Evidence of Mott physics in iron pnictides from x-ray spectroscopy

The existence of large instantaneous local magnetic moments in paramagnetic phases is a direct signature of Mott localization. In order to track the doping evolution of fluctuating local moments in iron-based superconductors, we jointly use two fast probes, x-ray emission and absorption spectroscopies. Exploring K- and Cr-hole-doped $\mathrm{BaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$, we find a systematic increase in the local moment with hole-doping, in contrast with inelastic neutron scattering measurements, which suggest an opposite trend. Our results support the theoretical scenario in which a Mott insulating state that would be realized for half-filled conduction bands has an influence throughout the phase diagram of these iron pnictides.

Figure 1

(a) Normalized Fe $K\beta$ CTC XES spectra of $\mathrm{BaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2, \mathrm{KF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2, \mathrm{Ba}{\left(\mathrm{F}{\mathrm{e}}_{0.53}\mathrm{C}{\mathrm{r}}_{0.47}\right)}_2\mathrm{A}{\mathrm{s}}_2$, and FeCrAs at room temperature together with the difference spectra between $\mathrm{BaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ and the $\mathrm{KF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ (blue) and $\mathrm{Ba}{\left(\mathrm{F}{\mathrm{e}}_{0.53}\mathrm{C}{\mathrm{r}}_{0.47}\right)}_2\mathrm{A}{\mathrm{s}}_2$ (green) compounds, respectively. Inset: Simplified one-electron scheme for the $K\beta$ CTC XES process, where filled and empty circles represent electrons and holes. (b) The IAD values derived from the Fe $K\beta$ CTC XES spectra of the $\mathrm{B}{\mathrm{a}}_{1-x}{\mathrm{K}}_x\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ and $\mathrm{Ba}{\left(\mathrm{F}{\mathrm{e}}_{1-x}\mathrm{C}{\mathrm{r}}_x\right)}_2\mathrm{A}{\mathrm{s}}_2$ series normalized to the spectral area, shown as a function of doped holes/Fe ($x_{\mathrm{K}}/2$ and $2x_{\mathrm{Cr}}$ for K- and Cr-doping series, respectively). Circles and triangles differentiate the K-doped samples from sets 1 and 2, respectively. The error bars are as estimated from comparison of equivalent measurements taken in the same conditions either during a different experimental session or in a sample from a different batch.

Figure 2

Normalized HERFD-XANES spectra at the Fe $K$ edge of $\mathrm{B}{\mathrm{a}}_{1-x}{\mathrm{K}}_x\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ ($0\le x\le 1$) and $\mathrm{Ba}{\left(\mathrm{F}{\mathrm{e}}_{1-x}\mathrm{C}{\mathrm{r}}_x\right)}_2\mathrm{A}{\mathrm{s}}_2$ ($0.026\le x\le 0.47$) series at room temperature. Inset: Evolution of $A$ peak intensity (symbols; left axis) as a function of doped holes/Fe ($x_{\mathrm{K}}/2$ and $2x_{\mathrm{Cr}}$ for K- and Cr-doping series, respectively). Circles and triangles differentiate the K-doped samples from sets 1 and 2, respectively. On the right axis, the data of the tetragonal lattice parameter $a$ from Refs. [12] and [14] are plotted for a direct comparison.

Figure 3

Rescaled IAD values taking into account the changes in the $A$ peak intensity derived from the HERFD-XANES data. Inset: The $\mathrm{DFT}+\mathrm{slave}$-spin mean-field calculations of the local magnetic moment for $\mathrm{BaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ (Fe in $d^6$ configuration) and $\mathrm{KF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ (Fe in $d^{5.5}$ configuration) as a function of the interaction strength $U$ for Hund's coupling $J/U=0.25$ [1]. A strong increase of the local moment with hole-doping is only observed in the region $(U>2.5\mathrm{eV})$ influenced by the Mott insulating phase realized for a half-filled configuration $d^5$. For further details see the Appendix.

Figure 4

Schematic (top view) of the measurement configuration, as described in the additional experimental details section.

Figure 5

Normalized Fe $K\beta$ VTC XES spectra of (a) $\mathrm{B}{\mathrm{a}}_{1-x}{\mathrm{K}}_x\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ ($0\le x\le 1$) and (b) $\mathrm{Ba}{\left(\mathrm{F}{\mathrm{e}}_{1-x}\mathrm{C}{\mathrm{r}}_x\right)}_2\mathrm{A}{\mathrm{s}}_2$ ($0.026\le x\le 0.47$) series after background removal. (c) Evolution of $K{\beta }_{2,5}$ peak center position in energy (symbols; left axis) as a function of doped holes/Fe. Circles and triangles differentiate the K-doped samples from sets 1 and 2, respectively. On the right axis, the data of the tetragonal lattice parameter $a$ from Refs. [12] and [14] are plotted for a direct comparison; they are shown with lines and symbols.

Figure 6

(a) Calculated XANES spectra for a cluster size of $6.6\AA$ around Fe (about 50 atoms) using the tetragonal crystal structures of $\mathrm{BaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ and $\mathrm{KF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$. To simulate the effects of Cr-doping, Fe atoms were randomly replaced by Cr for $50\%$ substitution rate while keeping the atomic positions of the $\mathrm{BaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ structure. (b) and (c) Panels show the effect of replacing Ba and K atoms in the clusters while maintaining the atomic positions of the $\mathrm{BaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ and $\mathrm{KF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ crystal structures, respectively, for 50 and 100% substitution rates.