Spin Excitation Anisotropy as a Probe of Orbital Ordering in the Paramagnetic Tetragonal Phase of Superconducting ${\mathrm{BaFe}}_{1.904}{\mathrm{Ni}}_{0.096}{\mathrm{As}}_2$

We use polarized neutron scattering to demonstrate that in-plane spin excitations in electron doped superconducting ${\mathrm{BaFe}}_{1.904}{\mathrm{Ni}}_{0.096}{\mathrm{As}}_2$ ($T_c=19.8\mathrm{K}$) change from isotropic to anisotropic in the tetragonal phase well above the antiferromagnetic (AFM) ordering and tetragonal-to-orthorhombic lattice distortion temperatures ($T_N\approx T_s=33\pm 2\mathrm{K}$) without an uniaxial pressure. While the anisotropic spin excitations are not sensitive to the AFM order and tetragonal-to-orthorhombic lattice distortion, superconductivity induces further anisotropy for spin excitations along the [110] and $[1\overline{1}0]$ directions. These results indicate that the spin excitation anisotropy is a probe of the electronic anisotropy or orbital ordering in the tetragonal phase of iron pnictides.

Figure 1

(a) Electronic phase diagram of ${\mathrm{BaFe}}_{2-x}{\mathrm{Ni}}_x{\mathrm{As}}_2$ as a function of Ni doping $x$, where $T^{*}$ is the zone boundary of anisotropic in-plane resistivity obtained from Ref. 29. The arrow indicates the doping level $x=0.096$ for our experiments. (b) Orthorhombic lattice distortion order parameter $\delta$ shows $T_s=33\pm 1\mathrm{K}$. The high resolution x-ray diffraction on nuclear peak (2, 2, 12) experiment was from Ref. 25. (c) In-plane resistance under zero and finite uniaxial stress $P$ along $b_o$, where $P=P_0$ is the detwinned pressure. From separate neutron scattering measurements, we know that $T_N$ and $T_s$ are uniaxial stress independent. (d) Temperature dependence of the AFM order parameter shows $T_N=33\pm 2\mathrm{K}$. (e),(g) Scattering plane and neutron polarization directions in our experiments. (f),(h) Magnetic response of SF channels in the neutron polarization analysis.

Figure 2

(a) Energy scans at $\mathbf{Q}=(0.5,0.5,3)$ for SF scattering at 22 K above $T_c$ for different neutron polarization directions, marked as ${\sigma }_{x,y,z}^{\mathrm{SF}}$. (b) The magnetic response $M_y$ and $M_z$ extracted from (a). (c) and (d) Identical energy scans at 2 K below $T_c$ in the neutron SF channel and $M_y$, $M_z$, respectively. (e) The total neutron SF scattering ${\sigma }_x^{\mathrm{SF}}$ at 2 and 22 K and (f) their difference, where a neutron spin resonance is seen at $E_r=7\mathrm{meV}$. (g) The ${\sigma }_y^{\mathrm{SF}}$ at 2 and 22 K and (h) their difference. (i),(j) Identical scans for ${\sigma }_z^{\mathrm{SF}}$. The solid lines in (b),(d),(h),(j) are guides to the eyes, and in (f) the solid line is the sum of (h) and (j).

Figure 3

(a),(b) Constant energy scans at 3 meV in the neutron SF channel ${\sigma }_{x,y,z}^{\mathrm{SF}}$ below and above $T_c$, respectively. The solid lines are Gaussian fits to the data on linear backgrounds. (c) and (d) Identical scans and results at the resonance energy of $E_r=7\mathrm{meV}$.

Figure 4

(a) Temperature dependence of neutron SF scattering cross section ${\sigma }_{x,y,z}^{\mathrm{SF}}$ at 3 meV and $\mathbf{Q}=(0.5,0.5,3)$. (b) The temperature dependence of magnetic response along the $[1\overline{1}0]$ ($M_y$) and $[11\overline{1/3}]$ ($M_z$) directions. Clear anisotropy persists up to $T^{*}=70\mathrm{K}$. (c) Temperature dependence of the dynamic susceptibility, ${\chi }_y^{\prime \prime }$ and ${\chi }_z^{\prime \prime }$. (d),(e),(f) Identical results at the resonance energy of $E_r=7\mathrm{meV}$.

Figure 5

(a)–(c) Temperature dependence of neutron SF scattering cross section ${\sigma }_{x,y,z}^{\mathrm{SF}}$ at 3 meV and ${\mathbf{Q}}_{1,2,3}=(0.5,0.5,L)$ with $L=1,3,5$. (d) The temperature dependence of magnetic response along the $[110]$ ($M_{110}$), $[1\overline{1}0]$ ($M_{1\overline{1}0}$), and $[001]$ ($M_{001}$) directions. Clear in-plane anisotropy persists up to $T^{*}=70K$.