Dispersive spin fluctuations in the nearly optimally doped superconductor $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ $\left(x=0.065\right)$

Inelastic neutron scattering is used to probe the collective spin excitations of the near optimally doped superconductor $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ $\left(x=0.065\right)$. Previous measurements on the antiferromagnetically ordered parents of this material show a strongly anisotropic spin-wave velocity. Here we measure the magnetic excitations up to 80 meV and show that a similar anisotropy persists for superconducting compositions. The dispersive mode measured here connects directly with the spin resonance previously observed in this compound. When placed on an absolute scale, our measurements show that the local- or wave-vector-integrated susceptibility is larger in magnitude than that of the ordered parents over the energy range probed.

Figure 1

(Color online) (a) The antiferromagnetic structure of the parent compound ${\text{BaFe}}_2{\text{As}}_2$. Axes refer to the tetragonal notation used throughout the paper. Solid lines denote the tetragonal unit cell. (b) Exchange couplings between Fe atoms referred to in the text. (c) Schematic illustration of reciprocal space (of a 2D square lattice). The ellipses represent the anisotropic excitations reported in this paper. The wave vectors are used to define the spin-wave velocities.

Figure 2

(Color online) (a)–(e) Constant-energy slices through the magnetic excitations in $\text{Ba}{\left({\text{Fe}}_{0.935}{\text{Co}}_{0.065}\right)}_2{\text{As}}_2$ as observed on MAPS. (f)–(j) Fits to a phenomenological spin-wave cross section [Eqs. (2, 3)]. (k)–(o) Fits to a phenomenological Sato-Maki cross sections [Eq. (6)] [e.g., for (n) $\kappa =0.21\pm 0.09$, $\delta =0.6\pm 0.2$, and $\lambda =5\pm 2$]. The incident energies used were (a) and (b) 60 and 140 meV (c)–(e) and the corresponding $l$ values were (a) and (b) $l=1$, (c) 2.5, (d) 4, and (e) 5.5. The $E_i=140\text{meV}$ data were collected using a proton beam current of $175\mu \text{A}$ for 80 h. A constant background has been subtracted from each plot.

Figure 3

(Color online) Constant $\hslash \omega$ and $l$ cuts along $\left(1/2-h,1/2+h,l\right)$ and $\left(1/2-h,1/2+h,l\right)$ (see Fig. 1) for various values of $\hslash \omega$. The blue solid line is a fit to the SW cross section [Eqs. (2, 3)] and the red dotted line to the Sato-Maki model [Eq. (6)]. Where only one line is drawn, the fits are indistinguishable.

Figure 4

(Color online) The dispersion of the magnetic excitations in $\text{Ba}{\left({\text{Fe}}_{0.935}{\text{Co}}_{0.065}\right)}_2{\text{As}}_2$ for $T=7\text{K}$ as determined from fitting the damped spin-wave cross section [Eqs. (3, 2)] along ${\text{q}}_{\parallel }$ (a) and ${\text{q}}_{\perp }$ (b) compared to that found in ${\text{CaFe}}_2{\text{As}}_2$ (Ref. 17) (blue dashed line) in each case. Symbols denote $l$ values: ◼ ($l$ even); ● ($l$ odd); and ◆ ($l$ noninteger).

Figure 5

(Color online) The local susceptibility ${\chi }^{″}\left(\omega \right)$ at 7 (closed symbols) and 26 K (open symbols). Symbols denote $l$ values: ◼ ($l$ even); ● ($l$ odd); and ◆ ($l$ noninteger). Dashed line shows the local susceptibility for ${\text{CaFe}}_2{\text{As}}_2$ (Refs. 17, 20).