Inelastic Neutron-Scattering Measurements of a Three-Dimensional Spin Resonance in the FeAs-Based ${\mathrm{BaFe}}_{1.9}{\mathrm{Ni}}_{0.1}{\mathrm{As}}_2$ Superconductor

We use inelastic neutron scattering to study magnetic excitations of the FeAs-based superconductor ${\mathrm{BaFe}}_{1.9}{\mathrm{Ni}}_{0.1}{\mathrm{As}}_2$ above and below its $T_c$ ($=20\mathrm{K}$). In addition to gradually open a spin gap at the in-plane antiferromagnetic ordering wave vector (1, 0, 0), the effect of superconductivity is to form a three-dimensional resonance with clear dispersion along the $c$ axis. The intensity of the resonance develops like a superconducting order parameter, and the mode occurs at distinctively different energies at (1, 0, 0) and (1, 0, 1). If the resonance energy is associated with the superconducting gap energy $\Delta$, then $\Delta$ is dependent on the wave vector transfers along the $c$ axis. These results suggest that one must be careful in interpreting the superconducting gap energies obtained by surface sensitive probes such as scanning tunneling microscopy and angle resolved photoemission.

Figure 1

(a) Schematic diagram of the Fe spin ordering in the ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ and we use the same unit cell for ${\mathrm{BaFe}}_{1.9}{\mathrm{Ni}}_{0.1}{\mathrm{As}}_2$ for easy comparison. (b) Reciprocal space probed in our experiment. (c) Resistivity and magnetic susceptibility measurements of $T_c$. (d,e) Elastic neutron-scattering $L$ scans through (1, 0, 1) and (1, 0, 3) magnetic Bragg peaks at 30 K, showing no evidence of static long-range AF order [15, 16].

Figure 2

Constant-energy scans around the (1, 0, 0) and (1, 0, 1) positions for $\hslash \omega =2$, 6, and 8.5 meV obtained with $k_f=1.55{\AA }^{-1}$. (a–c) $Q$ scan along the [$H$, 0, 0] direction for $\hslash \omega =2$, 6, and 8 meV at 30 and 3 K. The inset in (a) shows the temperature difference plot and a Gaussian fit to the data. The missing low-$Q$ data for scans in (b) and (c) are due to kinematic constraint. (d) $Q$ scan along the [1, 0, $L$] direction for $\hslash \omega =8.5\mathrm{meV}$ at 3 K. Note two clear peaks centered at (1, 0, $-1$) and (1, 0, 1), respectively. The dashed-line peak is the low-temperature spin waves of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ at $\hslash \omega =10\mathrm{meV}$ from Fig. 2f in 21.

Figure 3

(a) Energy scans at $Q=(1,0,0)$ from 2 to 9 meV at 30 and 3 K with $k_f=1.55{\AA }^{-1}$. The broad peak in energy near 6 meV was also seen in the background scattering collected at the (1.3, 0, 0) position (not shown) and were not intrinsic properties of the material. (b) Intensity difference between the 3 and 30 K data at $Q=(1,0,0)$. The negative scattering below 4 meV indicates the opening of a spin gap, while positive scattering above 6 meV suggests a magnetic intensity gain below $T_c$. (c) Temperature dependence of the scattering obtained at $Q=(1,0,0)$ and $\hslash \omega =2\mathrm{meV}$ with the vertical arrow indicating $T_c$. The solid line shows the expected $T$-dependent scattering due to the Bose population factor.

Figure 4

(a) Energy scans at $Q=(1,0,0)$ from 5 to 13 meV at 30 and 3 K with $k_f=2.662{\AA }^{-1}$. The background scattering at $Q=(1.3,0,-1)$ is weakly $T$ dependent between 30 and 3 K. (b) The temperature difference scattering between 3 and 30 K shows a clear resonant peak at $\hslash \omega =9.1\pm 0.4\mathrm{meV}$. (c) Energy scans at $Q=(1,0,-1)$ from 2 to 13 meV at 30 and 3 K. (d) The temperature difference plot confirms that the mode has now moved to $7.0\pm 0.5\mathrm{meV}$. (e) Wave vector dependence of the scattering at 30 and 3 K for $\hslash \omega =7\mathrm{meV}$, confirming that the resonance intensity gain occurs at $Q=(1,0,-1)$. (f) Temperature dependence of the scattering at $Q=(1,0,-1)$ and $\hslash \omega =7\mathrm{meV}$ shows a clear order-parameter-like increase below $T_c$. The solid line is the best fit to the data using $I=I_0+k(1-(T/T_c){)}^{\beta }$ yielding $\beta =0.5$ and $T_c=20\mathrm{K}$. The intensity differences in (c) and (f) are within $2\sigma$.