position of TR Lorentzian peaks (squares) to the dispersion (slanted dashed line) and peak splitting of the ballistic model (solid line). The horizontal dashed line corresponds to the energy $c/{\xi }_{\text{E}}$ as described in the text.

Figure 4

(Color online) (a) Energy dependence of INS at $\mathbf{Q}=\left(\frac{1}{2}\frac{1}{2}0\right)$ below (5 K) and above (30 K) $T_{\text{c}}$ (solid symbols) after background subtraction. The solid lines are fits as described in the text. (b) Raw scattering data as well as their respective backgrounds taken at $\mathbf{Q}=\left(0.6830.1830\right)$ from HB-3.