Dispersion of the superconducting spin resonance in underdoped and antiferromagnetic ${\text{BaFe}}_2{\text{As}}_2$

Inelastic neutron-scattering measurements have been performed on underdoped $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ $\left(x=4.7\mathrm{\%}\right)$ where superconductivity and long-range antiferromagnetic (AFM) order coexist. The magnetic spectrum found in the normal state is strongly damped and develops into a magnetic resonance feature below $T_c$ that has appreciable dispersion along $\mathbf{c}$ axis with a bandwidth of 3–4 meV. This is in contrast to the optimally doped $x=8.0\mathrm{\%}$ composition, with no long-range AFM order, where the resonance exhibits a much weaker dispersion. [see M. D. Lumsden et al., Phys. Rev. Lett. 102, 107005 (2009).] The results suggest that the resonance dispersion arises from interlayer spin correlations present in the AFM ordered state.

Figure 1

(Color online) (a) Monitor-normalized neutron intensity $I\left(\mathbf{Q},\omega \right)$ for $x=4.7\mathrm{\%}$ including background measurement for energy scans at ${\mathbf{Q}}_{\text{AFM}}=\left(\frac{1}{2}\frac{1}{2}1\right)$ both above (25 K, open circles) and below $T_c$ (5 K, filled circles). The arrow shows the location of the resonance. The dark gray shading highlights regions of increased intensity related to the resonance while the light gray shading highlights a loss of intensity. (b) Energy dependence of ${\chi }^{″}\left({\mathbf{Q}}_{\text{AFM}},\omega \right)$ at 5 and 25 K. The solid line is a fit to spin waves described in the text. (c) $\left[HH0\right]$ scans and (d) $\left[00L\right]$ scans through $\left(\frac{1}{2}\frac{1}{2}1\right)$ at 5, 7, and 10 meV. In (c) and (d) solid lines represent fits to the spin-wave model in the normal state. The inset to (d) shows $\left[00L\right]$ scans for $x=8.0\mathrm{\%}$ both above (30 K, open triangles) and below $T_c$ (10 K, filled triangles) at an energy transfer of 9.5 meV (close to the resonance peak) taken from Lumsden et al., Ref. 7.

Figure 2

(Color online) (a) Dispersion of the resonance shown by monitor-normalized constant-$\mathbf{Q}$ energy scans at $\left(\frac{1}{2}\frac{1}{2}L\right)$ for $x=4.7\mathrm{\%}$ for several values of $L$ at temperatures above and below $T_c$. (b) Difference of scattering intensity between temperatures 5 K and 25 K above and below $T_c$, respectively, for both $x=4.7\mathrm{\%}$ (open circles) and 8.0% (filled triangles) at $L=0$, 1/2, and 1. (c) Comparison of the dispersion of the resonance peak energies along the $L$ direction for $x=4.7\mathrm{\%}$ and 8.0%. The $x=8.0\mathrm{\%}$ data are taken from Ref. 7.

Figure 3

(Color online) Contour plots of the magnetic susceptibility as a function of $\hslash \omega$ and $L=1–2$. (a) Measured data at 25 K. The line shows the fitted normal-state spin-wave dispersion. This line also appears in panels (b) and (c). (b) Normal-state damped spin-wave fitting results which have been convoluted with the experimental resolution. (c) Measured data below $T_c$ at 5 K. The lower solid line is a fit to the square data points which represents the peak in the resonance. (d) The measured resonance susceptibility obtained from the difference of the data at 5 K [panel (c)] and 25 K [panel (a)].