Identical spin fluctuations in Cu- and Co-doped ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ independent of electron doping

We present ${}^{75}\mathrm{As}$ nuclear magnetic resonance measurements on single crystals of $\mathrm{Ba}{\mathrm{Fe}}_2{\mathrm{As}}_2$, $\mathrm{Ba}{\mathrm{Fe}}_{1.8}{\mathrm{Co}}_{0.2}{\mathrm{As}}_2$, and $\mathrm{Ba}{\mathrm{Fe}}_{1.82}{\mathrm{Cu}}_{0.18}{\mathrm{As}}_2$. While only Co doping induces bulk superconductivity on a broad doping range, the spin fluctuations probed by the nuclear spin-lattice relaxation rate ${\left(T_{1}T\right)}^{-1}$  are identical for both dopings down to $T_c$. Below this temperature, ${\left(T_{1}T\right)}^{-1}$ of the Cu-doped sample continues to rise, proving that (a) there is a quantum critical point below the superconducting dome, and (b) adding electrons does not affect the spin fluctuations. Consequently, we analyze the Knight shift data in terms of a two-component scenario, with one hyperfine coupling to an itinerant degree of freedom and the other to Fe moments.

Figure 1

(a) Spin-lattice relaxation rate divided by temperature for $\mathrm{Ba}{\mathrm{Fe}}_2{\mathrm{As}}_2$ (red squares), $\mathrm{Ba}{\mathrm{Fe}}_{1.82}{\mathrm{Cu}}_{0.18}{\mathrm{As}}_2$ (blue circles), and $\mathrm{Ba}{\mathrm{Fe}}_{1.8}{\mathrm{Co}}_{0.2}{\mathrm{As}}_2$ (orange triangles). The lines are fits as described in the text. (b) Anisotropy ratio $R=T_{1ab}^{-1}/T_{1c}^{-1}$. Data for underdoped $\mathrm{Ba}{\mathrm{Fe}}_{1.884}{\mathrm{Co}}_{0.116}{\mathrm{As}}_2$ (green diamonds) and $\mathrm{Ba}{\mathrm{Fe}}_{1.876}{\mathrm{Co}}_{0.124}{\mathrm{As}}_2$ (hexagons) has been taken from [4]. Note that for these dopings the field parallel $ab$ was $H=11.7$ T, while that for parallel $c$ was $H\sim 8.7$ T. The inset shows a zoom of the low-temperature data including the structural and magnetic transition temperatures $T_S$ and $T_N$, respectively.

Figure 2

(a) Knight shift for $H\parallel ab$ in $\mathrm{Ba}{\mathrm{Fe}}_2{\mathrm{As}}_2$ (red squares), $\mathrm{Ba}{\mathrm{Fe}}_{1.82}{\mathrm{Cu}}_{0.18}{\mathrm{As}}_2$ (blue circles), and $\mathrm{Ba}{\mathrm{Fe}}_{1.8}{\mathrm{Co}}_{0.2}{\mathrm{As}}_2$ (orange triangles). (b) Knight shift for $H\parallel c$, analogous to (a). In addition, three different fits to the $\mathrm{Ba}{\mathrm{Fe}}_{1.82}{\mathrm{Cu}}_{0.18}{\mathrm{As}}_2$ data are shown in (b): solid line: gap fit with $\Delta =450$ K fixed, dashed line: gap fit with $\Delta$ as a free parameter, dotted line: linear fit to the high temperature data.

Figure 3

Knight shift $K$ vs macroscopic susceptibility $\chi$ for $\mathrm{Ba}{\mathrm{Fe}}_2{\mathrm{As}}_2$ for $H\parallel ab$, upper panel, for $\mathrm{Ba}{\mathrm{Fe}}_{1.8}{\mathrm{Co}}_{0.2}{\mathrm{As}}_2$ for $H\parallel ab$ and $c$, middle row, and for $\mathrm{Ba}{\mathrm{Fe}}_{1.82}{\mathrm{Cu}}_{0.18}{\mathrm{As}}_2$ for $H\parallel ab$ and $c$, lower row. The data points with the large error bars at $\chi \approx$ 0 indicate the value of the orbital shift, $K_{\mathrm{orb}}$. The extracted values are summarized in Table 1.

Figure 4

(a)${}^{75}\mathrm{As}$ NMR spectra of $\mathrm{Ba}{\mathrm{Fe}}_{1.82}{\mathrm{Cu}}_{0.18}{\mathrm{As}}_2$ for $H\parallel ab$ taken at different temperatures. The quadrupole splitting of the two satellite lines decreases with decreasing temperature. (b) and (c) ${}^{75}\mathrm{As}$ NMR spectra of the central transition at different temperatures for $H\parallel c$ and $H\parallel ab$, respectively. (d) ${}^{63}\mathrm{Cu}$ NMR spectra of the central transition for $H\parallel c$ at 50 K. The dashed line indicates the unshifted resonance frequency of the bare ${}^{63}\mathrm{Cu}$ nucleus.

Figure 5

(a) Corrected intensity $I_{\mathrm{cor}}$ of the ${}^{75}\mathrm{As}$ NMR spectra for the central transition for $H\parallel c$ (open circles) and $ab$ (closed circles). The intensity was corrected for temperature $T$, number of scans $N_{\mathrm{scans}}$, and spin-spin relaxation $T_2$ effects according to Eq. (A1). (b) FWHM for $H\parallel ab$ (closed symbols) and $H\parallel c$ (open symbols) for $\mathrm{Ba}{\mathrm{Fe}}_2{\mathrm{As}}_2$ (red squares), $\mathrm{Ba}{\mathrm{Fe}}_{1.82}{\mathrm{Cu}}_{0.18}{\mathrm{As}}_2$ (blue circles), and $\mathrm{Ba}{\mathrm{Fe}}_{1.8}{\mathrm{Co}}_{0.2}{\mathrm{As}}_2$ (orange triangles).

Figure 6

(a) Zero-field cooled static magnetic susceptibility $\chi$ measured by SQUID for all three different samples and for $H\parallel ab$ and $c$. For comparison, the data of Wang et al. is also shown [26]. (b) Knight shift measured in $\mathrm{Ba}{\mathrm{Fe}}_2{\mathrm{As}}_2$ (red squares) and $\mathrm{Ba}{\mathrm{Fe}}_{1.8}{\mathrm{Co}}_{0.2}{\mathrm{As}}_2$ (orange triangles) for $H\parallel c$ in comparison to literature data from Ning et al. [$\mathrm{Ba}{\mathrm{Fe}}_2{\mathrm{As}}_2$ ($*$) and $\mathrm{Ba}{\mathrm{Fe}}_{1.84}{\mathrm{Co}}_{0.16}{\mathrm{As}}_2$ (green $\times$)], and $\mathrm{Ba}{\mathrm{Fe}}_{1.82}{\mathrm{Co}}_{0.18}{\mathrm{As}}_2$ (purple $+$) [7], and from Oh et al. [$\mathrm{Ba}{\mathrm{Fe}}_{1.86}{\mathrm{Co}}_{0.14}{\mathrm{As}}_2$ (pink $☆$)]. (c) Spin-spin relaxation time for $\mathrm{Ba}{\mathrm{Fe}}_{1.82}{\mathrm{Cu}}_{0.18}{\mathrm{As}}_2$ (blue circles), and $\mathrm{Ba}{\mathrm{Fe}}_{1.8}{\mathrm{Co}}_{0.2}{\mathrm{As}}_2$ (orange triangles) for $H\parallel c$. Data from Oh et al. [35] are shown for comparison. The vertical line indicates the $T_c\approx 18$ K of both Co-doped samples in $H=7$ and $6.4$ T, respectively.

Figure 7

(a)Spin-lattice relaxation rate divided by temperature for $\mathrm{Ba}{\mathrm{Fe}}_2{\mathrm{As}}_2$ (red squares), $\mathrm{Ba}{\mathrm{Fe}}_{1.82}{\mathrm{Cu}}_{0.18}{\mathrm{As}}_2$ (blue circles), and $\mathrm{Ba}{\mathrm{Fe}}_{1.8}{\mathrm{Co}}_{0.2}{\mathrm{As}}_2$ (orange triangles). All data are measured for $H\parallel c$. Data from Ning et al. are shown for comparison [43]. (b) Stretching exponent $\beta$ for all different dopings.