Neutron spin resonance as a probe of the superconducting energy gap of ${\text{BaFe}}_{1.9}{\text{Ni}}_{0.1}{\text{As}}_2$ superconductors

We use inelastic neutron scattering to show that for the optimally electron-doped ${\text{BaFe}}_{1.9}{\text{Ni}}_{0.1}{\text{As}}_2$ $\left(T_c=20\text{K}\right)$ iron arsenide superconductor, application of a magnetic field that partially suppresses the superconductivity and superconducting gap energy also reduces the intensity and energy of the resonance. These results demonstrate that the energy of the resonance is intimately connected to the electron pairing energy, and thus indicate that the mode is a direct probe for measuring electron pairing and superconductivity in iron arsenides.

Figure 1

(Color online) (a) Schematic of the Fe spin ordering in ${\text{BaFe}}_2{\text{As}}_2$. (b) Reciprocal space probed and the direction of applied field in tetragonal notation (Ref. 10). (c) Susceptibility of our sample indicating $T_c=20\text{K}$. The inset shows schematic of how the resonance is produced by quasiparticle excitations between the hole and electron pockets. (d) Energy scans at the signal $Q=\left(0.5,0.5,0\right)$ and background $Q=\left(0.62,0.62,0\right)$ rlu positions for various fields and temperatures. For clarity, the 14.5-T data at 25 K are not shown. (e) Temperature and field dependence of ${\chi }^{″}\left(Q,\omega \right)$ at $Q=\left(0.5,0.5,0\right)$. The black and (blue/grey) solid lines are Lorentzian fits to the resonance on sloped linear backgrounds. Horizontal bar indicates instrumental energy resolution. (f) Difference spectra of the neutron intensity between $T=2\text{K}\left(<T_c\right)$ and $T=25\text{K}\left(T_c+5\text{K}\right)$ at $Q=\left(0.5,0.5,0\right)$ for $B=0$ and a 14.5-T $c$-axis-aligned field. The black dotted lines indicate the expected Zeeman splitting under 14.5-T field using the corresponding instrumental resolution. The green line is the expected resonance scattering profiles at 14.5 T.

Figure 2

(Color online) (a) $h\omega =0\text{meV}$ and (b) $h\omega =2\text{meV}$. Spin-spin correlation length at 2 K and 14.5 T is $\xi =64\pm 16\text{Å}$. Note that the vertical scales for the $B=0\text{-T}$ data in (a) and (b) were offset for clarity; (c) $\hslash \omega =3\text{meV}$ at 2 K. At zero field, $\xi =65\pm 10\text{Å}$. At 14.5 T, $\xi =47\pm 10\text{Å}$; (d) $\hslash \omega =8\text{meV}$ at 2 K. At zero field, $\xi =57\pm 2\text{Å}$. At 14.5 T, $\xi =53\pm 3\text{Å}$; (e) $\hslash \omega =3\text{meV}$ at 25 K. At zero field, $\xi =62\pm 5\text{Å}$. At 14.5 T, $\xi =54\pm 6\text{Å}$; (f) $\hslash \omega =8\text{meV}$ at 25 K. At zero field, $\xi =55\pm 5\text{Å}$. At 14.5 T, $\xi =49\pm 4\text{Å}$. The solid lines are Gaussian fits to the data on linear backgrounds and horizontal bars in (b)–(f) are the instrumental resolution.

Figure 3

(Color online) (a) Temperature dependence of the scattering at $\hslash \omega =2\text{meV}$ and zero field shows the opening of a spin gap slightly below $T_c$ (Refs. 15, 16). (b) The same temperature dependence at 14.5 T. (c) Temperature dependence of the scattering at $\hslash \omega =8\text{meV}$ and zero field displays order parameter like intensity increase below $T_c=20\text{K}$. (d) Application of a 14.5-T field suppresses $T_c$ to $\sim 16\text{K}$.

Figure 4

(Color online) (a) The magnetic field dependence of the scattering at $\hslash \omega =8\text{meV}$, $Q=\left(0.5,0.5,0\right)$, and 2 K. While the solid line is a fit using $I/I_0=1-B/B_{char}$ with $B_{char}\approx 32\text{T}$, the dotted line represents $I/I_0=1-{\left(B/B_{char}\right)}^{1/2}$, where $B_{char}\approx 66\text{T}$. (b) The scattering at 25 K has no observable field dependence. (c) The difference spectrum of the neutron-scattering intensities between zero and 14.5-T field at 2 K and $Q=\left(0.5,0.5,0\right)$.