Electron doping evolution of the magnetic excitations in ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$

We use time-of-flight (TOF) inelastic-neutron-scattering (INS) spectroscopy to investigate the doping dependence of magnetic excitations across the phase diagram of ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ with $x=0$, 0.0175, 0.0215, 0.05, and $0.11$. The effect of electron doping by partially substituting Fe by Co is to form resonances that couple with superconductivity, broaden, and suppress low-energy ($E\le 80$ meV) spin excitations compared with spin waves in undoped NaFeAs. However, high-energy ($E>80$ meV) spin excitations are weakly Co-doping-dependent. Integration of the local spin dynamic susceptibility ${\chi }^{\prime \prime }\left(\omega \right)$ of ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ reveals a total fluctuating moment of 3.6 ${\mu }_B^2$/Fe and a small but systematic reduction with electron doping. The presence of a large spin gap in Co-overdoped nonsuperconducting ${\mathrm{NaFe}}_{0.89}{\mathrm{Co}}_{0.11}\mathrm{As}$ suggests that Fermi surface nesting is responsible for low-energy spin excitations. These results parallel the Ni-doping evolution of spin excitations in ${\mathrm{BaFe}}_{2-x}{\mathrm{Ni}}_x{\mathrm{As}}_2$ in spite of the differences in crystal structures and Fermi surface evolution in these two families of iron pnictides, thus confirming the notion that low-energy spin excitations coupling with itinerant electrons are important for superconductivity, while weakly doping-dependent high-energy spin excitations result from localized moments.

Figure 1

(a) Schematic phase diagram of NaFeCoAs from thermodynamic measurements [48]. Colored arrows above the figure indicate doping values used in this paper. (b) In-plane magnetic order in twinned orthorhombic domains. (c) dc magnetic susceptibility $\chi$. (d) Neutron scattering schematic indicating intensity at [1,0] and [0,1] originates from different crystal domains.

Figure 2

Two-dimensional slices from ToF INS of ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ measured with an incident energy of 80 meV at energy transfers of $12\pm 4$ meV (a)–(e), $28\pm 4$ meV (f)–(j), and $52\pm 4$ meV (k)–(o) for doping values $x=0$, 0.0175, 0.0215, 0.05, and 0.11, respectively. The white box in (a) indicates first magnetic BZ.

Figure 3

(a)–(c) Illustrations of one-dimensional transverse cuts from Figs. 2, 2, and 2. Cuts measured with an incident energy of 80 meV at energy transfers of 124 meV (d)–(h), 284 meV (i)–(m), and 524 meV (n)–(r) for doping values $x=0$, 0.0175, 0.0215, 0.05, and 0.11, respectively. All cuts integrated over $0.9<H<1.1$. Black curves are a Gaussian fit to the parent compound at identical energy transfer.

Figure 4

Two-dimensional slices from ToF INS of ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ measured with an incident energy of 250 meV at energy transfers of $67\pm 13$ meV (a)–(e), $119\pm 13$ meV (f)–(j), and $171\pm 13$ meV (k)–(o) for doping values $x=0$, 0.0175, 0.0215, 0.05, and 0.11, respectively.

Figure 5

Illustrations of one-dimensional transverse cuts from Figs. 4, 4, and 4. Cuts measured with an incident energy of 250 meV at energy transfers of $67\pm 13$ meV (d)–(f), $119\pm 13$ meV (i)–(m), and $171\pm 13$ meV (n)–(r) for doping values $x=0$, 0.0175, 0.0215, 0.05, and 0.11, respectively. All cuts integrated over $0.9<H<1.1$. Black line in each row is a Gaussian fitting to the parent compound for peak comparison.

Figure 6

(a)–(e) Two dimensional $Q\text{−}E$ slices of ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ for $x=0$, 0.0175, 0.0215, 0.05, and 0.11 along $H$ integrated on the window $K=[-0.10.1]$ r.l.u. in absolute units. (f)–(j) Similar slices along $K$ for $x=0$, 0.0175, 0.0215, 0.05, and 0.11 integrated across the window $K=[0.91.1]$ r.l.u. All figures use representative data from all incident energies measured and have been smoothed once using nearest-neighbor points.

Figure 7

One-dimensional constant $Q$ cuts obtained by integrating along $H=[0.91.1]$ and (a)–(e) $K=[-0.10.1]$, (f)–(j) $K=[0.20.4]$, and (k)–(o) $K=[0.50.7]$ for dopings of $x=0$, 0.0175, 0.0215, 0.05, and 0.11, respectively. Black lines are damped harmonic-oscillator fits to parent compound data for comparison. Symbols correspond to incident energy (see Table 2). (p) Overplot of low energy constant $Q$ points at the AF wave vector with integration windows of $\pm 0.1$ in both directions. Solid lines are guides to the eye.

Figure 8

(a) Inset: schematic showing direction of cuts at the AF wave vector [1 0]. Solid arrow (and points) indicates a longitudinal cut and open arrow (points) indicates a transverse cut. (a)–(e) FWHM of single Gaussian peak fits to constant energy cuts. Dashed and solid lines are guides to the eye for longitudinal and transverse cuts, respectively. (f) Overplot of guides from (b)–(f).

Figure 9

(a)–(e) Dispersion along the [1 K] direction from two-Gaussian fits to constant energy cuts (open symbols) and damped harmonic-oscillator fits to constant energy cuts (filled symbols) for $x=0$, 0.0175, 0.0215, 0.05, and 0.11, respectively. Solid lines are guides to the eye. (f) Overplot of guides from (a)–(e).

Figure 10

Energy dependence of the local dynamic susceptibility ${\chi }^{\prime \prime }\left(E\right)$ in ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ in absolute units (a)–(e) for $x=0$, 0.0175, 0.0215, 0.05, and 0.11, respectively. Solid lines are a combination of a smoothed moving average below $E=70$ meV and a damped harmonic-oscillator fit to all data sets above 70 meV. (f) Overplot of guides from (a)–(e). (g) Energy dependence of the local susceptibility in the parent compounds of NaFeAs (solid line), ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ (dashed-dotted line), and FeSe (dashed line). (h) Dependence of total fluctuating moment on doped electrons in ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ (circles), ${\mathrm{BaFe}}_{2-x}{\mathrm{Ni}}_x{\mathrm{As}}_2$ (diamonds), and FeSe (square). Solid line is a linear fit to the electron doping dependency of the moment in ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$. Dashed line is an identical fitting for ${\mathrm{BaFe}}_{2-x}{\mathrm{Ni}}_x{\mathrm{As}}_2$

Figure 11

Schematic Fermi surface for ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ and $\mathrm{Ba}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\right)}_2{\mathrm{As}}_2$ in the (a,d) parent [8, 70], (b,e) optimally doped [8, 71], and (c,f) overdoped [8, 67] regimes, respectively. ARPES results show the $\alpha$ and $\gamma$ bands are holelike whereas $\beta$ and $\eta$ are electron bands. Dashed lines indicate that a band is very near but just below the Fermi surface.

Figure 12

(a) Background subtracted local susceptibility of ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ ($x=0.0215$) and (b) the difference in susceptibility between the superconducting ($T=5$ K) and normal ($T=25$ K) state. High-temperature data are measured from the same samples and environment as other data for $x=0.0215$ in the present report.

Figure 13

Self-consistent normalization using the top of the $(2,2,1)$ acoustic phonon. (a)–(d) Background subtracted cuts along the $[H,H]$ direction at $E=12\pm 0.5$, $13\pm 0.5$, $14\pm 0.5$, and $15\pm 0.5$ meV, respectively. Dopings are noted by color and labeled at the top of the figure. Single-peak Gaussian fits are plotted in solid lines. (e) Integrated intensity for cuts in (a)–(d) is plotted as a function of energy. Integrated intensity is calculated from fits with error bars derived from fit parameters. (f) Intensity ratio ($I_{x=0}/I_x$) is plotted as a function of energy. Horizontal lines depict the weighted average of corresponding data.

Figure 14

(a) Optical phonon near the zone center seen with $E_i=50$ meV and $E=34.5\pm 0.5$ meV. (b)–(e) Cuts through the phonon for ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ with $x=0$ (black) and 0.11 (red). Cuts fit with single Gaussians (solid lines) constrained to share a center. (e) Ratios of integrated intensity for fits in (b)–(d). The blue line is a weighted average.

Figure 15

(a) Acoustic phonon from $(2,0,1)$ determined by constant $E$ and $\mathbf{Q}$ scans. Red line is a polynomial fit used to determine the phonon speed. (b) Transverse cuts at $3\pm 1$ (lower) and $5\pm 1$ meV (higher) fit with two Gaussians on a linear background (solid lines). (c) Following Ref. [72], the inverse scale factor resulting from self-normalization with phonon shown in (a) and (b).

Figure 16

Background subtraction process at low energies. Raw data (a) are masked according to the method outlined in the text (b). Ring-integrated radial data (c) and vertical linear background (d) are subtracted to give a background-free slice (e).