Temperature and polarization dependence of low-energy magnetic fluctuations in nearly optimally doped ${\mathrm{NaFe}}_{0.9785}{\mathrm{Co}}_{0.0215}\mathrm{As}$

We use unpolarized and polarized neutron scattering to study the temperature and polarization dependence of low-energy magnetic fluctuations in nearly optimally doped ${\mathrm{NaFe}}_{0.9785}{\mathrm{Co}}_{0.0215}\mathrm{As}$, with coexisting superconductivity $(T_{\mathrm{c}}\approx 19$ K) and weak antiferromagnetic order $(T_{\mathrm{N}}\approx 30$ K, ordered moment $\approx 0.02{\mu }_{\mathrm{B}}/\mathrm{Fe})$. A single spin resonance mode with intensity tracking the superconducting order parameter is observed, although energy of the mode only softens slightly upon approaching $T_{\mathrm{c}}$. Polarized neutron scattering reveals that the single resonance is mostly isotropic in spin space, similar to overdoped ${\mathrm{NaFe}}_{0.935}{\mathrm{Co}}_{0.045}\mathrm{As}$ but different from optimal electron-, hole-, and isovalently doped ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ compounds, all featuring an additional prominent anisotropic component. Spin anisotropy in ${\mathrm{NaFe}}_{0.9785}{\mathrm{Co}}_{0.0215}\mathrm{As}$ is instead present at energies below the resonance, which becomes partially gapped below $T_{\mathrm{c}}$, similar to the situation in optimally doped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.9}$. Our results indicate that anisotropic spin fluctuations in ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ appear in the form of a resonance in the underdoped regime, become partially gapped below $T_{\mathrm{c}}$ near optimal doping, and disappear in overdoped compounds.

Figure 1

(a) Constant-$\mathbf{Q}$ scans at $\mathbf{Q}=(1,0,1)$ for $T=4$, 22, and 35 K. The solid line is an empirical fit to the data at 35 K. The dashed line is a fit to the background (BKG) intensity. (b) Comparison of the difference between 4 K and 35 K for constant-$\mathbf{Q}$ scans at $\mathbf{Q}=(1,0,1)$ and $(1,0,1.5)$. The solid lines are guides to the eye. (c) Temperature dependence of spin fluctuations for $E=4$, 8, and 12 meV at $\mathbf{Q}=(1,0,1)$. The solid lines are guides to the eye. Data in this figure are obtained on HB-3 using unpolarized neutron scattering.

Figure 2

(a) Constant-$\mathbf{Q}$ scans at $\mathbf{Q}=(1,0,1)$ for several temperatures below $T_{\mathrm{c}}$, subtracted by the empirical fit to 35 K data. The solid lines are fits to Gaussian peaks in the energy range $5\le E\le 10$ meV. (b) Color-coded and interpolated temperature dependence of low-energy magnetic fluctuations. The empirical fit to 35 K data has been subtracted. The circles correspond to points where measurements were taken. (c) Temperature dependence for the center and the area of the resonance mode, obtained from Gaussian fits in (a). The solid line for the resonance energy is a guide to the eye, and the solid line for the total area is a fit to the superconducting order parameter [49]. The dashed vertical lines represent $T_{\mathrm{c}}\approx 19\mathrm{K}$. Data in this figure are obtained on HB-3 using unpolarized neutron scattering.

Figure 3

(a) Constant-$\mathbf{Q}$ scans at $\mathbf{Q}=(1,0,1)$ for several temperatures below $T_{\mathrm{c}}$, subtracted by the fit to background (BKG) intensity. The solid lines are fits to damped harmonic oscillator responses in the energy range $3\le E\le 12$ meV. (b) Color-coded and interpolated temperature dependence of low-energy magnetic fluctuations. The fit to background has been subtracted. The circles correspond to points where measurements were taken. (c) Temperature dependence for $E_0,E_{\max }$, and $\gamma$ from damped harmonic oscillator fits in (a). The solid lines are guides to the eye. The dashed vertical lines represent $T_{\mathrm{c}}\approx 19\mathrm{K}$. Data in this figure are obtained on HB-3 using unpolarized neutron scattering.

Figure 4

Constant-$\mathbf{Q}$ scans of ${\sigma }_x^{\mathrm{SF}},{\sigma }_y^{\mathrm{SF}}$, and ${\sigma }_z^{\mathrm{SF}}$ at $\mathbf{Q}=(1,0,0.5)$ (a) well below $T_{\mathrm{c}}$ $\left(T=2\mathrm{K}\right)$ and (b) just above $T_{\mathrm{c}}$ $\left(T=21\mathrm{K}\right)$. The differences ${\sigma }_x^{\mathrm{SF}}-{\sigma }_y^{\mathrm{SF}}$ and ${\sigma }_x^{\mathrm{SF}}-{\sigma }_z^{\mathrm{SF}}$, which are respectively proportional to $M_y$ and $M_z$, are correspondingly shown in (c) and (d). The solid lines are guides to the eye. Data in this figure are obtained on IN22 using polarized neutron scattering.

Figure 5

Temperature dependence of ${\sigma }_x^{\mathrm{SF}},{\sigma }_y^{\mathrm{SF}}$, and ${\sigma }_z^{\mathrm{SF}}$ at $\mathbf{Q}=(1,0,0.5)$ for (a) $E=3$ meV and (b) $E=5$ meV. The differences ${\sigma }_x^{\mathrm{SF}}-{\sigma }_y^{\mathrm{SF}}$ and ${\sigma }_x^{\mathrm{SF}}-{\sigma }_z^{\mathrm{SF}}$, which are respectively proportional to $M_y$ and $M_z$, are correspondingly shown in (c) and (d). The solid lines are guides to the eye. The vertical dashed lines represent $T_{\mathrm{c}}$. Data in this figure are obtained on IN22 using polarized neutron scattering.

Figure 6

(a) Resistivity change under uniaxial stress $\zeta$ along the (100) direction for the orthorhombic unit cell [(110) direction for the tetragonal unit cell]. The solid red line is a CW fit for $T\ge 40\mathrm{K}$. (b) Reduced ${\chi }^2$ from CW fits of data in (a), by setting the fitting ranges to be from different temperatures to 300 K. The same standard deviation is used for all measured data points to obtain reduced ${\chi }^2$, and is estimated from the standard deviation of data with $T>100\mathrm{K}$. (c) ${(\zeta -{\zeta }_0)}^{-1}$ for the fit shown in (a). The error bars for $\zeta$ are estimated from standard deviation of data with $T>100\mathrm{K}$, and the error bars for ${(\zeta -{\zeta }_0)}^{-1}$ are obtained through propagation of error. (d) Zoom-in of results in (c).

Figure 7

(a) Schematic phase diagram of ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ [59]. The three concentrations for which polarized neutron scattering have been carried out are marked by arrows. Sketches of isotropic and anisotropic magnetic fluctuations well below $T_{\mathrm{c}}$ and just above $T_{\mathrm{c}}$ for $x=0.015$ are respectively shown in (b) and (c). Similar sketches for $x=0.0215$ are shown in (d) and (e), and for $x=0.045$ in (f) and (g).