High-$T_c$ iron phosphide superconductivity enhanced by reemergent antiferromagnetic spin fluctuations in $\left[{\mathrm{Sr}}_4{\mathrm{Sc}}_2{\mathrm{O}}_6\right]{\mathrm{Fe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x{)}_2$ probed by NMR

We report a systematic NMR study on $\left[{\mathrm{Sr}}_4{\mathrm{Sc}}_2{\mathrm{O}}_6\right]{\mathrm{Fe}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$, for which the local lattice parameters of the iron-pnictogen ($\mathrm{Fe}Pn$) layer are similar to those of the series $\mathrm{LaFe}\left({\mathrm{As}}_{1-x^{\prime }}{\mathrm{P}}_{x^{\prime }}\right)\mathrm{O}$, which exhibits two segregated antiferromagnetic (AFM) order phases, AFM1 at $x^{\prime }=0-0.2$ and AFM2 at $x^{\prime }=0.4-0.7$. Our results reveal that the parent AFM1 phase at $x=0$ disappears at $x=0.3-0.4$, corresponding to a pnictogen height ($h_{pn}$) from the Fe plane of 1.3–1.32 Å, which is similar to that of $\mathrm{LaFe}\left({\mathrm{As}}_{1-x^{\prime }}{\mathrm{P}}_{x^{\prime }}\right)\mathrm{O}$ and various parent Fe pnictides. By contrast, the AFM2 order reported for $\mathrm{LaFe}\left({\mathrm{As}}_{0.4}{\mathrm{P}}_{0.6}\right)\mathrm{O}$ does not appear at $x\sim 0.8$, although the local lattice parameters of the $\mathrm{Fe}Pn$ layer and the microscopic electronic states are quite similar. Despite the absence of the static AFM2 order, reemergent dynamical AFM spin fluctuations were observed at approximately $x\sim 0.8$, which can be attributed to the instability of the AFM2 phase. We suggest this re-enhancement of AFM spin fluctuations plays a significant role in enhancing the $T_c$ to 17 K for $x=0.8-1$. Finally, we discuss the universality and diversity of the complicated magnetic ground states from a microscopic point of view, including the difference in the origins of the AFM1 and AFM2 phases, and their relations with the high superconducting transitions in Fe pnictides.

Figure 1

(a) $T$ dependence of ${}^{75}\mathrm{As}$-NMR spectra of $x=0$. The solid curves for the spectra below 35 K are the results of simulation for an internal field of ${}^{75}{B}_{\mathrm{int}}=\pm 0.5\mathrm{T}$ and ${}^{75}{\nu }_Q=8.8$ MHz at the As site, taking the presence of subtle ingredients of the paramagnetic domains into account. At the bottom, we show a typical simulation for the spectra of the AFM domain (denoted as A), the paramagnetic domain (B), and their superposition (A $+$ B). (b) $T$ dependence of the volume fraction of AFM domains evaluated from the fractional intensity of the broad spectra, namely, $\sim \mathrm{A}$/(A $+$ B), which increases significantly below $T_{\mathrm{N}}=35$ K. (c) ${}^{45}\mathrm{Sc}$-NMR spectra at 4.2 K reproduced by simulation (solid curve) for the case of zero internal field at the ${}^{45}\mathrm{Sc}$ site in the blocking layer.

Figure 2

(a) Internal field at the ${}^{75}\mathrm{As}$ site (${}^{75}{B}_{\mathrm{int}}$) evaluated by NMR and plotted against the internal field at the ${}^{57}\mathrm{Fe}$ site (${}^{57}{B}_{\mathrm{int}}$) evaluated by ${}^{57}\mathrm{Fe}$ Mössbauer studies for various undoped Fe pnictides in the AFM ordered state [2, 3, 4, 5, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45]. (b) ${}^{57}{B}_{\mathrm{int}}$ is proportional to the AFM ordered moment ($M_{\mathrm{AFM}}$) estimated by a neutron diffraction experiment [2, 3, 4, 5, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45]. The linear relation of these values holds for various Fe pnictides of which the $\mathrm{Fe}Pn$ layer possesses different local lattice parameters. The weak internal field at $x=0$ [SrSc42622(As)] is due to the small $M_{\mathrm{AFM}}$. This relation may enable us to infer the unknown values of $M_{\mathrm{AFM}}$, ${}^{57}{B}_{\mathrm{int}}$, and ${}^{75}{B}_{\mathrm{int}}$, if one of them is obtained, as shown by the broken arrows in (a).

Figure 3

${}^{75}\mathrm{As}$-NQR frequencies vs Fe-Fe bond length $d_{\mathrm{Fe}-\mathrm{Fe}}$ for $x=0$ [SrSc42622(As)], together with data for $Ln\mathrm{FeAsO}$ [46, 47, 48], $M42622$ [13, 30, 49], and $A\mathrm{FeAs}(A$= Li,Na) [50, 51]. The smallest value of ${}^{75}{\nu }_{\mathrm{Q}}$ for $x=0$ [SrSc42622(As)] corresponds to the longest $d_{\mathrm{Fe}-\mathrm{Fe}}$ and lowest $h_{Pn}$ among them.

Figure 4

$T$ dependence of field-swept ${}^{31}\mathrm{P}$-NMR spectra for (a) $x=0.2$, (b) 0.4, (c) 0.6, (d) 0.8, and (e) 1.0 of SrSc42622(${\mathrm{As}}_{1-x}{\mathrm{P}}_x$) at a fixed frequency $f_0=103.422\mathrm{MHz}(B\sim 6$ T). (f) FWHM at ${}^{31}\mathrm{P}$ site normalized by the value at 120 K, which is summarized in (g), the contour plot, revealing the evolution of the internal field at the ${}^{31}\mathrm{P}$ site as functions of $T$ and $x$. The FWHM increases upon cooling, especially below the broken line extrapolated to $T_{\mathrm{N}}=35$ K at $x=0$, suggesting that the AFM1 order phase disappears at $x=0.3$–0.4.

Figure 5

Plot of the ground states of parent and isovalent substituted Fe pnictides with a formal valence of ${\mathrm{Fe}}^{2+}$ as functions of $h_{Pn}$ and $d_{\mathrm{Fe}-\mathrm{Fe}}$, which represents the revised situation subsequent to previous reports [13, 52]. The solid, open, and cross symbols represent the AFM order, the SC, and non-SC states, respectively. The data were derived from previous results $\left[{\mathrm{Sr}}_4{\mathrm{Sc}}_2{\mathrm{O}}_6\right]{\mathrm{Fe}}_2{(\mathrm{As},\mathrm{P})}_2$ [21, 22], LaFe(As,P/Sb)O [14, 16, 17, 53, 54], ThFeAsN [55, 56, 57], $\left[{\mathrm{Ca}}_4{\mathrm{Al}}_2{\mathrm{O}}_6\right]{\mathrm{Fe}}_2{(\mathrm{As},\mathrm{P})}_2$ [13, 58], $\left[{\mathrm{Sr}}_4{\mathrm{MgTiO}}_6\right]{\mathrm{Fe}}_2{(\mathrm{As},\mathrm{P})}_2({\mathrm{Mg}}_{0.5}{\mathrm{Ti}}_{0.5}42622)$ [30, 59], ${\mathrm{BaFe}}_2{(\mathrm{As},\mathrm{P})}_2$ [60], $\mathrm{Ba}{(\mathrm{Fe},\mathrm{Ru})}_2{\mathrm{As}}_2$ [61, 62, 63], ${\mathrm{SrFe}}_2{(\mathrm{As},\mathrm{P})}_2$ [52, 64, 65], $\mathrm{Sr}{(\mathrm{Fe},\mathrm{Ru})}_2{\mathrm{As}}_2$ [66], and so on. The ground states for 0 $<x<$ 1 of SrSc42622(${\mathrm{As}}_{1-x}{\mathrm{P}}_x$) were obtained in this work. Note that the static AFM2 phase, which reemerged in the range $0.4\le x^{\prime }\le 0.7$ for $\mathrm{LaFe}\left({\mathrm{As}}_{1-x^{\prime }}{\mathrm{P}}_{x^{\prime }}\right)\mathrm{O}$, was not observed in $0.6\le x\le 1$ for SrSc42622(${\mathrm{As}}_{1-x}{\mathrm{P}}_x$) even at a comparable value of $h_{pn}$. However, the reemergent AFM spin fluctuations are observed in the range $0.6\le x\le 1$ [see Fig. 7].

Figure 6

$T$ dependencies of $K(T$) probed by ${}^{31}\mathrm{P}$-NMR for (a) SrSc42622(${\mathrm{As}}_{1-x}{\mathrm{P}}_x$) in comparison with that of (b) $\mathrm{LaFe}\left({\mathrm{As}}_{1-x^{\prime }}{\mathrm{P}}_{x^{\prime }}\right)\mathrm{O}$ [14, 15, 16, 17]. The dependence of $K_s(T\to 0$) on $x$ estimated by extrapolation to $T=0$ in the paramagnetic state for (c) SrSc42622(${\mathrm{As}}_{1-x}{\mathrm{P}}_x$) and (d) $\mathrm{LaFe}\left({\mathrm{As}}_{1-x^{\prime }}{\mathrm{P}}_{x^{\prime }}\right)\mathrm{O}$. The large increase in $K_s$ upon cooling observed from $x=0.6$ to 1.0 for both compounds is due to the appearance of a sharp peak of DOS mainly from the $d_{3z^2-r^2}$ orbital [16, 75]. (e) Plot of ${(1/T_{1}T)}^{1/2}$ vs $K$ with an implicit parameter of $T$, together with data of $\mathrm{LaFe}\left({\mathrm{As}}_{1-x^{\prime }}{\mathrm{P}}_{x^{\prime }}\right)({\mathrm{O}}_{1-y}{\mathrm{F}}_y$) in the paramagnetic states at $T\sim 250$ K. The relation ${(1/T_{1}T)}^{1/2}\propto K_{\mathrm{chem}}+K_s\left(T\right)$ is linear with $K_{\mathrm{chem}}\sim 0.03$%.

Figure 7

(a) $T$ dependencies of $(1/T_{1}T)$ and $K_s^2\left(T\right)$ probed by ${}^{31}\mathrm{P}$-NMR for $0.2\le x\le 1.0$. The hatched area denoted as ($1/T_1{T)}_{\mathrm{AFM}}$ corresponds to the component of $1/T_{1}T$ due to the AFMSFs at a finite $Q$. The SC states at $x=0.8$ and 1.0 are measured at $B=1$ T, enabling us to detect the decrease in the Knight shift and the increase in the linewidth below $T_c$ (1T). (b) Contour plot of low-energy AFMSFs probed by ($1/T_1{T)}_{\mathrm{AFM}}$. Evolution of AFMSFs upon cooling are observed significantly at $x=0.8$ with the highest $T_c$, which is discontinuous from that of the AFM1 phase. Here the broken line of the AFM1 phase is derived from the significant increase in FWHM of the spectra [see Fig. 4]. (c) Contour plot of AFMSFs in $\mathrm{LaFe}\left({\mathrm{As}}_{1-x^{\prime }}{\mathrm{P}}_{x^{\prime }}\right)\mathrm{O}$ referred from a previous study [73].

Figure 8

Ground state classified as functions of the doping levels of electrons/holes and the pnictogen height [2, 3, 4, 5, 6, 7, 8, 13]. The undoped ${\mathrm{Fe}}^{2+}$ state in Fig. 5 corresponds to a doping level of $6.0e^{-}$ per Fe atom in this plot, and the electron- and hole-doping correspond to the region above and below $6.0e^{-}$/Fe, respectively. The solid and open symbols represent the AFM order and the SC states, respectively. The AFM1 phase is widely observed in the parent Fe pnictides for 1.3 $\AA <h_{Pn}<1.42$ Å around $6.0e^{-1}$/Fe, whereas the AFM2 and AFM3 phases are reported to occur only in LaFe(As,P)O [14, 15, 16, 17] and the heavily electron doped state $Ln\mathrm{FeAs}$(O,H) [18, 19, 20], respectively. Most of the nodeless and nodal SC phases in the Fe pnictides are roughly classified by the border of the AFM1 and nodal SC phases around $h_{Pn}$ = 1.3–1.32 Å [87]. The region in which $T_c$ is the highest with $T_c>50$ K, is the region enclosed within a dashed circle, is the region in which the AFM1 phase is suppressed by electron-doping at $h_{\mathrm{Pn}}$ = 1.35–1.39 Å in the middle of the AFM1 phase. Here we omit the data of SrSc42622(${\mathrm{As}}_{1-x}{\mathrm{P}}_x$) on $6.0e^{-1}$/Fe to avoid the overlap with the data of $\mathrm{LaFe}\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)\mathrm{O}$.