Itinerant electrons, local moments, and magnetic correlations in the pnictide superconductors CeFeAsO${}_{1-x}$F${}_x$ and Sr(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$

A direct and element-specific measurement of the local Fe spin moment has been provided by analyzing the Fe 3$s$ core level photoemission spectra in the parent and optimally doped CeFeAsO${}_{1-x}$F${}_x$ ($x$ $=$ 0, 0.11) and Sr(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ ($x$ $=$ 0, 0.10) pnictides. The rapid time scales of the photoemission process allowed the detection of large local spin moments fluctuating on a 10${}^{-15}$ s time scale in the paramagnetic, antiferromagnetic, and superconducting phases, indicative of the occurrence of ubiquitous strong Hund's magnetic correlations. The magnitude of the spin moment is found to vary significantly among different families, 1.3${\mu }_B$ in CeFeAsO and 2.1${\mu }_B$ in SrFe${}_2$As${}_2$. Surprisingly, the spin moment is found to decrease considerably in the optimally doped samples, 0.9${\mu }_B$ in CeFeAsO${}_{0.89}$F${}_{0.11}$ and 1.3${\mu }_B$ in Sr(Fe${}_{0.9}$Co${}_{0.1}$)${}_2$As${}_2$. The strong variation of the spin moment against doping and material type indicates that the spin moments and the motion of itinerant electrons are influenced reciprocally in a self-consistent fashion, reflecting the strong competition between the antiferromagnetic superexchange interaction among the spin moments and the kinetic energy gain of the itinerant electrons in the presence of a strong Hund's coupling. By describing the evolution of the magnetic correlations concomitant with the appearance of superconductivity, these results constitute a fundamental step toward attaining a correct description of the microscopic mechanisms shaping the electronic properties in the pnictides, including magnetism and high-temperature superconductivity.

Figure 1

Multiplet splittings in Fe 3$s$ core level HAXPES and PES spectra: Evidence of strong on-site Hund coupling $J_{\mathrm{H}}$ on Fe sites. (a) HAXPES ($h$ν $=$ 7689 eV) Fe 3$s$ core level spectra in CeFeAsO (CFAO), CeFeAsO${}_{0.89}$F${}_{0.11}$ (CFAO-11$\%$), SrFe${}_2$As${}_2$ (SFA), and Sr(Co${}_{0.12}$Fe${}_{0.88}$)${}_2$As${}_2$ (SFA-10$\%$) at different temperatures in the antiferromagnetic (AFM), paramagnetic (PM), and superconducting (SC) phases. (b) PES ($h$ν $=$ 216 eV) Fe 3$s$ core level spectra in SrFe${}_2$As${}_2$ at different temperatures in the PM and AFM phases. A Shirley-type background has been subtracted from the data points (circles). An additional background has been subtracted in the BE region ≈105 eV to account for some spectral weight originating from a nearby Auger peak for the spectra excited in SrFe${}_2$As${}_2$ with $h$ν $=$ 216 eV. The M-SP of the BE is clearly visible as a doublet structure consisting of a main line and a satellite peak at higher BE. The continuous black line through the data points is the result of the two-component fit of the doublet (blue and orange lines beneath). The distance between these two peaks maxima provides the multiplet separation $\Delta E_{3s}$, with experimental uncertainty on $\Delta E_{3s}$ of $\pm 100$ meV in (a) and $\pm 50$ meV in (b).

Figure 2

Estimate of the spin moment on the Fe sites from the multiplet energy separation $\Delta E_{3s}$. The data points denote the values of the multiplet energy separation $\Delta E_{3s}$ for CeFeAsO (CFAO), CeFeAsO${}_{0.89}$F${}_{0.11}$ (CFAO-11$\%$), SrFe${}_2$As${}_2$ (SFA), and Sr(Co${}_{0.12}$Fe${}_{0.88}$)${}_2$As${}_2$ (SFA-10$\%$) at different temperatures and phases studied in this work. The continuous line is the extrapolation of the linear fit of the $\Delta E_{3s}$ values plotted against (2$S_V$ $+$ 1) for the Fe ionic compounds FeF${}_3$, FeF${}_2$, FeO, for which $S_V$ is known to be 5/2 (FeF${}_3$) and 2 (FeF${}_2$, FeO) (Ref. 28). The linear fit results in the relation $\Delta E_{3s}$ $=$ 0.94 $+$ 1.01 (2$S_V$ $+$ 1). Notably, the value of the SM of metallic Fe is found to be ≈2.5${\mu }_B$, remarkably close to the values of 2.2${\mu }_B$ and 2.33${\mu }_B$ measured with neutrons and magnetic susceptibility, giving us confidence in the correctness of this analysis procedure. The size of the symbol is much bigger than the experimental uncertainties: It denotes the range of values for the splitting $\Delta E_{3s}$, the correspondent values for $S_V$, and the Fe LSM as shown in the inset.

Figure 3

Reduction of the local moment upon enhanced kinetic energy gain. Schematic of spatial distribution of the fluctuating spins centered at Fe sites (labeled by integer numbers), upon “integrating out” the higher-energy degrees of freedom that correspond to fluctuations faster than the PES time scale (≈10${}^{-16}$ s). More precisely, the schematic illustrates the spin-polarized Wannier orbitals that span the remaining low-energy fermionic space. With enhanced effective kinetic processes (upon doping away from an integer number of electrons per Fe, applying pressure, or changing the Fe-As-Fe bond angle), the spatial extent of the fluctuating spin increases, as shown in the right panel, and consequently the central contribution decreases. In turn, the exchange field applied to the region spanned by the 3$s$ core orbital (within dashed lines) reduces, producing a smaller multiplet splitting in the 3$s$ PES. Such a high-energy kinetic driven reduction is most visible in the presence of strong short-range AFM correlations, in which case the tails from neighboring spins gives opposite contributions.