Measurement of a Double Neutron-Spin Resonance and an Anisotropic Energy Gap for Underdoped Superconducting ${\mathrm{NaFe}}_{0.985}{\mathrm{Co}}_{0.015}\mathrm{As}$ Using Inelastic Neutron Scattering

We use inelastic neutron scattering to show that superconductivity in electron-underdoped ${\mathrm{NaFe}}_{0.985}{\mathrm{Co}}_{0.015}\mathrm{As}$ induces a dispersive sharp resonance near $E_{r1}=3.25\mathrm{meV}$ and a broad dispersionless mode at $E_{r2}=6\mathrm{meV}$. However, similar measurements on overdoped superconducting ${\mathrm{NaFe}}_{0.935}{\mathrm{Co}}_{0.045}\mathrm{As}$ find only a single sharp resonance at $E_r=7\mathrm{meV}$. We connect these results with the observations of angle-resolved photoemission spectroscopy that the superconducting gaps in the electron Fermi pockets are anisotropic in the underdoped material but become isotropic in the overdoped case. Our analysis indicates that both the double neutron spin resonances and gap anisotropy originate from the orbital dependence of the superconducting pairing in the iron pnictides. Our discovery also shows the importance of the inelastic neutron scattering in detecting the multiorbital superconducting gap structures of iron pnictides.

Figure 1

(a) The electronic phase diagram of ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$, where the arrows indicate the Co-doping levels of our samples. The temperature dependence of the bulk susceptibility in the inset shows $T_c=15\mathrm{K}$. (b) The schematics of the $c$-axis dispersion of the double resonances. (c), (d) The schematics of Fermi surfaces and SC gaps in underdoped and overdoped samples near $\Gamma$ and $M$ points [28]. (e) Double resonances obtained by taking temperature difference plots (3 K–28 K) of constant-$Q$ scans at (0.5, 0.5, 0.5) in ${\mathrm{NaFe}}_{0.985}{\mathrm{Co}}_{0.015}\mathrm{As}$. (f) Similar data in ${\mathrm{NaFe}}_{0.935}{\mathrm{Co}}_{0.045}\mathrm{As}$ showing only a single resonance. The horizontal bars in (e) and (f) indicate instrumental energy resolution.

Figure 2

(a)–(c) ${\chi }^{\prime \prime }(Q,E)$ at $\mathbf{Q}=(0.5,0.5,L)$ with $L=0$, 0.25 and 0.5, respectively, at 3, 18, 28 and 40 K. (d)–(g) The difference of $L$-modulations above and below $T_c$ at $E=2$, 3.25, 4.5 and 6 meV, respectively.

Figure 3

(a)–(c) $\mathbf{Q}$ scans along the [$H$, $H$, 0] direction at $E=2\mathrm{meV}$, $E_{r1}=4.5\mathrm{meV}$, and $E_{r2}=6.5\mathrm{meV}$, respectively, with $L=0$. (d)–(f) $\mathbf{Q}$ scans along the [$H$, $H$, 0.5] direction at $E=2\mathrm{meV}$, $E_{r1}=3.25\mathrm{meV}$, and $E_{r2}=6\mathrm{meV}$, respectively, for SC ${\mathrm{NaFe}}_{0.985}{\mathrm{Co}}_{0.015}\mathrm{As}$. The horizontal bars indicate instrumental resolution. The solid lines are fits to Gaussians.

Figure 4

(a) The temperature dependence of AFM peak intensity at $\mathbf{Q}=(0.5,0.5,0.5)$ with vertical dashed line indicating $T_c=15\mathrm{K}$ and $T_N=30\mathrm{K}$. (b) and (c) Temperature dependence of the scattering at $E=2\mathrm{meV}$ at $\mathbf{Q}=(0.5,0.5,0)$ and (0.5, 0.5, 0.5), respectively. Temperature dependence of the scattering at (d) $E_{r1}=3.25\mathrm{meV}$ and (0.5, 0.5, 0.5), (e) $E_{r2}=4.5\mathrm{meV}$ and (0.5, 0.5, 0), and (f) $E_{r2}=6\mathrm{meV}$ and (0.5, 0.5, 0.5).

Figure 5

The imaginary part of the dynamical susceptibility, ${\chi }^{\prime \prime }(\mathbf{Q},\omega )$ at $\mathbf{Q}=(\pi ,0)$ in the SC phase obtained from a five-orbital t-$J_1$-$J_2$ model. For the case of sufficiently large gap anisotropy shown here, two resonance peaks are obtained.