Magnonlike Dispersion of Spin Resonance in Ni-doped $\mathrm{Ba}{\mathrm{Fe}}_2{\mathrm{As}}_2$

Inelastic neutron scattering measurements on $\mathrm{Ba}({\mathrm{Fe}}_{0.963}{\mathrm{Ni}}_{0.037}{)}_2{\mathrm{As}}_2$ manifest a neutron spin resonance in the superconducting state with anisotropic dispersion within the Fe layer. Whereas the resonance is sharply peaked at the antiferromagnetic (AFM) wave vector ${\mathbf{Q}}_{\mathrm{AFM}}$ along the orthorhombic $\mathbf{a}$ axis, the resonance disperses upwards away from ${\mathbf{Q}}_{\mathrm{AFM}}$ along the $\mathbf{b}$ axis. In contrast to the downward dispersing resonance and hourglass shape of the spin excitations in superconducting cuprates, the resonance in electron-doped $\mathrm{Ba}{\mathrm{Fe}}_2{\mathrm{As}}_2$ compounds possesses a magnonlike upwards dispersion.

Figure 1

(a) Spin fluctuations in the cuprates showing the hourglass shape of the spin excitations. The downward dispersing part [gray (orange) line] is the resonance mode for a $d$-wave gap and the upward part (black line) is the competing AFM spin fluctuations. (b) Spin fluctuations in our Ni-doped iron arsenide superconductor where both the resonance and competing AFM fluctuations disperse upwards.

Figure 2

The imaginary part of the magnetic susceptibility measured on HB3 at (a) ${\mathbf{Q}}_{\mathrm{AFM}}=(1,0,1)$, (c) $\mathbf{Q}=(1,-0.1,1)$, and (e) $\mathbf{Q}=(1,-0.15,1)$ in the normal state at $T=20\mathrm{K}$ (filled circles) and the superconducting state at $T=4\mathrm{K}$ (open circles). Solid red lines are model calculations of the normal state susceptibility assuming the NAFL spin fluctuations, as described in the text. The difference between superconducting and normal state susceptibilities is shown at (b) ${\mathbf{Q}}_{\mathrm{AFM}}$, (d) $\mathbf{Q}=(1,-0.1,1)$, and (f) $\mathbf{Q}=(1,-0.15,1)$. Black lines are guide to the eyes and arrows indicate the resonance peak obtained from Gaussian fit.

Figure 3

(a) The imaginary part of the magnetic susceptibility measured on HB3 at various energy transfers along the [0, $K$, 0] direction transverse to ${\mathbf{Q}}_{\mathrm{AFM}}=(1,0,1)$ in the normal state at $T=20\mathrm{K}$ (filled circles) and the superconducting state at $T=4\mathrm{K}$ (open circles). (b) The difference of superconducting minus normal state susceptibilities from (a). (c) The susceptibilities along the [$H$, 0, $H$] direction longitudinal to ${\mathbf{Q}}_{\mathrm{AFM}}$ in the normal (filled circles) and superconducting states (open circles) and (d) the difference. Red and blue lines are model calculations of the normal state susceptibility and superconducting resonance, respectively, as described in the text. (e) CNCS measurements of the normal state spin fluctuations in the ($H$, $K$, 1) plane at $\omega =6\mathrm{meV}$ and $T=25\mathrm{K}$. (f) Fit of the CNCS data to a model of NAFL, as described in the text. (g) Contour plot showing the difference of the magnetic susceptibilities in the superconducting and normal states measured on HB3 depicting the dispersion of the resonance in the transverse direction. Symbols correspond to fitted values of the resonance maxima and the line is a fit to the magnonlike dispersion given in Eq. (4). The vertical error bars indicate the energy resolution of HB3 and horizontal error bars indicate the FWHM of fits.