Doping dependence of spin dynamics in electron-doped $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$

The spin dynamics in single crystal, electron-doped $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ has been investigated by inelastic neutron scattering over the full range from undoped to the overdoped regime. We observe damped magnetic fluctuations in the normal state of the optimally doped compound $\left(x=0.06\right)$ that share a remarkable similarity with those in the paramagnetic state of the parent compound $\left(x=0\right)$. In the overdoped superconducting compound $\left(x=0.14\right)$, magnetic excitations show a gaplike behavior, possibly related to a topological change in the hole Fermi surface (Lifshitz transition) while the imaginary part of the spin susceptibility ${\chi }^{″}$ prominently resembles that of the overdoped cuprates. For the heavily overdoped, nonsuperconducting compound $\left(x=0.24\right)$ the magnetic scattering disappears, which could be attributed to the absence of a hole Fermi-surface pocket observed by photoemission.

Figure 1

(Color online) Constant-$Q$ scans were measured on samples of four cobalt concentrations (a) $x=0$ at $Q=\left(1,0,1\right)$ (BT7), (b) $x=0.06$ at $Q=\left(1,0,1\right)$ (HB3), (c) $x=0.14$ at $Q=\left(1,0,0\right)$ (GPTAS), and (d) $x=0.24$ (HB3). Background is shown by open symbols. For $x=0$, background was estimated from constant-energy scans at $\hslash \omega =3$, 5, 8, and 15 meV. In (a), open red circles and open blue squares denote background calculated from constant-energy scans at 140 K and 250 K, respectively. For $x=0.06$ and 0.14 background was measured away from the peak positions at $Q=\left(1.2,0,1\right)$ and (3,0,0), respectively. For $x=0.24$, both constant-$Q$ and constant-energy scans do not show scattering intensity above background, which was measured at $Q=\left(1.5,0,1\right)$. The dotted lines in (a)–(c) denote the fitted background

Figure 2

Representative [(a)–(d)] in-plane and [(e)–(h)] out-of-plane constant-energy scans at $\hslash \omega =5\text{meV}$ in the paramagnetic state of the parent compound. The solid lines denote the results of the global fit.

Figure 3

Representative [(a) and (b)] in-plane and [(c) and (d)] out-of-plane constant-energy scans at $\hslash \omega =9\text{meV}$ in the normal state of the optimally doped compound. The solid lines denote the results of the global fit.

Figure 4

(Color online) The background subtracted scattering intensity and the imaginary part of the spin susceptibility ${\chi }^{″}$ at different cobalt concentrations [(a) and (b)] $x=0$ at $Q=\left(1,0,1\right)$, [(c) and (d)] $x=0.06$ at $Q=\left(1,0,1\right)$, and [(e) and (f)] $x=0.14$ at $Q=\left(1,0,0\right)$. The dotted lines are guides to the eye. The solid lines denote the global fits to Eq. (1) convoluted with the resolution function. We note that ${\chi }^{″}\left(Q,\omega \right)$ is identically zero for $\omega =0$ since it is required to be an odd function of $\omega$.

Figure 5

(Color online) The damping constant $\Gamma$ as a function of temperature. Red circles and blue squares represent the damping constants of the parent and optimally doped compounds, respectively. The dotted line shows the linear relation measured on the optimally doped compound $\left(x=0.075\right)$ (Ref. 28). The solid line denotes our result (see the text).