Neutron spin resonance as a probe of superconducting gap anisotropy in partially detwinned electron underdoped ${\mathrm{NaFe}}_{0.985}{\mathrm{Co}}_{0.015}\mathrm{As}$

We use inelastic neutron scattering (INS) to study the spin excitations in partially detwinned ${\mathrm{NaFe}}_{0.985}{\mathrm{Co}}_{0.015}\mathrm{As}$ which has coexisting static antiferromagnetic (AF) order and superconductivity ($T_c=15$ K, $T_N=30$ K). In previous INS work on a twinned sample, spin excitations formed a dispersive sharp resonance near $E_{r1}=3.25$ meV and a broad dispersionless mode at $E_{r1}=6$ meV at the AF ordering wave vector ${\mathbf{Q}}_{\mathrm{AF}}={\mathbf{Q}}_1=(1,0)$ and its twinned domain ${\mathbf{Q}}_2=(0,1)$. For partially detwinned ${\mathrm{NaFe}}_{0.985}{\mathrm{Co}}_{0.015}\mathrm{As}$ with the static AF order mostly occurring at ${\mathbf{Q}}_{\mathrm{AF}}=(1,0)$, we still find a double resonance at both wave vectors with similar intensity. Since ${\mathbf{Q}}_1=(1,0)$ characterizes the explicit breaking of the spin rotational symmetry associated with the AF order, these results indicate that the double resonance cannot be due to the static and fluctuating AF orders but originate from the superconducting gap anisotropy.

Figure 1

(a) The electronic phase diagram of ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$, where the arrow indicates the Co-doping level of our sample. The inset shows the magnetic structure in orthorhombic notation. (b) In a 100% detwinned sample, one should observe magnetic order at ${\mathbf{Q}}_{\mathrm{AF}}={\mathbf{Q}}_1=(1,0)$ but not at ${\mathbf{Q}}_2=(0,1)$. (c) The schematic drawings of the Fermi surfaces in a detwinned sample. (d) Its twin domain rotated ${90}^{\circ }$ away. The arrows mark Fermi surface nesting wave vectors. (e) In a twinned sample, one cannot distinguish ${\mathbf{Q}}_1=(1,0)$ and ${\mathbf{Q}}_2=(0,1)$, and therefore there should be two resonances at both wave vectors. (f) In the AF order and superconductivity coexisting theory, $E_{r1}$ should appear at ${\mathbf{Q}}_1$ and $E_{r2}$ at ${\mathbf{Q}}_2$ in a completely detwinned superconducting sample with static AF order at ${\mathbf{Q}}_1$.

Figure 2

Temperature differences of the elastic scattering below (2 K) and above (41 K) the Néel temperature ($T_N=33$ K) at reciprocal positions (a) $(0,1,0.5)$ and (b) $(1,0,0.5)$ in a uniaxial strained ${\mathrm{NaFe}}_{0.985}{\mathrm{Co}}_{0.015}\mathrm{As}$ single crystal. The uniaxial strain along the $b$ axis is $\sim 10$ MPa, and data were collected on BT-7. By comparing the area ratio of the two peaks, we estimate that $\sim 58\%$ ($\approx \left[I\right(1,0,0.5)-I(0,1,0.5\left)\right]/\left[I\right(1,0,0.5)+I(0,1,0.5\left)\right]$) of the crystal is detwinned. The solid lines are Gaussian fits to the data. A similar detwinning ratio is also obtained at PUMA. After releasing the uniaxial strain, we find that the sample returns to the twinned state. (c) Temperature dependence of the magnetic order parameters at ${\mathbf{Q}}_1$ and ${\mathbf{Q}}_2$ in uniaxially strained detwinned ${\mathrm{NaFe}}_{0.985}{\mathrm{Co}}_{0.015}\mathrm{As}$. (d) and (e) Constant $\mathbf{Q}$ scans at ${\mathbf{Q}}_1$ and ${\mathbf{Q}}_2$ below and above $T_c$, respectively, in the partially detwinned sample. The peaks around $\sim 9$ mV in the raw data are mostly temperature-independent background scattering. (f) Temperature differences between 5 and 21 K, revealing the superconductivity-induced resonance at ${\mathbf{Q}}_1$ and ${\mathbf{Q}}_2$. The nearly identical resonances at these two vectors suggest that the coupling between spin waves and superconductivity is weak in Co-doped NaFeAs. The solid line is a guide to the eye.

Figure 3

Constant-energy scans at the low-energy resonance $E_{r1}=3.75$ meV for detwinned ${\mathrm{NaFe}}_{0.985}{\mathrm{Co}}_{0.015}\mathrm{As}$. (a) and (b) The rocking scans across ${\mathbf{Q}}_2=(0,1,0.5)$ and ${\mathbf{Q}}_1=(1,0,0.5)$ positions above (21 K) and below (5 K) $T_c$, respectively. The wave-vector-independent background scattering increases slightly on warming. (c) and (d) Corresponding difference between the two temperatures after the background subtraction. The solid lines are fits to Gaussians on flat backgrounds set to zero.

Figure 4

Constant-energy scans through the high-energy resonance $E_{r2}=6.5$ meV for detwinned ${\mathrm{NaFe}}_{0.985}{\mathrm{Co}}_{0.015}\mathrm{As}$. (a) and (b) The rocking scans across the ${\mathbf{Q}}_2=(0,1,0.5)$ and ${\mathbf{Q}}_1=(1,0,0.5)$ positions above (21 K) and below (5 K) $T_c$, respectively. (c) and (d) The corresponding difference between the two temperatures. The solid lines are fits to Gaussians on zero backgrounds.

Figure 5

Imaginary part of the dynamic spin susceptibility ${\chi }^{\prime \prime }$ in the superconducting state of a multiorbital $t-J_1-J_2$ model with a nonzero splitting between the $d_{xz}$ and $d_{yz}$ orbitals, $\epsilon =0.02$ eV. Two resonance peaks are present in each of the ${\mathbf{Q}}_1$ and ${\mathbf{Q}}_2$ wave vectors. In the calculation, $J_1/J_2=0.1$ is taken such that the pairing amplitudes show strong orbital selectivity. See Ref. [31] for details of the model and the method.