Transition from Three-Dimensional Anisotropic Spin Excitations to Two-Dimensional Spin Excitations by Electron Doping the FeAs-Based ${\mathrm{BaFe}}_{1.96}{\mathrm{Ni}}_{0.04}{\mathrm{As}}_2$ Superconductor

We use neutron scattering to study the effect of electron doping on the structural or magnetic order in ${\mathrm{BaFe}}_2{\mathrm{As}}_2$. In the undoped state, ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ exhibits simultaneous structural and magnetic phase transitions below 143 K. Upon electron doping to form ${\mathrm{BaFe}}_{1.96}{\mathrm{Ni}}_{0.04}{\mathrm{As}}_2$, the system first displays the lattice distortion near $\sim 97\mathrm{K}$, and then orders antiferromagnetically at 91 K before developing weak superconductivity below $\sim 15\mathrm{K}$. The effect of electron doping is to reduce the $c$-axis exchange coupling in ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ and induce quasi-two-dimensional (2D) spin excitations. These results suggest that the transition from 3D spin waves to quasi-2D spin excitations by electron doping is important for the separated structural and magnetic phase transitions in iron arsenides.

Figure 1

(a) Diagram of the parent compound ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ with Fe spin ordering and magnetic exchange couplings depicted. (b) Electronic phase diagram from Ref. 6. (c) Temperature dependence of the resistance showing anomalies at $T_s$, $T_N$, and $T_c$. (d) Temperature dependence of the Meissner and shielding signals on a small crystal (field cooled $4\pi \chi =-0.001$ at 4.5 K) and the (1, 0, 1) magnetic Bragg peak intensity. (e) The structural distortion of the lattice as determined by tracking the width of the (2, 0, 0) nuclear Bragg peak using $\lambda /2$ scattering without Be filter. (f) Magnetic order parameter determined by $Q$ scans around (1, 0, 1) magnetic Bragg peak above background. The solid line shows order parameter fit using $(1-T/T_N{)}^{2\beta }$ with $T_N=91.3\pm 0.7\mathrm{K}$ and $\beta =0.3\pm 0.02$.

Figure 2

(a) Energy scans at $Q=(1,0,1)$ and $Q=(1.2,0,1)$ above and below $T_c$. (b) ${\chi }^{\prime \prime }(Q,\omega )$ at $Q=(1,0,1)$. (c) Energy scans at higher temperatures and, (d) the corresponding ${\chi }^{\prime \prime }(Q,\omega )$. The solid lines in (b) and (d) are guides to the eye. (e) $Q$ scans along the [$H$, 0, 1] direction at 4 meV. At 86 K, the Gaussian peak has $\mathrm{FWHM}=0.098\pm 0.006\mathrm{rlu}$ which corresponds to minimum correlation lengths of $\xi =57\pm 4\AA$. (f) Estimated ${\chi }^{\prime \prime }(Q,\omega )$ at 4 meV. (g) ${\chi }^{\prime \prime }(Q,\omega )$ at 7 meV with $\mathrm{FWHM}=0.103\pm 0.013\mathrm{rlu}$ and minimum correlation length of $\xi =54\pm 6\AA$. (h) Low temperature $Q$ scans along the [1, 0, $L$] direction ($c$ axis) at 4 meV ($\mathrm{FWHM}=0.58\pm 0.06\mathrm{rlu}$) and 7 meV ($\mathrm{FWHM}=0.9\pm 0.3\mathrm{rlu}$) correspond to $\xi \approx 14\pm 5$ and $21\pm 2\AA$, respectively. The solid curves in $e\mathrm{\text{−}}h$) are Gaussian fits with centers fixed at (1, 0, 1) rlu. For ${\mathrm{BaFe}}_2{\mathrm{As}}_2$, low-temperature spin wave scans along the [$H$, 0, 1] direction at 10 and 12 meV have $\mathrm{FWHM}=0.106\pm 0.008$ and $0.12\pm 0.01\mathrm{rlu}$, respectively [15]. Along the $c$-axis direction, the [1, 0, $L$] scan has $\mathrm{FWHM}=0.37\pm 0.05\mathrm{rlu}$ at 10 meV [15].

Figure 3

(a) Energy scans at $Q=(1,0,0)$ and $Q=(1.4,0,0)$ from 0.5 meV to 7 meV at 3.5 K and 18 K. (b) Background corrected ${\chi }^{\prime \prime }(Q,\omega )$ showing clear evidence for a 4 meV spin gap. (c) Temperature dependence of the signal [$Q=(1,0,0)$] and background [$Q=(1.4,0,0)$] scattering at various temperatures. (d) ${\chi }^{\prime \prime }(Q,\omega )$ at different temperatures. The solid lines in (b) and (d) are guides to the eye. (e) $Q$ scans along the [$H$, 0, 0] direction at 4 meV and different temperatures. (f) Background corrected ${\chi }^{\prime \prime }(Q,\omega )$. (g) Temperature dependence of the $Q$ scans along the [$H$, 0, 0] direction at 6 meV ($\mathrm{FWHM}=0.10\pm 0.01\mathrm{rlu}$). (h) Temperature dependence of the ${\chi }^{\prime \prime }(Q,\omega )$ at 6 meV. Gaussian fits to the data in ($e\mathrm{\text{−}}h$) have fixed centers at $Q=(1,0,1)\mathrm{rlu}$.

Figure 4

(a) Temperature dependence of the 1 meV scattering at the signal $Q=(1,0,0)$ and background $Q=(1.4,0,0)$ positions. The inset shows $Q$ scans along the [$H$, 0, 0] at 1 meV and different temperatures. The scattering shows no anomaly across $T_c$ but clearly peaks at $T_N$. (b) Temperature dependence of the scattering at 4 meV and $Q=(1,0,1)$ again peaks at $T_N$.