Direct observation of spin excitation anisotropy in the paramagnetic orthorhombic state of ${\mathbf{BaFe}}_{\mathit{2}-\mathit{x}}{\mathbf{Ni}}_{\mathit{x}}{\mathbf{As}}_{\mathbf{2}}$

We use transport and inelastic neutron-scattering measurements to investigate single crystals of iron pnictide ${\mathrm{BaFe}}_{2-x}{\mathrm{Ni}}_x{\mathrm{As}}_2(x=0,0.03)$, which exhibit a tetragonal-to-orthorhombic structural transition at $T_s$ and stripe antiferromagnetic order at $T_N(T_s\ge T_N)$. Using a tunable uniaxial pressure device, we detwin the crystals and study their transport and spin excitation properties at antiferromagnetic wave-vector $S_1(1,0)$ and its ${90}^{\circ }$ rotated wave-vector $S_2(0,1)$ under different pressure conditions. We find that uniaxial pressure necessary to detwin and maintain the single domain orthorhombic antiferromagnetic phase of ${\mathrm{BaFe}}_{2-x}{\mathrm{Ni}}_x{\mathrm{As}}_2$ induces resistivity and spin excitation anisotropy at temperatures above zero pressure $T_s$. In the uniaxial pressure-free detwinned sample, spin excitation anisotropy between $S_1(1,0)$ and $S_2(0,1)$ first appears in the paramagnetic orthorhombic phase below $T_s$. These results are consistent with predictions of spin nematic theory, suggesting the absence of structural or nematic phase transition above $T_s$ in iron pnictides.

Figure 1

(a) The electronic phase diagram of ${\mathrm{BaFe}}_{2-x}{\mathrm{Ni}}_x{\mathrm{As}}_2$ as a function of Ni doping as determined from previous work [6]. The AF orthorhombic (AF Ort), paramagnetic orthorhombic (PM Ort), paramagnetic tetragonal (PM Tet), and superconductivity (SC) phases are clearly marked. The black square points mark the Ni-doping levels measured in this Rapid Communication. (b) Schematic of the Fe-As layer at different temperatures and its corresponding reciprocal space for temperatures $T<T_N,T_N>T>T_s$, and $T>T_s$. The AF ordering wave vector and its ${90}^{\circ }$ rotation are marked as $S_1(1,0)$ and $S_2(0,1)$, respectively. The dotted curves are in-plane projection of neutron-scattering scan trajectories in reciprocal space. (c) Temperature dependence of the spin-spin correlation length at $S_1(1,0)$ (blue) and $S_2(0,1)$ (orange) across $T_s$ as predicted by spin nematic theory [28]. (d) The corresponding temperature dependence of the magnetic intensity difference between $S_1(1,0)$ and $S_2(0,1)$. (e) Schematics of the in situ device used to change pressure on the sample. A micrometer and a spring are used to adjust the pressure applied to the sample [32]. The applied pressure can be released by a full retreat of the micrometer, leaving the sample partially detwinned at low temperatures.

Figure 2

Inelastic neutron-scattering measurements of 10-meV spin excitations of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ under different conditions at $S_1(1,0)$ and $S_2(0,1)$. Transverse $A3$ (rocking) scans at different temperature and pressure conditions. The corresponding wave-vector directions in reciprocal space are shown in the insets of (a) and (b). The scans are measured under 25 MPa pressure (red), pressure-released (black), and stress-free (green) cases. (a) and (b) at 110 K ($<T_N/T_s$), (c) and (d) 138 K ($\approx T_N/T_s$), and (e) and (f) 150 K ($>T_N/T_s$).

Figure 3

Temperature dependence of spin excitations at 10 meV in ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ under 25 MPa uniaxial pressure, pressure-released, and stress-free conditions at (a) AF wave-vector $S_1(1,0)=(1,0,3)$ and (b) $S_1(0,1)=(0,1,3)$. The negative scattering is due to imperfect background scattering subtraction. (c) Temperature dependence of spin excitation anisotropy under 25 MPa pressure and pressure released.

Figure 4

Temperature dependence of resistivity and spin excitation anisotropy for ${\mathrm{BaFe}}_{1.97}{\mathrm{Ni}}_{0.03}{\mathrm{As}}_2$. (a) Temperature dependence of the 10-meV spin excitations under 22 MPa, released, and stress-free conditions at $S_1(1,0)$. (b) Similar measurements at $S_2(0,1)$. Temperature dependence of the (c) resistivity and (d) spin excitation anisotropy under 22 MPa and pressure-released conditions. (e) Temperature dependence of the FWHM of the 10-meV spin excitations at $S_1(1,0)$ and $S_2(0,1)$. The scan directions are marked by the dotted curve in the inset. (f) Temperature dependence of the first derivative of resistivity, where $T_N$ and $T_s$ are marked as vertical lines.