NMR study of electronic correlations in Mn-doped Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ and BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$

We probe the real-space electronic response to a local magnetic impurity in isovalent and heterovalent doped BaFe${}_2$As${}_2$ (122) using nuclear magnetic resonance (NMR). The local moments carried by Mn impurities doped into Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ (Co-122) and BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ (P-122) at optimal doping induce a spin polarization in the vicinity of the impurity. The amplitude, shape, and extension of this polarization is given by the real part of the susceptibility ${\chi }^{\prime }\left(r\right)$ of FeAs layers and is consequently related to the nature and strength of the electronic correlations present in the system. We study this polarization using ${}^{75}$As NMR in Co-122 and both ${}^{75}$As and ${}^{31}$P NMR in P-122. The NMR spectra of Mn-doped materials are made of two essential features. First, there is a satellite line associated with nuclei located as nearest neighbors of Mn impurities. The analysis of the temperature dependence of the shift of this satellite line shows that Mn local moments behave as isolated Curie moments. The second feature is a temperature dependent broadening of the central line. We show that the broadening of the central line follows the susceptibility of Mn local moments, as expected from typical Ruderman-Kittel-Kasuya-Yosida (RKKY)-like interactions. This demonstrates that the susceptibility ${\chi }^{\prime }\left(r\right)$ of FeAs layers does not make significant contribution to the temperature dependent broadening of the central line. ${\chi }^{\prime }\left(r\right)$ is consequently only weakly temperature dependent in optimally doped Co-122 and P-122. This behavior is in contrast with that of strongly correlated materials such as underdoped cuprate high-$T_{\mathrm{c}}$ superconductors where the central line broadens faster than the impurity susceptibility grows, because of the development of strong magnetic correlations when $T$ is lowered. Moreover, the FeAs layer susceptibility is found quantitatively similar in both heterovalent doped and isolvalent doped BaFe${}_2$As${}_2$.

Figure 1

(a) and (b) ${}^{75}$As NMR measured with $H_0=13.3$ T, $H_0\parallel c$, in Co-Mn-122 single crystals with $x_{\mathrm{Co}}=6.5$%, $y_{\mathrm{Mn}}=0.65$% (a) and $1.5$% (pb). The main line develops a structure at high temperature indicating that it is composed of several peaks with similar intensities. This structure might be a consequence of a modification of the hyperfine coupling or quadrupolar environment due to Co atoms. (c)–(e) ${}^{31}$P NMR measured with $H_0=7.5$ T, $H_0\parallel c$, in P-Mn-122 powders with $x_{\mathrm{P}}=35$%, $y_{\mathrm{Mn}}=0$ (c), $1.5$% (d), and $3.0$% (e). In (a), (b), (d), and (e), the arrow points to the satellite associated with As nuclei nearest neighbor to Mn atoms. In all panels, curves are arbitrarily shifted vertically for clarity.

Figure 2

Typical ${}^{75}$As NMR spectra at $T=260$ K in Mn-122 compounds, measured with $H_0=13.3$ T, $H_0\parallel c$. Pure Mn-122 ($y_{\mathrm{Mn}}=2.5$%) is shown in green (bottom axis) and features a satellite on the right wing of the central line associated with As nuclei nearest neighbor to Mn, as sketched in inset c (from Ref. [15]). Red curve (top axis) shows Co-Mn-122 with $x_{\mathrm{Co}}=6.5$%, $y_{\mathrm{Mn}}=0.65$%. The satellite associated with Mn is still visible (the right-hand side of central line), and an additional satellite due to the modification of the second-order quadrupole effect of As nuclei nearest neighbor to Co atoms (inset a) appears on the left wing of the central line. Blue curve (top axis) shows P-Mn-122 with $x_{\mathrm{P}}=35$%, $y_{\mathrm{Mn}}=3.0$%. The central linewidth has significantly increased in comparison to Co-Mn-122 because of higher disorder for $x_{\mathrm{P}}=35$% than for $x_{\mathrm{Co}}=6.5$%. The satellite associated with Mn is still here but is merged with the central line. Curves are shifted vertically.

Figure 3

Zoom on the ${}^{75}$As NMR satellite associated with As nearest neighbor to Mn atoms in Co-Mn-122 with $x_{\mathrm{Co}}=6.5$%, for $15<T<300$ K, measured with $H_0=13.3$ T, $H_0\parallel c$. Green lines are fits to the experimental data used to determine the shift of satellite line ${}^{75}{K}_{\mathrm{sat}}$. (Top) $y_{\mathrm{Mn}}=0.65$%. (Bottom) $y_{\mathrm{Mn}}=1.5$%. In all cases, the satellite line merges with the main line for $T\lesssim 50$ K, preventing us to confidently determine the shift of the satellite line in this temperature range.

Figure 4

Determination of Mn impurity local moments susceptibility ${\chi }_{\mathrm{Mn}}^{\prime }$ in Co-Mn-122 ($x_{\mathrm{Co}}=6.5$%) for $y_{\mathrm{Mn}}=0.65$% (red) and $1.5$% (blue). (a) ${\chi }_{\mathrm{Mn}}^{\prime }\left(T\right)$ determined with the ${}^{75}$As NMR shift. Continuous and dashed black lines are fits to the data with a Curie-Weiss model $y_0+C/(T+\theta )$ with $\theta$ respectively fixed to 0 and 40 K. (b) ${\chi }_{\mathrm{Mn}}^{\prime }\left(T\right)$ determined with macroscopic susceptibility measurements where the Fe layer contribution to the homogeneous susceptibility, namely, ${\chi }_{\mathrm{Fe}}^{\prime }\left(T\right){\propto }^{75}{K}_{\mathrm{central}}\left(T\right)$ has been subtracted. Black lines are fits to the data with a Curie law $y_0+C/T$.

Figure 5

Central line broadening plotted as $(\Delta \nu -\Delta {\nu }_{\mathrm{high}-T})/y_{\mathrm{Mn}}$. (a) From ${}^{75}$As NMR spectra in both Co-Mn-122 (dark and light blue markers) and P-Mn-122 (black and green squares). (b) From ${}^{31}$P NMR spectra in P-Mn-122. In both panels, red dashed line is a least square $y_0+C/T^2$ fit to the data and red continuous line is a least square Curie law $y_0+C/T$ fit to the data, while ${}^{75}$As NMR $\Delta \nu \left(T\right)$ is best reproduced by a Curie model in both cases. Incompatibility with the $1/T^2$ fit is more obvious in the case of $\Delta \nu \left(T\right)$ deduced from ${}^{31}$P NMR in P-Mn-122.

Figure 6

${}^{75}$As NMR central line broadening plotted as a function of the Mn local moments susceptibility ${\chi }_{\mathrm{Mn}}^{\prime }\left(T\right)$ derived from ${}^{75}$As NMR satellite shift, for all Co-Mn-122 samples studied here. This plot shows that, within error bars, $\Delta \nu \left(T\right)\propto {\chi }_{\mathrm{Mn}}^{\prime }\left(T\right)$, such that the FeAs layer susceptibility has a very weak $T$ dependence. There is remarkable agreement for all Co and Mn contents, indicating that Mn doping is within the diluted regime and that magnetic correlations are not dependent on carrier concentration within the error bars.

Figure 7

Temperature dependence of the shift of the ${}^{75}$As NMR satellite line, ${}^{75}$K${}_{\mathrm{sat}}$, in Co-Mn-122 for all Mn contents studied here.

Figure 8

Illustration of the method for the extraction of the macroscopic susceptibility of Mn local moments, using SQUID and NMR measurements. Green squares (left axis): sample (raw) macroscopic susceptibility obtained using the slope of $M\left(H\right)$ isotherms measured with SQUID. Blue circles (left axis): Mn local moments susceptibility contribution to the sample macroscopic susceptibility. It is obtained by subtracting the FeAs layer susceptibility, measured here with the shift ${}^{75}K$ of the central NMR line in the same sample of Co-Mn-122 (red triangles, right axis), to the sample macroscopic susceptibility (green squares).

Figure 9

Simulations of ${}^{75}$As NMR in Co-Mn-122 with $y_{\mathrm{Mn}}=0.65$% and $x_{\mathrm{Co}}=6.5$%. (a) Simulated spectra obtained with different forms of polarization (see text). Green circles highlight the satellite line, which would be compatible with the experiment. Models giving rise to more than one satellite line (red circles) are not compatible with the experimental data. (b) Experimental spectra ($H_0=13.3$ T, $H_0\parallel c$) at different temperatures compared with simulations obtained with $f_{\mathrm{Stretched}}$, $\gamma =1.5$, $Q=Q_{\mathrm{stripe}}$ and $\lambda =4$ (red lines). A zoom on the satellite line is shown in (c).