Anisotropic neutron spin resonance in superconducting ${\text{BaFe}}_{1.9}{\text{Ni}}_{0.1}{\text{As}}_2$

We use polarized inelastic neutron scattering to show that the neutron spin resonance below $T_c$ in superconducting ${\text{BaFe}}_{1.9}{\text{Ni}}_{0.1}{\text{As}}_2$ $\left(T_c=20\text{K}\right)$ is purely magnetic in origin. Our analysis further reveals that the resonance peak near 7 meV only occurs for the planar response. This challenges the common perception that the spin resonance in the pnictides is an isotropic triplet excited state of the singlet Cooper pairs, as our results imply that only the $S_{001}=\pm 1$ components of the triplet are involved.

Figure 1

(Color online) (a) Crystal structure of ${\text{BaFe}}_2{\text{As}}_2$. (b) Magnetic and superconducting phase diagram of ${\text{BaFe}}_{2-x}{\text{Ni}}_x{\text{As}}_2$ with the present composition highlighted with an arrow (Ref. 13). (c) Schematic showing a fluctuating atomic magnetic moment vector $\mathbf{m}$, and the components $m_y$ and $m_z$ which are probed. Neutron-scattering intensity is related to the square of the fluctuating moment components in the $y$ and $z$ direction, $M_y=⟨m_y^2⟩$ and $M_z=⟨m_z^2⟩$, respectively (which are both defined perpendicular to $x$, where $x$ is parallel to the wave vector $\mathbf{Q}$). (d) Schematic showing crystallographic in-plane (1,1,0), $\left(1,-1,0\right)$, and out of plane (0,0,1) directions compared with the $x$, $y$, and $z$ directions defined above.

Figure 2

(Color online) Energy scans at $\mathbf{Q}=\left(0.5,0.5,1\right)$, showing ${\sigma }_x^{\text{SF}}$ (magnetic) and ${\sigma }_x^{\text{NSF}}$ (nuclear) scattering for (a) 1.5 K and (b) 30 K. (c) $\left(H,H,1.1\right)$ $Q$ scan through the resonance position, showing ${\sigma }_x^{\text{SF}}$ and ${\sigma }_x^{\text{NSF}}$ measured at a constant energy 7 meV. The narrow peak at (0.625,0.625) is temperature-independent spurious scattering. (d) Trajectory in reciprocal space of the $\left(H,H,1.1\right)$ scan. Solid lines are guides to the eyes for all plots except where otherwise stated.

Figure 3

(Color online) Energy scans at $\mathbf{Q}=\left(0.5,0.5,1\right)$. Raw (a) 1.5 K ${\sigma }_{x,y,z}^{\text{SF}}$ and (b) 1.5 K ${\sigma }_{x,y,z}^{\text{NSF}}$ cross-section data. Clear anisotropy is evident because ${\sigma }_y^{\text{SF}}\ne {\sigma }_z^{\text{SF}}$ and ${\sigma }_y^{\text{NSF}}\ne {\sigma }_z^{\text{NSF}}$. (c) and (d) Raw data taken at 30 K. (e) and (f) In-plane and out-of-plane magnetic response [the extracted $M\left(110\right)$ and $M\left(001\right)$ using raw data in Eq. (2), divided by the Bose factor (b.f.)] at 1.5 K and 30 K, respectively. Data in (e) and (f) are also corrected for second-order monitor overcounting.

Figure 4

(Color online) (a)–(c) $Q$ Scans along the $\left(H,H,1.1\right)$ direction at 2.5, 7, and 11 meV, respectively, with all three spin flip cross sections measured. (d) $L$ scan at the resonance energy. Crosses resemble estimated instrumental background points, extracted from the data shown and ${\sigma }_{x,y}^{\text{NSF}}$ (not shown) using Eq. (1) (assuming $b_1\approx b_2$). The solid line shows the expected magnetic scattering assuming an ${\text{Fe}}^{2+}$ form factor.

Figure 5

(Color online) Intensity expected for energy scans at (0.5,0.5,0) for an unpolarized experiment, calculated using $M\left(110\right)$ and $M\left(001\right)$ from the present polarized data.