Electron-doping evolution of the low-energy spin excitations in the iron arsenide superconductor ${\text{BaFe}}_{2-x}{\text{Ni}}_x{\text{As}}_2$

We use elastic and inelastic neutron scattering to systematically investigate the evolution of the low-energy spin excitations of the iron arsenide superconductor ${\text{BaFe}}_{2-x}{\text{Ni}}_x{\text{As}}_2$ as a function of nickel doping $x$. In the undoped state, ${\text{BaFe}}_2{\text{As}}_2$ exhibits a tetragonal-to-orthorhombic structural phase transition and simultaneously develops a collinear antiferromagnetic (AF) order below $T_N=143\text{K}$. Upon electron doping of $x=0.075$ to induce bulk superconductivity with $T_c=12.2\text{K}$, the AF ordering temperature reduces to $T_N\approx 58\text{K}$. We show that the appearance of bulk superconductivity in ${\text{BaFe}}_{1.925}{\text{Ni}}_{0.075}{\text{As}}_2$ coincides with a dispersive neutron spin resonance in the spin excitation spectra and a reduction in the static ordered moment. For optimally doped ${\text{BaFe}}_{1.9}{\text{Ni}}_{0.1}{\text{As}}_2$ $\left(T_c=20\text{K}\right)$ and overdoped ${\text{BaFe}}_{1.85}{\text{Ni}}_{0.15}{\text{As}}_2$ $\left(T_c=14\text{K}\right)$ superconductors, the static AF long-range order is completely suppressed and the spin excitation spectra are dominated by a resonance and spin gap at lower energies. We determine the electron-doping dependence of the neutron spin resonance and spin gap energies and demonstrate that the three-dimensional nature of the resonance survives into the overdoped regime. If spin excitations are important for superconductivity, these results would suggest that the three-dimensional characters of the electronic superconducting gaps are prevalent throughout the phase diagram and may be critical for superconductivity in these materials.

Figure 1

(Color online) (a) Electronic phase diagram of ${\text{BaFe}}_{2-x}{\text{Ni}}_x{\text{As}}_2$ as determined from our previous (Refs. 21, 22, 43) and current neutron scattering works. Inset shows schematic illustration of quasiparticle excitations from the hole pocket at the $\Gamma$ point to the electron pocket at the $M$ point as predicted by various theories (Refs. 15, 16, 17, 18). [(b) and (c)] Temperature dependence of the Meissner and shielding signals on thin slabs of ${\text{BaFe}}_{1.925}{\text{Ni}}_{0.075}{\text{As}}_2$ ($V=2.17\times 0.76\times 0.058{\text{mm}}^3$ and mass 0.62 mg) and ${\text{BaFe}}_{1.85}{\text{Ni}}_{0.15}{\text{As}}_2$ ($V=4.16\times 1.16\times 0.092{\text{mm}}^3$ and mass 2.88 mg). These measurements were taken in zero-field cooling (ZFC) with 5 Oe applied field along the thin slab’s direction. The superconducting volume fractions were estimated to be about 100% for both samples. (d) Temperature dependence of the $Q=\left(0.5,0.5,3\right)$ magnetic Bragg peak in ${\text{BaFe}}_{1.925}{\text{Ni}}_{0.075}{\text{As}}_2$, showing a clear anomaly at $T_N$ and $T_c$. Inset shows an expanded view of the $Q=\left(0.5,0.5,3\right)$ magnetic Bragg peak near $T_c$. (e) Temperature dependence of the quasielastic scattering at $E=1.5\text{meV}$ and $Q=\left(0.525,0.525,1\right)$ shows a clear anomaly at $T_N=58\text{K}$. The rather high background scattering in (e) may be due to the fact that the probed energy is too close to the elastic scattering.

Figure 2

(Color online) (a) Energy scans at $Q=\left(0.5,0.5,0\right)$ (signal) and $Q=\left(0.7,0.7,0\right)$ (background) positions above and below $T_c$ for ${\text{BaFe}}_{1.925}{\text{Ni}}_{0.075}{\text{As}}_2$. (b) Temperature difference plot (low temperature minus high temperature) in $S\left(Q,\omega \right)$ shows a clear neutron spin resonance at $E=7\text{meV}$ below $T_c$. Solid line is a guide to the eye. (c) Estimation of the temperature dependence of ${\chi }^{″}\left(Q,\omega \right)$ above and below $T_c$ using the background determined both from constant-energy scans and from constant-$Q$ scans at background position.

Figure 3

(Color online) (a) Constant-energy scans near the resonance energy $\left(E=7\text{meV}\right)$ along the $\left(H,H,0\right)$ direction across $T_c$ for ${\text{BaFe}}_{1.925}{\text{Ni}}_{0.075}{\text{As}}_2$. The scattering clearly increases at the $Q=\left(0.5,0.5,0\right)$ below $T_c$. The small peak at $Q=\left(0.6,0.6,0\right)$ is spurious. (b) Temperature difference plot confirms the intensity gain at $Q=\left(0.5,0.5,0\right)$ below $T_c$. (c) Wave-vector scans at $E=3\text{meV}$. Here, the scattering at $Q=\left(0.5,0.5,0\right)$ decreases below $T_c$ but there is no spin gap at $E=3\text{meV}$. The scattering near $Q=\left(0.57,0.57,0\right)$ in the normal state is spurious.

Figure 4

(Color online) (a) Constant-$Q$ scans at $Q=\left(0.5,0.5,1\right)$ above and below $T_c$ for ${\text{BaFe}}_{1.925}{\text{Ni}}_{0.075}{\text{As}}_2$. The scattering shows clear asymmetric enhancement around $E=5\text{meV}$ below $T_c$. (b) Temperature difference plot reveals a neutron spin resonance at $E=5\text{meV}$, clearly below the energy of the mode at $Q=\left(0.5,0.5,0\right)$ as shown in Fig. 2.

Figure 5

(Color online) (a) $Q$-scans along the $\left(H,H,1\right)$ direction at $E=2.5\text{meV}$ above and below $T_c$ for ${\text{BaFe}}_{1.925}{\text{Ni}}_{0.075}{\text{As}}_2$. (b) Temperature difference plot shows that the scattering at $Q=\left(0.5,0.5,1\right)$ and $E=2.5\text{meV}$ decreases below $T_c$. (c) Identical $Q$-scans across $T_c$ at the resonance energy of $E=5.5\text{meV}$. The scattering enhances below $T_c$. (d) Temperature difference plot between 2 and 20 K, showing clear field-induced scattering below $T_c$ at $Q=\left(0.5,0.5,1\right)$.

Figure 6

(Color online) (a) Temperature dependence of the $E=7\text{meV}$ scattering at $Q=\left(0.5,0.5,0\right)$ for ${\text{BaFe}}_{1.925}{\text{Ni}}_{0.075}{\text{As}}_2$. The scattering increases in intensity below $T_c$ of 12.2 K.

Figure 7

(Color online) Constant-energy scans along the $\left(0.5,0.5,L\right)$ (signal) and $\left(0.7,0.7,L\right)$ (background) directions at $E=3\text{meV}$ and various temperatures. (a) The scattering at 2 and 20 K shows well-defined peaks centered at $L=\pm 1$. Fourier transform of these peaks gives a $c$-axis spin-spin correlation length of $\sim 14\text{Å}$. (b) Signal and background scattering at 2 K. Solid lines are Gaussian fits to the data. Dashed line shows the expected magnetic scattering at $Q=\left(0.5,0.5,3\right)$ assuming ${\text{Fe}}^{2+}$ form factor. The absence of clear peaks at $L=\pm 3$ suggests that magnetic scattering in ${\text{BaFe}}_{1.925}{\text{Ni}}_{0.075}{\text{As}}_2$ damps out much faster than expected. (c) Similar scans at 50 and 70 K. (d) Solid lines show the effect of Bose population factor as a function of increasing temperature if one normalizes the magnetic scattering above background at 2 K. The magnetic intensity changes in the system clearly do not obey the Bose statistics, indicating that the scattering is not spin waves.

Figure 8

(Color online) Constant-energy scans along the $\left(0.5,0.5,L\right)$ (signal) and $\left(0.7,0.7,L\right)$ (background) directions at the resonance energy of $E=5.5\text{meV}$ and various temperatures. (a) $c$-axis scattering at 70 K. Solid line shows the Gaussian fits to the data using ${\text{Fe}}^{2+}$ form factor, which describes the data reasonably well. (b) Signal and background scattering at 50 K. The data again show clear peaks at $L=\pm 1$ but much weaker peaks at $L=\pm 3$. (c) Signal and background scattering at 2 and 20 K. Superconductivity clearly enhances magnetic scattering at $L=0$ and $L=\pm 1$. The spin-spin correlation length is again about $14\text{Å}$ and is weakly temperature dependent in the probed temperature range (2–70 K).

Figure 9

(Color online) $L$ dependence of the magnetic scattering for ${\text{BaFe}}_{1.925}{\text{Ni}}_{0.075}{\text{As}}_2$. (a) Identical scans as Fig. 8 except we now change the excitation energy to $E=7\text{meV}$. Comparison of the 2 and 20 K data here indicates that the magnetic scattering enhancement below $T_c$ at $L=0$ is larger than that at $L=1$. (b) Signal and background scattering at 50 K. Solid line shows the expected $L$ dependence of the magnetic scattering assuming simple ${\text{Fe}}^{2+}$ form factor, which clearly fails to describe the data.

Figure 10

(Color online) Summary of constant-$Q$ scans at various temperatures for ${\text{BaFe}}_{1.85}{\text{Ni}}_{0.15}{\text{As}}_2$ with $E_f=5$ and 13.5 meV. (a) Energy dependence of scattering at $Q=\left(0.5,0.5,0\right)$ above and below $T_c$. The scattering shows a clear drop in intensity below $E=4\text{meV}$ and enhancement around 8 meV. One can only probe magnetic scattering below $E=9\text{meV}$ due to kinematic constraints with $E_f=5\text{meV}$. Circles are background scattering estimated from constant-energy scans at $E=1$, 4, and 6 meV. (b) Energy dependence of the scattering above and below $T_c$, now at $Q=\left(0.5,0.5,1\right)$. (c) Temperature difference plot between 4 and 20 K showing the intensity gain below $T_c$ near $E=8\text{meV}$. (d) Temperature difference data confirm the formation of the neutron spin resonance at $E=6\text{meV}$. (e) Our estimated ${\chi }^{″}\left(Q,\omega \right)$ for ${\text{BaFe}}_{1.85}{\text{Ni}}_{0.15}{\text{As}}_2$ above and below $T_c$ at $Q=\left(0.5,0.5,0\right)$, after subtracting the background and correcting for the Bose factor. The magnitude of the superconducting spin gap is about $E\approx 2.5\text{meV}$. (f) ${\chi }^{″}\left(Q,\omega \right)$ for ${\text{BaFe}}_{1.85}{\text{Ni}}_{0.15}{\text{As}}_2$ above and below $T_c$ at $Q=\left(0.5,0.5,1\right)$. The system again has a spin gap of $\sim 2\text{meV}$ in the superconducting state. (g) Identical scan as that of (a) except we used $E_f=13.5\text{meV}$. Superconductivity-induced neutron spin resonance can now be seen around $E=8\text{meV}$. (h) Temperature difference plot confirms the presence of the resonance at $E=8\text{meV}$.

Figure 11

(Color online) Summary of constant-energy scans at an energy below the spin gap energy and at the resonance energy below and above $T_c$. (a) $Q$ scan along the $\left[H,H,0\right]$ direction below and above $T_c$ at $E=1\text{meV}$. There is a clear peak centered at (0.5,0.5,0) that disappears below $T_c$, thus suggesting the opening of a spin gap at $E=1\text{meV}$ and (0.5,0.5,0). (b) Similar scan along the $\left[H,H,1\right]$ direction, again indicating the opening a spin gap at $E=1\text{meV}$ and (0.5,0.5,1). [(c) and (d)] Temperature-difference plots confirm that superconductivity-induced spin gaps occur at (0.5,0.5,0) and (0.5,0.5,1) positions. (e) Constant-energy scans along the $\left[H,H,0\right]$ direction below and above $T_c$ at the resonance energy of $E=8\text{meV}$. (f) Similar scans at $E=6\text{meV}$ along the $\left[H,H,1\right]$ direction. In both cases, we find that superconductivity-induced changes happen at the expected wave vectors. (g) Temperature dependence of the scattering at $E=8\text{meV}$ and $Q=\left(0.5,0.5,0\right)$. Data show clear order-parameter-like increase below $T_c$, a hallmark of the neutron spin resonance.

Figure 12

(Color online) Summary of electron-doping dependence of the neutron spin resonance energies at $Q=\left(0.5,0.5,0\right)$ and (0.5,0.5,1) as a function of $T_c$. Data for ${\text{BaFe}}_{2-x}{\text{Ni}}_x{\text{As}}_2$ are from Refs. 21, 22, 43, 46 and present work. Data for ${\text{BaFe}}_{2-x}{\text{Co}}_x{\text{As}}_2$ are from Refs. 20, 24, 25, 26. Solid lines are linear fits to the data.