Polarized neutron scattering studies of magnetic excitations in electron-overdoped superconducting BaFe${}_{1.85}$Ni${}_{0.15}$As${}_2$

We use polarized inelastic neutron scattering to study low-energy spin excitations and their spatial anisotropy in electron-overdoped superconducting BaFe${}_{1.85}$Ni${}_{0.15}$As${}_2$ ($T_c=14$ K). In the normal state, the imaginary part of the dynamic susceptibility ${\chi }^{\prime \prime }(Q,\omega )$ at the antiferromagnetic wave vector $\mathbf{Q}=(0.5,0.5,1)$ increases linearly with energy for $E\le 13$ meV. Upon entering the superconducting state, a spin gap opens below $E\approx 3$ meV and a broad neutron spin resonance appears at $E\approx 7$ meV. Our careful neutron polarization analysis reveals that ${\chi }^{\prime \prime }(Q,\omega )$ is isotropic for the in-plane and out-of-plane components in both the normal and superconducting states. A comparison of these results with those of undoped BaFe${}_2$As${}_2$ and optimally electron-doped BaFe${}_{1.9}$Ni${}_{0.1}$As${}_2$ ($T_c=20$ K) suggests that the spin anisotropy observed in BaFe${}_{1.9}$Ni${}_{0.1}$As${}_2$ is likely due to its proximity to the undoped BaFe${}_2$As${}_2$. Therefore, the neutron spin resonance is mostly isotropic in the optimal and electron overdoped iron pnictides, consistent with a singlet to triplet excitation and isotropic paramagnetic scattering.

Figure 1

(a) The schematic antiferromagnetic and superconducting phase diagram of BaFe${}_{2-x}$Ni${}_x$As${}_2$ as determined from neutron diffraction experiments (Ref. 11). The present composition is highlighted with an arrow. The inset shows an illustration of quasiparticle excitations from the hole Fermi pocket at the $\Gamma$ point to the electron pocket at the $M$ point as predicted by Fermi surface nesting theories. (b) The three neutron polarization directions ($x$, $y$, and $z$) oriented in the $(H,H,L)$ plane of the reciprocal space. (c) The relationship between magnetic components $M_y$ and $M_z$ measured by polarized neutron scattering and in-plane ($M_{110}$) and out-of-plane ($M_{001}$) dynamic spin susceptibility. The solid arrow denotes the measured magnetic component in a SF channel, and the dashed arrow denotes the component measured in a NSF channel. In this geometry, we have $M_z\propto M_{1\overline{1}0}=M_{110}$, due to tetragonal symmetry, and $M_y\sim M_{001}$, given that $\theta$ is a small value.

Figure 2

Constant-$Q$ scans at $\mathbf{Q}=(0.5,0.5,1)$ below and above $T_c$. Using polarized neutrons, we can measure six independent scattering cross sections: incoming neutrons polarized along the $x$, $y$, or $z$ directions, with outgoing neutrons flipped (SF) or not flipped (NSF). (a) The raw data for SF scattering at 2 K, denoted as ${\sigma }_{x,y,z}^{\mathrm{SF}}$; (b) identical scans in NSF channel, or ${\sigma }_{x,y,z}^{\mathrm{NSF}}$; (c) SF scattering ${\sigma }_{x,y,z}^{\mathrm{SF}}$ at 20 K; and (d) NSF scattering ${\sigma }_{x,y,z}^{\mathrm{NSF}}$ at 20 K.

Figure 3

(a) Simulation of unpolarized energy scans using ${\sigma }_{\alpha }^{\mathrm{SF}}+{\sigma }_{\alpha }^{\mathrm{NSF}}$ with $\alpha =x,y,z$ at 2 K and (b) 20 K. The wave vector is fixed at $\mathbf{Q}=(0.5,0.5,1)$. (c) Unpolarized energy scan at $(1/2,1/2,1)$ below and above $T_c$ obtained by adding all six channels together. (d) Temperature difference plot between 2 K and 20 K reveals a neutron spin resonance at $E=7$ meV and negative scattering below 4 meV, very similar to the earlier unpolarized measurements on the same Ni-doping level (Ref. 16).

Figure 4

Neutron polarization analysis used to extract the in-plane ($M_{110}$) and out-of-plane $M_{001}$ components of spin excitations in BaFe${}_{1.85}$Ni${}_{0.15}$As${}_2$ from SF and NSF data in Fig. 2. $M_{110}$ and $M_{001}$ at 2 K are extracted from (a) SF and (b) NSF data in Fig. 2. (d), (e) $M_{110}$ and $M_{001}$ at 20 K. The above analysis is based on the assumption that the background scattering for the $x$, $y$, and $z$ spin polarizations are different [see Eqs. (2) and (3)]. (c) The combination of SF and NSF data at 2 K. (f) The combination of SF and NSF data at 20 K. These data reveal isotropic paramagnetic scattering at the probed energies and temperatures.

Figure 5

Constant-energy scans along the $[H,H,1]$ direction at the resonance energy of $E=7$ meV at 2 K for different neutron polarization directions. (a) Neutron SF scattering cross sections for the $x$, $y$, and $z$ polarization directions. (b) NSF scattering cross sections. A clear peak is seen at $\mathbf{Q}=(0.5,0.5,1)$ in the ${\sigma }_x^{\mathrm{SF}}$ channel that is absent in the ${\sigma }_x^{\mathrm{NSF}}$ channel, thus confirming the magnetic nature of the resonance.

Figure 6

Constant-energy scans along $(0.5,0.5,L)$ at the resonance energy of $E=7$ meV. The ${\sigma }_x^{\mathrm{SF}}$ and ${\sigma }_x^{\mathrm{NSF}}$ data show no $L$ dependence. The solid and dashed lines show the expected magnetic scattering intensity assuming an Fe${}^{2+}$ form factor.

Figure 7

Constant-$Q$ scans at $\mathbf{Q}=(0.5,0.5,2)$ at 2 K. (a) The three neutron SF scattering energy scans below $T_c$, marked as ${\sigma }_{x,y,z}^{\mathrm{SF}}$. (b) Identical scans in the neutron NSF channel, marked as ${\sigma }_{x,y,z}^{\mathrm{NSF}}$.

Figure 8

Constant-$Q$ scans at $\mathbf{Q}=(0.5,0.5,2)$ at 2 K. The in-plane ($M_{110}$) and out-of-plane ($M_{001}$) magnetic response extracted from the (a) SF data and (b) NSF data, respectively; (c) the combination of SF and NSF data at 2 K shows no difference between the two magnetic moment components, indicating isotropic paramagnetic scattering.